%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWW379+1 : TPTP v8.2.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n007.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 18:08:51 EDT 2024 % Result : Theorem 154.70s 154.54s % Output : CNFRefutation 155.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SWW379+1 : TPTP v8.2.0. Released v5.2.0. % 0.03/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.11/0.32 % Computer : n007.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Wed Jun 19 08:17:09 EDT 2024 % 0.11/0.32 % CPUTime : % 0.51/0.57 start to proof:theBenchmark % 154.32/154.38 %------------------------------------------- % 154.32/154.38 % File :CSE---1.7 % 154.32/154.38 % Problem :theBenchmark % 154.32/154.38 % Transform :cnf % 154.32/154.38 % Format :tptp:raw % 154.32/154.38 % Command :java -jar mcs_scs.jar %d %s % 154.32/154.38 % 154.32/154.38 % Result :Theorem 132.430000s % 154.32/154.38 % Output :CNFRefutation 132.430000s % 154.32/154.38 %------------------------------------------- % 154.32/154.39 %------------------------------------------------------------------------------ % 154.32/154.39 % File : SWW379+1 : TPTP v8.2.0. Released v5.2.0. % 154.32/154.39 % Domain : Software Verification % 154.32/154.39 % Problem : Hoare's Logic with Procedures 435576, 5000 axioms selected % 154.32/154.39 % Version : Especial. % 154.32/154.39 % English : % 154.32/154.39 % 154.32/154.39 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 154.32/154.39 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 154.32/154.39 % Source : [Bla11] % 154.32/154.39 % Names : hoare_435576.5000.p [Bla11] % 154.32/154.39 % 154.32/154.39 % Status : ContradictoryAxioms % 154.32/154.39 % Rating : 0.75 v7.5.0, 0.81 v7.4.0, 0.87 v7.3.0, 0.83 v7.1.0, 0.78 v7.0.0, 0.87 v6.4.0, 0.81 v6.3.0, 0.79 v6.2.0, 0.88 v6.1.0, 0.90 v6.0.0, 0.91 v5.5.0, 0.96 v5.3.0, 1.00 v5.2.0 % 154.32/154.39 % Syntax : Number of formulae : 5240 (1727 unt; 0 def) % 154.32/154.39 % Number of atoms : 12608 (4519 equ) % 154.32/154.39 % Maximal formula atoms : 13 ( 2 avg) % 154.32/154.39 % Number of connectives : 8382 (1014 ~; 155 |; 717 &) % 154.32/154.39 % ( 896 <=>;5600 =>; 0 <=; 0 <~>) % 154.32/154.39 % Maximal formula depth : 22 ( 6 avg) % 154.32/154.39 % Maximal term depth : 19 ( 2 avg) % 154.32/154.39 % Number of predicates : 144 ( 143 usr; 2 prp; 0-6 aty) % 154.32/154.39 % Number of functors : 384 ( 384 usr; 56 con; 0-7 aty) % 154.32/154.39 % Number of variables : 16658 (16514 !; 144 ?) % 154.32/154.39 % SPC : FOF_CAX_RFO_SEQ % 154.32/154.39 % 154.32/154.39 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 154.32/154.39 % 2011-03-01 12:53:15 % 154.32/154.39 %------------------------------------------------------------------------------ % 154.32/154.39 %----Relevant facts (4986) % 154.32/154.39 fof(fact_ext,axiom, % 154.32/154.39 ! [V_g_2,V_f_2] : % 154.32/154.39 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) % 154.32/154.39 => V_f_2 = V_g_2 ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_empty,axiom, % 154.32/154.39 ! [V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))) ). % 154.32/154.39 % 154.32/154.39 fof(fact_hoare__derivs_Oequations_I1_J,axiom, % 154.32/154.39 ! [V_a_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))) ). % 154.32/154.39 % 154.32/154.39 fof(fact_triple_Oinject,axiom, % 154.32/154.39 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_a] : % 154.32/154.39 ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_H_2),V_com_H_2),V_fun2_H_2) % 154.32/154.39 <=> ( V_fun1_2 = V_fun1_H_2 % 154.32/154.39 & V_com_2 = V_com_H_2 % 154.32/154.39 & V_fun2_2 = V_fun2_H_2 ) ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_cut,axiom, % 154.32/154.39 ! [V_Ga_2,V_ts_2,V_G_H_2,T_a] : % 154.32/154.39 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2) % 154.32/154.39 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_G_H_2) % 154.32/154.39 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_hoare__derivs_Oinsert,axiom, % 154.32/154.39 ! [V_ts_2,V_t_2,V_Ga_2,T_a] : % 154.32/154.39 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 154.32/154.39 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) % 154.32/154.39 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2)) ) ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_derivs__insertD,axiom, % 154.32/154.39 ! [V_ts_2,V_t_2,V_Ga_2,T_a] : % 154.32/154.39 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2)) % 154.32/154.39 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 154.32/154.39 & c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_weak__Body,axiom, % 154.32/154.39 ! [V_Q_2,V_pn_2,V_P_2,V_Ga_2,T_a] : % 154.32/154.39 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 154.32/154.39 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_hoare__derivs_OBody,axiom, % 154.32/154.39 ! [V_Procsa_2,V_Q_2,V_P_2,V_Ga_2,T_a] : % 154.32/154.39 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procsa_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procsa_2)) % 154.32/154.39 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procsa_2)) ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_BodyN,axiom, % 154.32/154.39 ! [V_Ga_2,V_Q_2,V_pn_2,V_P_2,T_a] : % 154.32/154.39 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),V_Ga_2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 154.32/154.39 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_evalc__elim__cases_I6_J,axiom, % 154.32/154.39 ! [V_s1,V_s,V_P] : % 154.32/154.39 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1)) % 154.32/154.39 => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1)) ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_evalc_OBody,axiom, % 154.32/154.39 ! [V_s1,V_s0,V_pn] : % 154.32/154.39 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1)) % 154.32/154.39 => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1)) ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_Body__sound__lemma,axiom, % 154.32/154.39 ! [V_Procsa_2,V_Q_2,V_P_2,V_Ga_2,T_a] : % 154.32/154.39 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procsa_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procsa_2)) % 154.32/154.39 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procsa_2)) ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_evalc_Oequations_I9_J,axiom, % 154.32/154.39 ! [V_a3_2,V_a2_2,V_a1_2] : % 154.32/154.39 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2)) % 154.32/154.39 <=> hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_a1_2))),V_a2_2),V_a3_2)) ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_MGT__BodyN,axiom, % 154.32/154.39 ! [V_Ga_2,V_pn_2] : % 154.32/154.39 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,V_pn_2))),V_Ga_2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 154.32/154.39 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,V_pn_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_Body1,axiom, % 154.32/154.39 ! [V_pn_2,V_Procsa_2,V_Q_2,V_P_2,V_Ga_2,T_a] : % 154.32/154.39 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procsa_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procsa_2)) % 154.32/154.39 => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procsa_2)) % 154.32/154.39 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(V_P_2,V_pn_2)),hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(V_Q_2,V_pn_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_image__constant__conv,axiom, % 154.32/154.39 ! [V_c_2,T_b,T_a,V_A_2] : % 154.32/154.39 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.32/154.39 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 154.32/154.39 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.32/154.39 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_insert__is__Un,axiom, % 154.32/154.39 ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_A_2) ). % 154.32/154.39 % 154.32/154.39 fof(fact_sup1E,axiom, % 154.32/154.39 ! [V_x_2,V_B_2,V_A_2,T_a] : % 154.32/154.39 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 154.32/154.39 => ( ~ hBOOL(hAPP(V_A_2,V_x_2)) % 154.32/154.39 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_sup1CI,axiom, % 154.32/154.39 ! [T_a,V_A_2,V_x_2,V_B_2] : % 154.32/154.39 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2)) % 154.32/154.39 => hBOOL(hAPP(V_A_2,V_x_2)) ) % 154.32/154.39 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_sup__fun__def,axiom, % 154.32/154.39 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 154.32/154.39 ( class_Lattices_Olattice(T_a) % 154.32/154.39 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_bot__fun__def,axiom, % 154.32/154.39 ! [V_x_2,T_b,T_a] : % 154.32/154.39 ( class_Orderings_Obot(T_a) % 154.32/154.39 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_equalityCE,axiom, % 154.32/154.39 ! [V_c_2,T_a,V_B_2,V_A_2] : % 154.32/154.39 ( V_A_2 = V_B_2 % 154.32/154.39 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 154.32/154.39 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) % 154.32/154.39 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 154.32/154.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_emptyE,axiom, % 154.32/154.39 ! [V_a_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 154.32/154.39 % 154.32/154.39 fof(fact_insertCI,axiom, % 154.32/154.39 ! [V_b_2,V_B_2,V_a_2,T_a] : % 154.32/154.39 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 154.32/154.39 => V_a_2 = V_b_2 ) % 154.32/154.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_insertE,axiom, % 154.32/154.39 ! [V_A_2,V_b_2,V_a_2,T_a] : % 154.32/154.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2))) % 154.32/154.39 => ( V_a_2 != V_b_2 % 154.32/154.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_image__eqI,axiom, % 154.32/154.39 ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_b_2] : % 154.32/154.39 ( V_b_2 = hAPP(V_f_2,V_x_2) % 154.32/154.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 154.32/154.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_UnCI,axiom, % 154.32/154.39 ! [V_A_2,V_B_2,V_c_2,T_a] : % 154.32/154.39 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) % 154.32/154.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) % 154.32/154.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_UnE,axiom, % 154.32/154.39 ! [V_B_2,V_A_2,V_c_2,T_a] : % 154.32/154.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.32/154.39 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 154.32/154.39 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 154.32/154.39 % 154.32/154.39 fof(fact_mem__def,axiom, % 154.32/154.39 ! [V_A_2,V_x_2,T_a] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.32/154.40 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_eq__mem,axiom, % 154.32/154.40 ! [V_y_2,V_x_2,T_a] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2))) % 154.32/154.40 <=> V_x_2 = V_y_2 ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_pred__equals__eq,axiom, % 154.32/154.40 ! [V_S_2,V_R_2,T_a] : % 154.32/154.40 ( 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) % 154.32/154.40 <=> V_R_2 = V_S_2 ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_eqset__imp__iff,axiom, % 154.32/154.40 ! [V_x_2,T_a,V_B_2,V_A_2] : % 154.32/154.40 ( V_A_2 = V_B_2 % 154.32/154.40 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.32/154.40 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_eqelem__imp__iff,axiom, % 154.32/154.40 ! [V_A_2,T_a,V_y_2,V_x_2] : % 154.32/154.40 ( V_x_2 = V_y_2 % 154.32/154.40 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.32/154.40 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_eq__mem__trans,axiom, % 154.32/154.40 ! [V_A_2,T_a,V_b_2,V_a_2] : % 154.32/154.40 ( V_a_2 = V_b_2 % 154.32/154.40 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 154.32/154.40 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_equals0D,axiom, % 154.32/154.40 ! [V_a_2,T_a,V_A_2] : % 154.32/154.40 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.32/154.40 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_empty__iff,axiom, % 154.32/154.40 ! [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)))) ). % 154.32/154.40 % 154.32/154.40 fof(fact_ex__in__conv,axiom, % 154.32/154.40 ! [V_A_2,T_a] : % 154.32/154.40 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.32/154.40 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_all__not__in__conv,axiom, % 154.32/154.40 ! [V_A_2,T_a] : % 154.32/154.40 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.32/154.40 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_insert__absorb,axiom, % 154.32/154.40 ! [V_A_2,V_a_2,T_a] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.32/154.40 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = V_A_2 ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_insertI2,axiom, % 154.32/154.40 ! [V_b_2,V_B_2,V_a_2,T_a] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 154.32/154.40 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_insert__ident,axiom, % 154.32/154.40 ! [V_B_2,V_A_2,V_x_2,T_a] : % 154.32/154.40 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.32/154.40 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 154.32/154.40 => ( hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2) % 154.32/154.40 <=> V_A_2 = V_B_2 ) ) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_insert__iff,axiom, % 154.32/154.40 ! [V_A_2,V_b_2,V_a_2,T_a] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2))) % 154.32/154.40 <=> ( V_a_2 = V_b_2 % 154.32/154.40 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_insertI1,axiom, % 154.32/154.40 ! [V_B_2,V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))) ). % 154.32/154.40 % 154.32/154.40 fof(fact_rev__image__eqI,axiom, % 154.32/154.40 ! [T_b,V_f_2,V_b_2,V_A_2,V_x_2,T_a] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.32/154.40 => ( V_b_2 = hAPP(V_f_2,V_x_2) % 154.32/154.40 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_imageI,axiom, % 154.32/154.40 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.32/154.40 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_image__iff,axiom, % 154.32/154.40 ! [V_A_2,V_f_2,T_b,V_z_2,T_a] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 154.32/154.40 <=> ? [B_x] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 154.32/154.40 & V_z_2 = hAPP(V_f_2,B_x) ) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_UnI2,axiom, % 154.32/154.40 ! [V_A_2,V_B_2,V_c_2,T_a] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) % 154.32/154.40 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_UnI1,axiom, % 154.32/154.40 ! [V_B_2,V_A_2,V_c_2,T_a] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 154.32/154.40 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_Un__iff,axiom, % 154.32/154.40 ! [V_B_2,V_A_2,V_c_2,T_a] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.32/154.40 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 154.32/154.40 | hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_bot__empty__eq,axiom, % 154.32/154.40 ! [V_x_2,T_a] : % 154.32/154.40 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) % 154.32/154.40 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_sup__Un__eq,axiom, % 154.32/154.40 ! [V_x_2,V_S_2,V_R_2,T_a] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(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)),V_x_2)) % 154.32/154.40 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_singletonE,axiom, % 154.32/154.40 ! [V_a_2,V_b_2,T_a] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 154.32/154.40 => V_b_2 = V_a_2 ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_singleton__iff,axiom, % 154.32/154.40 ! [V_a_2,V_b_2,T_a] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 154.32/154.40 <=> V_b_2 = V_a_2 ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_insert__image,axiom, % 154.32/154.40 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.32/154.40 => hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_image__constant,axiom, % 154.32/154.40 ! [V_c_2,T_b,V_A_2,V_x_2,T_a] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.32/154.40 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_hoare__sound,axiom, % 154.32/154.40 ! [V_ts_2,V_Ga_2,T_a] : % 154.32/154.40 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) % 154.32/154.40 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,V_ts_2) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_insert__code,axiom, % 154.32/154.40 ! [V_x_2,V_A_2,V_y_2,T_a] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2),V_x_2)) % 154.32/154.40 <=> ( V_y_2 = V_x_2 % 154.32/154.40 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_insert__commute,axiom, % 154.32/154.40 ! [V_A_2,V_y_2,V_x_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) ). % 154.32/154.40 % 154.32/154.40 fof(fact_insert__absorb2,axiom, % 154.32/154.40 ! [V_A_2,V_x_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2) ). % 154.32/154.40 % 154.32/154.40 fof(fact_sup__assoc,axiom, % 154.32/154.40 ! [V_z,V_y,V_x,T_a] : % 154.32/154.40 ( class_Lattices_Osemilattice__sup(T_a) % 154.32/154.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_inf__sup__aci_I6_J,axiom, % 154.32/154.40 ! [V_z,V_y,V_x,T_a] : % 154.32/154.40 ( class_Lattices_Olattice(T_a) % 154.32/154.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_sup_Oassoc,axiom, % 154.32/154.40 ! [V_c,V_b,V_a,T_a] : % 154.32/154.40 ( class_Lattices_Osemilattice__sup(T_a) % 154.32/154.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_sup__left__commute,axiom, % 154.32/154.40 ! [V_z,V_y,V_x,T_a] : % 154.32/154.40 ( class_Lattices_Osemilattice__sup(T_a) % 154.32/154.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_inf__sup__aci_I7_J,axiom, % 154.32/154.40 ! [V_z,V_y,V_x,T_a] : % 154.32/154.40 ( class_Lattices_Olattice(T_a) % 154.32/154.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_sup_Oleft__commute,axiom, % 154.32/154.40 ! [V_c,V_a,V_b,T_a] : % 154.32/154.40 ( class_Lattices_Osemilattice__sup(T_a) % 154.32/154.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_sup__left__idem,axiom, % 154.32/154.40 ! [V_y,V_x,T_a] : % 154.32/154.40 ( class_Lattices_Osemilattice__sup(T_a) % 154.32/154.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_inf__sup__aci_I8_J,axiom, % 154.32/154.40 ! [V_y,V_x,T_a] : % 154.32/154.40 ( class_Lattices_Olattice(T_a) % 154.32/154.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_sup_Oleft__idem,axiom, % 154.32/154.40 ! [V_b,V_a,T_a] : % 154.32/154.40 ( class_Lattices_Osemilattice__sup(T_a) % 154.32/154.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_sup__commute,axiom, % 154.32/154.40 ! [V_y,V_x,T_a] : % 154.32/154.40 ( class_Lattices_Osemilattice__sup(T_a) % 154.32/154.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_inf__sup__aci_I5_J,axiom, % 154.32/154.40 ! [V_y,V_x,T_a] : % 154.32/154.40 ( class_Lattices_Olattice(T_a) % 154.32/154.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_sup_Ocommute,axiom, % 154.32/154.40 ! [V_b,V_a,T_a] : % 154.32/154.40 ( class_Lattices_Osemilattice__sup(T_a) % 154.32/154.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_a) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_sup__idem,axiom, % 154.32/154.40 ! [V_x,T_a] : % 154.32/154.40 ( class_Lattices_Osemilattice__sup(T_a) % 154.32/154.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_sup_Oidem,axiom, % 154.32/154.40 ! [V_a,T_a] : % 154.32/154.40 ( class_Lattices_Osemilattice__sup(T_a) % 154.32/154.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_sup1I2,axiom, % 154.32/154.40 ! [V_A_2,T_a,V_x_2,V_B_2] : % 154.32/154.40 ( hBOOL(hAPP(V_B_2,V_x_2)) % 154.32/154.40 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_sup1I1,axiom, % 154.32/154.40 ! [V_B_2,T_a,V_x_2,V_A_2] : % 154.32/154.40 ( hBOOL(hAPP(V_A_2,V_x_2)) % 154.32/154.40 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_ball__Un,axiom, % 154.32/154.40 ! [V_P_2,V_B_2,V_A_2,T_a] : % 154.32/154.40 ( ! [B_x] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.32/154.40 => hBOOL(hAPP(V_P_2,B_x)) ) % 154.32/154.40 <=> ( ! [B_x] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.32/154.40 => hBOOL(hAPP(V_P_2,B_x)) ) % 154.32/154.40 & ! [B_x] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 154.32/154.40 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_bex__Un,axiom, % 154.32/154.40 ! [V_P_2,V_B_2,V_A_2,T_a] : % 154.32/154.40 ( ? [B_x] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.32/154.40 & hBOOL(hAPP(V_P_2,B_x)) ) % 154.32/154.40 <=> ( ? [B_x] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.32/154.40 & hBOOL(hAPP(V_P_2,B_x)) ) % 154.32/154.40 | ? [B_x] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 154.32/154.40 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_Un__assoc,axiom, % 154.32/154.40 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 154.32/154.40 % 154.32/154.40 fof(fact_Un__left__commute,axiom, % 154.32/154.40 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 154.32/154.40 % 154.32/154.40 fof(fact_Un__left__absorb,axiom, % 154.32/154.40 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 154.32/154.40 % 154.32/154.40 fof(fact_Un__commute,axiom, % 154.32/154.40 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) ). % 154.32/154.40 % 154.32/154.40 fof(fact_Un__absorb,axiom, % 154.32/154.40 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ). % 154.32/154.40 % 154.32/154.40 fof(fact_com__det,axiom, % 154.32/154.40 ! [V_u,V_t,V_s,V_c] : % 154.32/154.40 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c),V_s),V_t)) % 154.32/154.40 => ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c),V_s),V_u)) % 154.32/154.40 => V_u = V_t ) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_image__image,axiom, % 154.32/154.40 ! [V_A_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_c,T_a,hAPP(hAPP(c_COMBB(T_b,T_a,T_c),V_f_2),V_g_2)),V_A_2) ). % 154.32/154.40 % 154.32/154.40 fof(fact_MGF__complete,axiom, % 154.32/154.40 ! [V_Q_2,V_P_2,V_c_2] : % 154.32/154.40 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 154.32/154.40 => ( c_Hoare__Mirabelle_Ohoare__valids(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 154.32/154.40 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_MGT__def,axiom, % 154.32/154.40 ! [V_c_2] : c_Hoare__Mirabelle_OMGT(V_c_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),V_c_2),hAPP(c_Natural_Oevalc,V_c_2)) ). % 154.32/154.40 % 154.32/154.40 fof(fact_bot__apply,axiom, % 154.32/154.40 ! [V_x_2,T_b,T_a] : % 154.32/154.40 ( class_Orderings_Obot(T_a) % 154.32/154.40 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_singleton__inject,axiom, % 154.32/154.40 ! [V_b_2,V_a_2,T_a] : % 154.32/154.40 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) % 154.32/154.40 => V_a_2 = V_b_2 ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_doubleton__eq__iff,axiom, % 154.32/154.40 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 154.32/154.40 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 154.32/154.40 <=> ( ( V_a_2 = V_c_2 % 154.32/154.40 & V_b_2 = V_d_2 ) % 154.32/154.40 | ( V_a_2 = V_d_2 % 154.32/154.40 & V_b_2 = V_c_2 ) ) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_insert__not__empty,axiom, % 154.32/154.40 ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 154.32/154.40 % 154.32/154.40 fof(fact_empty__not__insert,axiom, % 154.32/154.40 ! [V_A_2,V_a_2,T_a] : c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) ). % 154.32/154.40 % 154.32/154.40 fof(fact_sup__eq__bot__iff,axiom, % 154.32/154.40 ! [V_y_2,V_x_2,T_a] : % 154.32/154.40 ( class_Lattices_Obounded__lattice__bot(T_a) % 154.32/154.40 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_a) % 154.32/154.40 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_a) % 154.32/154.40 & V_y_2 = c_Orderings_Obot__class_Obot(T_a) ) ) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_sup__bot__right,axiom, % 154.32/154.40 ! [V_x,T_a] : % 154.32/154.40 ( class_Lattices_Obounded__lattice__bot(T_a) % 154.32/154.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_sup__bot__left,axiom, % 154.32/154.40 ! [V_x,T_a] : % 154.32/154.40 ( class_Lattices_Obounded__lattice__bot(T_a) % 154.32/154.40 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_image__is__empty,axiom, % 154.32/154.40 ! [V_A_2,V_f_2,T_a,T_b] : % 154.32/154.40 ( hAPP(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)) % 154.32/154.40 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 154.32/154.40 % 154.32/154.40 fof(fact_image__empty,axiom, % 154.32/154.40 ! [V_f_2,T_a,T_b] : hAPP(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)) ). % 154.32/154.40 % 154.32/154.40 fof(fact_empty__is__image,axiom, % 154.32/154.40 ! [V_A_2,V_f_2,T_b,T_a] : % 154.32/154.40 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) % 154.32/154.40 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 154.32/154.40 % 154.32/154.41 fof(fact_Un__empty,axiom, % 154.32/154.41 ! [V_B_2,V_A_2,T_a] : % 154.32/154.41 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.32/154.41 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.32/154.41 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_Un__empty__right,axiom, % 154.32/154.41 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ). % 154.32/154.41 % 154.32/154.41 fof(fact_Un__empty__left,axiom, % 154.32/154.41 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = V_B_2 ). % 154.32/154.41 % 154.32/154.41 fof(fact_image__insert,axiom, % 154.32/154.41 ! [V_B_2,V_a_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)) ). % 154.32/154.41 % 154.32/154.41 fof(fact_Un__insert__left,axiom, % 154.32/154.41 ! [V_C_2,V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 154.32/154.41 % 154.32/154.41 fof(fact_Un__insert__right,axiom, % 154.32/154.41 ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 154.32/154.41 % 154.32/154.41 fof(fact_sup__apply,axiom, % 154.32/154.41 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 154.32/154.41 ( class_Lattices_Olattice(T_a) % 154.32/154.41 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_image__Un,axiom, % 154.32/154.41 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)) ). % 154.32/154.41 % 154.32/154.41 fof(fact_the__elem__eq,axiom, % 154.32/154.41 ! [V_x_2,T_a] : c_Set_Othe__elem(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ). % 154.32/154.41 % 154.32/154.41 fof(fact_MGT__alternI,axiom, % 154.32/154.41 ! [V_c_2,V_Ga_2] : % 154.32/154.41 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 154.32/154.41 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_Com_Ostate),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies)),hAPP(c_Natural_Oevalc,V_c_2))))),c_fequal))),V_c_2),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_triple_Osimps_I2_J,axiom, % 154.32/154.41 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_a,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_b,T_a,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ). % 154.32/154.41 % 154.32/154.41 fof(fact_triple_Orecs,axiom, % 154.32/154.41 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_a,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_b,T_a,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ). % 154.32/154.41 % 154.32/154.41 fof(fact_escape,axiom, % 154.32/154.41 ! [V_Q_2,V_c_2,V_Ga_2,T_a,V_P_2] : % 154.32/154.41 ( ! [B_Z,B_s] : % 154.32/154.41 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 154.32/154.41 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),B_s))),V_c_2),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(V_Q_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) % 154.32/154.41 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_MGT__alternD,axiom, % 154.32/154.41 ! [V_c_2,V_Ga_2] : % 154.32/154.41 ( c_Hoare__Mirabelle_Ostate__not__singleton % 154.32/154.41 => ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_Com_Ostate),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies)),hAPP(c_Natural_Oevalc,V_c_2))))),c_fequal))),V_c_2),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 154.32/154.41 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_hoare__derivs_Oequations_I7_J,axiom, % 154.32/154.41 ! [V_a2_2,V_a1_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_a2_2),c_Com_Ocom_OSKIP),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ). % 154.32/154.41 % 154.32/154.41 fof(fact_hoare__derivs_OSkip,axiom, % 154.32/154.41 ! [V_P_2,V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OSKIP),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ). % 154.32/154.41 % 154.32/154.41 fof(fact_conseq1,axiom, % 154.32/154.41 ! [V_P_2,V_Q_2,V_c_2,V_P_H_2,V_Ga_2,T_a] : % 154.32/154.41 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_H_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 154.32/154.41 => ( ! [B_Z,B_s] : % 154.32/154.41 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 154.32/154.41 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) ) % 154.32/154.41 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_conseq2,axiom, % 154.32/154.41 ! [V_Q_2,V_Q_H_2,V_c_2,V_P_2,V_Ga_2,T_a] : % 154.32/154.41 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 154.32/154.41 => ( ! [B_Z,B_s] : % 154.32/154.41 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s)) % 154.32/154.41 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) ) % 154.32/154.41 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_Comp,axiom, % 154.32/154.41 ! [V_R_2,V_d_2,V_Q_2,V_c_2,V_P_2,V_Ga_2,T_a] : % 154.32/154.41 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 154.32/154.41 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_Q_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 154.32/154.41 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OSemi(V_c_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_LoopF,axiom, % 154.32/154.41 ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),V_P_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),V_b_2))),c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ). % 154.32/154.41 % 154.32/154.41 fof(fact_evalc_OWhileFalse,axiom, % 154.32/154.41 ! [V_c_2,V_s_2,V_b_2] : % 154.32/154.41 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 154.32/154.41 => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_s_2)) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_evalc_OWhileTrue,axiom, % 154.32/154.41 ! [V_s2_2,V_s1_2,V_c_2,V_s0_2,V_b_2] : % 154.32/154.41 ( hBOOL(hAPP(V_b_2,V_s0_2)) % 154.32/154.41 => ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c_2),V_s0_2),V_s1_2)) % 154.32/154.41 => ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s1_2),V_s2_2)) % 154.32/154.41 => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s0_2),V_s2_2)) ) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_evalc_OSemi,axiom, % 154.32/154.41 ! [V_s2,V_c1,V_s1,V_s0,V_c0] : % 154.32/154.41 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c0),V_s0),V_s1)) % 154.32/154.41 => ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c1),V_s1),V_s2)) % 154.32/154.41 => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_evalc_OSkip,axiom, % 154.32/154.41 ! [V_s] : hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSKIP),V_s),V_s)) ). % 154.32/154.41 % 154.32/154.41 fof(fact_evalc__elim__cases_I1_J,axiom, % 154.32/154.41 ! [V_t,V_s] : % 154.32/154.41 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSKIP),V_s),V_t)) % 154.32/154.41 => V_t = V_s ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_evalc_Oequations_I7_J,axiom, % 154.32/154.41 ! [V_a2_2,V_a3_2,V_a1_2] : % 154.32/154.41 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2)) % 154.32/154.41 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 154.32/154.41 => ? [B_s1] : % 154.32/154.41 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a3_2),V_a2_2),B_s1)) % 154.32/154.41 & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2)) ) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_evalc_Oequations_I8_J,axiom, % 154.32/154.41 ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] : % 154.32/154.41 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2)) % 154.32/154.41 <=> ( ( V_a5_2 = V_a2_2 % 154.32/154.41 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) % 154.32/154.41 | ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 154.32/154.41 & ? [B_s1] : % 154.32/154.41 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a3_2),V_a2_2),B_s1)) % 154.32/154.41 & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2)) ) ) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_evalc_Oequations_I4_J,axiom, % 154.32/154.41 ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] : % 154.32/154.41 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2)) % 154.32/154.41 <=> ? [B_s1] : % 154.32/154.41 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a1_2),V_a2_2),B_s1)) % 154.32/154.41 & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a4_2),B_s1),V_a5_2)) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_evalc_Oequations_I1_J,axiom, % 154.32/154.41 ! [V_a] : hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSKIP),V_a),V_a)) ). % 154.32/154.41 % 154.32/154.41 fof(fact_com_Osimps_I13_J,axiom, % 154.32/154.41 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ). % 154.32/154.41 % 154.32/154.41 fof(fact_com_Osimps_I12_J,axiom, % 154.32/154.41 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ). % 154.32/154.41 % 154.32/154.41 fof(fact_com_Osimps_I17_J,axiom, % 154.32/154.41 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ). % 154.32/154.41 % 154.32/154.41 fof(fact_com_Osimps_I16_J,axiom, % 154.32/154.41 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 154.32/154.41 % 154.32/154.41 fof(fact_com_Osimps_I47_J,axiom, % 154.32/154.41 ! [V_com2_2,V_com1_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ). % 154.32/154.41 % 154.32/154.41 fof(fact_com_Osimps_I46_J,axiom, % 154.32/154.41 ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 154.32/154.41 % 154.32/154.41 fof(fact_com_Osimps_I18_J,axiom, % 154.32/154.41 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 154.32/154.41 % 154.32/154.41 fof(fact_com_Osimps_I19_J,axiom, % 154.32/154.41 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ). % 154.32/154.41 % 154.32/154.41 fof(fact_com_Osimps_I49_J,axiom, % 154.32/154.41 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ). % 154.32/154.41 % 154.32/154.41 fof(fact_com_Osimps_I48_J,axiom, % 154.32/154.41 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 154.32/154.41 % 154.32/154.41 fof(fact_com_Osimps_I59_J,axiom, % 154.32/154.41 ! [V_com_2,V_fun_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OWhile(V_fun_2,V_com_2) ). % 154.32/154.41 % 154.32/154.41 fof(fact_com_Osimps_I6_J,axiom, % 154.32/154.41 ! [V_pname_H_2,V_pname_2] : % 154.32/154.41 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2) % 154.32/154.41 <=> V_pname_2 = V_pname_H_2 ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_com_Osimps_I5_J,axiom, % 154.32/154.41 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] : % 154.32/154.41 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) % 154.32/154.41 <=> ( V_fun_2 = V_fun_H_2 % 154.32/154.41 & V_com_2 = V_com_H_2 ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_com_Osimps_I3_J,axiom, % 154.32/154.41 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] : % 154.32/154.41 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) % 154.32/154.41 <=> ( V_com1_2 = V_com1_H_2 % 154.32/154.41 & V_com2_2 = V_com2_H_2 ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_com_Osimps_I58_J,axiom, % 154.32/154.41 ! [V_pname_H_2,V_com_2,V_fun_2] : c_Com_Ocom_OWhile(V_fun_2,V_com_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ). % 154.32/154.41 % 154.32/154.41 fof(fact_the__elem__def,axiom, % 154.32/154.41 ! [V_X_2,T_a] : c_Set_Othe__elem(T_a,V_X_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),hAPP(c_fequal,V_X_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ). % 154.32/154.41 % 154.32/154.41 fof(fact_MGF,axiom, % 154.32/154.41 ! [V_c_2] : % 154.32/154.41 ( c_Hoare__Mirabelle_Ostate__not__singleton % 154.32/154.41 => ( c_Com_OWT__bodies % 154.32/154.41 => ( hBOOL(hAPP(c_Com_OWT,V_c_2)) % 154.32/154.41 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_image__ident,axiom, % 154.32/154.41 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ). % 154.32/154.41 % 154.32/154.41 fof(fact_imageE,axiom, % 154.32/154.41 ! [V_A_2,V_f_2,T_b,V_b_2,T_a] : % 154.32/154.41 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 154.32/154.41 => ~ ! [B_x] : % 154.32/154.41 ( V_b_2 = hAPP(V_f_2,B_x) % 154.32/154.41 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_evalc__elim__cases_I4_J,axiom, % 154.32/154.41 ! [V_t,V_s,V_c2,V_c1] : % 154.32/154.41 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_t)) % 154.32/154.41 => ~ ! [B_s1] : % 154.32/154.41 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c1),V_s),B_s1)) % 154.32/154.41 => ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c2),B_s1),V_t)) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_Loop__sound__lemma,axiom, % 154.32/154.41 ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_a] : % 154.32/154.41 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_c_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 154.32/154.41 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_Loop,axiom, % 154.32/154.41 ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_a] : % 154.32/154.41 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_c_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 154.32/154.41 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_finite__pointwise,axiom, % 154.32/154.41 ! [V_Q_2,V_P_2,V_Q_H_2,V_c0_2,V_P_H_2,V_Ga_2,T_b,V_U_2,T_a] : % 154.32/154.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_U_2)) % 154.32/154.41 => ( ! [B_p] : % 154.32/154.41 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(V_P_H_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_H_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 154.32/154.41 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(V_P_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) % 154.32/154.41 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(c_Set_Oimage(T_a,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(T_a,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),T_a),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_H_2)),V_c0_2)),V_Q_H_2)),V_U_2)) % 154.32/154.41 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(c_Set_Oimage(T_a,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(T_a,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),T_a),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),V_c0_2)),V_Q_2)),V_U_2)) ) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_Sup__fin_Oidem,axiom, % 154.32/154.41 ! [V_x,T_a] : % 154.32/154.41 ( class_Lattices_Olattice(T_a) % 154.32/154.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_MGF__lemma1,axiom, % 154.32/154.41 ! [V_c_2,V_Ga_2] : % 154.32/154.41 ( c_Hoare__Mirabelle_Ostate__not__singleton % 154.32/154.41 => ( ! [B_x] : % 154.32/154.41 ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) % 154.32/154.41 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,B_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) % 154.32/154.41 => ( hBOOL(hAPP(c_Com_OWT,V_c_2)) % 154.32/154.41 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_vimage__insert,axiom, % 154.32/154.41 ! [V_B_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ). % 154.32/154.41 % 154.32/154.41 fof(fact_vimageI,axiom, % 154.32/154.41 ! [T_b,V_B_2,T_a,V_b_2,V_a_2,V_f_2] : % 154.32/154.41 ( hAPP(V_f_2,V_a_2) = V_b_2 % 154.32/154.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_B_2)) % 154.32/154.41 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_WTs__elim__cases_I6_J,axiom, % 154.32/154.41 ! [V_c_2,V_b_2] : % 154.32/154.41 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2))) % 154.32/154.41 => hBOOL(hAPP(c_Com_OWT,V_c_2)) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_WTs__elim__cases_I4_J,axiom, % 154.32/154.41 ! [V_c2,V_c1] : % 154.32/154.41 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2))) % 154.32/154.41 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1)) % 154.32/154.41 => ~ hBOOL(hAPP(c_Com_OWT,V_c2)) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_vimage__code,axiom, % 154.32/154.41 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 154.32/154.41 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2),V_x_2)) % 154.32/154.41 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_o__eq__elim,axiom, % 154.32/154.41 ! [V_d_2,V_c_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] : % 154.32/154.41 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,V_c_2),V_d_2) % 154.32/154.41 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_o__eq__dest,axiom, % 154.32/154.41 ! [V_v_2,V_d_2,V_c_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] : % 154.32/154.41 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,V_c_2),V_d_2) % 154.32/154.41 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_o__apply,axiom, % 154.32/154.41 ! [V_x_2,V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ). % 154.32/154.41 % 154.32/154.41 fof(fact_vimage__compose,axiom, % 154.32/154.41 ! [V_x_2,V_f_2,V_g_2,T_c,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_a,T_c,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_g_2),V_x_2)) ). % 154.32/154.41 % 154.32/154.41 fof(fact_vimage__ident,axiom, % 154.32/154.41 ! [V_Y_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ). % 154.32/154.41 % 154.32/154.41 fof(fact_o__assoc,axiom, % 154.32/154.41 ! [V_h_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),hAPP(c_Fun_Ocomp(T_d,T_c,T_a,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_h_2) ). % 154.32/154.41 % 154.32/154.41 fof(fact_o__def,axiom, % 154.32/154.41 ! [V_x_2,V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ). % 154.32/154.41 % 154.32/154.41 fof(fact_image__compose,axiom, % 154.32/154.41 ! [V_r_2,V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_a,T_b,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_c,T_a,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),V_r_2)) ). % 154.32/154.41 % 154.32/154.41 fof(fact_finite__dom__body,axiom, % 154.32/154.41 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ). % 154.32/154.41 % 154.32/154.41 fof(fact_vimageI2,axiom, % 154.32/154.41 ! [T_b,V_A_2,V_a_2,V_f_2,T_a] : % 154.32/154.41 ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_a_2)),V_A_2)) % 154.32/154.41 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_vimageD,axiom, % 154.32/154.41 ! [V_A_2,V_f_2,T_b,V_a_2,T_a] : % 154.32/154.41 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2))) % 154.32/154.41 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_vimage__eq,axiom, % 154.32/154.41 ! [V_B_2,V_f_2,T_b,V_a_2,T_a] : % 154.32/154.41 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2))) % 154.32/154.41 <=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_vimage__empty,axiom, % 154.32/154.41 ! [V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,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)) ). % 154.32/154.41 % 154.32/154.41 fof(fact_vimage__Un,axiom, % 154.32/154.41 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ). % 154.32/154.41 % 154.32/154.41 fof(fact_peek__and__def,axiom, % 154.32/154.41 ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_a] : % 154.32/154.41 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_p_2),V_Z_2),V_s_2)) % 154.32/154.41 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2)) % 154.32/154.41 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_While,axiom, % 154.32/154.41 ! [V_b_2,V_c_2] : % 154.32/154.41 ( hBOOL(hAPP(c_Com_OWT,V_c_2)) % 154.32/154.41 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2))) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_WT_Oequations_I6_J,axiom, % 154.32/154.41 ! [V_a1_2,V_a2_2] : % 154.32/154.41 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2))) % 154.32/154.41 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_WT_OSemi,axiom, % 154.32/154.41 ! [V_c1,V_c0] : % 154.32/154.41 ( hBOOL(hAPP(c_Com_OWT,V_c0)) % 154.32/154.41 => ( hBOOL(hAPP(c_Com_OWT,V_c1)) % 154.32/154.41 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1))) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_WT_Oequations_I4_J,axiom, % 154.32/154.41 ! [V_a2_2,V_a1_2] : % 154.32/154.41 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2))) % 154.32/154.41 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2)) % 154.32/154.41 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_WT_Oequations_I1_J,axiom, % 154.32/154.41 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ). % 154.32/154.41 % 154.32/154.41 fof(fact_WT_OSkip,axiom, % 154.32/154.41 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ). % 154.32/154.41 % 154.32/154.41 fof(fact_vimage__singleton__eq,axiom, % 154.32/154.41 ! [V_b_2,V_f_2,T_b,V_a_2,T_a] : % 154.32/154.41 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 154.32/154.41 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_finite__imageI,axiom, % 154.32/154.41 ! [V_h_2,T_b,V_F_2,T_a] : % 154.32/154.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 154.32/154.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_h_2),V_F_2))) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_finite_OinsertI,axiom, % 154.32/154.41 ! [V_a_2,V_A_2,T_a] : % 154.32/154.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_finite_OemptyI,axiom, % 154.32/154.41 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 154.32/154.41 % 154.32/154.41 fof(fact_hoare__derivs_OIf,axiom, % 154.32/154.41 ! [V_d_2,V_Q_2,V_c_2,V_b_2,V_P_2,V_Ga_2,T_a] : % 154.32/154.41 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 154.32/154.41 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2))),V_d_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 154.32/154.41 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OCond(V_b_2,V_c_2,V_d_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_finite__Un,axiom, % 154.32/154.41 ! [V_Ga_2,V_F_2,T_a] : % 154.32/154.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_Ga_2))) % 154.32/154.41 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 154.32/154.41 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2)) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_finite__UnI,axiom, % 154.32/154.41 ! [V_Ga_2,V_F_2,T_a] : % 154.32/154.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 154.32/154.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2)) % 154.32/154.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_finite__insert,axiom, % 154.32/154.41 ! [V_A_2,V_a_2,T_a] : % 154.32/154.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) % 154.32/154.41 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_finite_Oequations_I1_J,axiom, % 154.32/154.41 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 154.32/154.41 % 154.32/154.41 fof(fact_image__eq__fold__image,axiom, % 154.32/154.41 ! [V_f_2,T_b,V_A_2,T_a] : % 154.32/154.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.41 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_b,tc_HOL_Obool),T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Set_Oinsert(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_Sup__fin_Oinsert,axiom, % 154.32/154.41 ! [V_x_2,V_A_2,T_a] : % 154.32/154.41 ( class_Lattices_Olattice(T_a) % 154.32/154.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.32/154.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.32/154.41 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) ) ) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_the__eq__trivial,axiom, % 154.32/154.41 ! [V_a_2,T_a] : c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2 ). % 154.32/154.41 % 154.32/154.41 fof(fact_evalc__elim__cases_I5_J,axiom, % 154.32/154.41 ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_b_2] : % 154.32/154.41 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)),V_s_2),V_t_2)) % 154.32/154.41 => ( ( hBOOL(hAPP(V_b_2,V_s_2)) % 154.32/154.41 => ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c1_2),V_s_2),V_t_2)) ) % 154.32/154.41 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 154.32/154.41 => ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c2_2),V_s_2),V_t_2)) ) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_evalc_OIfTrue,axiom, % 154.32/154.41 ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_b_2] : % 154.32/154.41 ( hBOOL(hAPP(V_b_2,V_s_2)) % 154.32/154.41 => ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c0_2),V_s_2),V_s1_2)) % 154.32/154.41 => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_evalc_OIfFalse,axiom, % 154.32/154.41 ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] : % 154.32/154.41 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 154.32/154.41 => ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c1_2),V_s_2),V_s1_2)) % 154.32/154.41 => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_WTs__elim__cases_I5_J,axiom, % 154.32/154.41 ! [V_c2_2,V_c1_2,V_b_2] : % 154.32/154.41 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2))) % 154.32/154.41 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1_2)) % 154.32/154.41 => ~ hBOOL(hAPP(c_Com_OWT,V_c2_2)) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_com_Osimps_I4_J,axiom, % 154.32/154.41 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : % 154.32/154.41 ( c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) = c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) % 154.32/154.41 <=> ( V_fun_2 = V_fun_H_2 % 154.32/154.41 & V_com1_2 = V_com1_H_2 % 154.32/154.41 & V_com2_2 = V_com2_H_2 ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_fold__image__empty,axiom, % 154.32/154.41 ! [V_z_2,V_g_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ). % 154.32/154.41 % 154.32/154.41 fof(fact_evalc_Oequations_I6_J,axiom, % 154.32/154.41 ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] : % 154.32/154.41 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(V_a1_2,V_a5_2,V_a3_2)),V_a2_2),V_a4_2)) % 154.32/154.41 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 154.32/154.41 & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a5_2),V_a2_2),V_a4_2)) ) % 154.32/154.41 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 154.32/154.41 & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a3_2),V_a2_2),V_a4_2)) ) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_evalc_Oequations_I5_J,axiom, % 154.32/154.41 ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] : % 154.32/154.41 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a5_2)),V_a2_2),V_a4_2)) % 154.32/154.41 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 154.32/154.41 & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a3_2),V_a2_2),V_a4_2)) ) % 154.32/154.41 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 154.32/154.41 & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a5_2),V_a2_2),V_a4_2)) ) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_WT_OIf,axiom, % 154.32/154.41 ! [V_b_2,V_c1_2,V_c0_2] : % 154.32/154.41 ( hBOOL(hAPP(c_Com_OWT,V_c0_2)) % 154.32/154.41 => ( hBOOL(hAPP(c_Com_OWT,V_c1_2)) % 154.32/154.41 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2))) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_WT_Oequations_I5_J,axiom, % 154.32/154.41 ! [V_a2_2,V_a1_2,V_a3_2] : % 154.32/154.41 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2))) % 154.32/154.41 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2)) % 154.32/154.41 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_com_Osimps_I54_J,axiom, % 154.32/154.41 ! [V_pname_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ). % 154.32/154.41 % 154.32/154.41 fof(fact_com_Osimps_I55_J,axiom, % 154.32/154.41 ! [V_com2_2,V_com1_2,V_fun_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ). % 154.32/154.41 % 154.32/154.41 fof(fact_com_Osimps_I53_J,axiom, % 154.32/154.41 ! [V_com2_2,V_com1_2,V_fun_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ). % 154.32/154.41 % 154.32/154.41 fof(fact_com_Osimps_I52_J,axiom, % 154.32/154.41 ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 154.32/154.41 % 154.32/154.41 fof(fact_com_Osimps_I44_J,axiom, % 154.32/154.41 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ). % 154.32/154.41 % 154.32/154.41 fof(fact_com_Osimps_I45_J,axiom, % 154.32/154.41 ! [V_com2_2,V_com1_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ). % 154.32/154.41 % 154.32/154.41 fof(fact_com_Osimps_I14_J,axiom, % 154.32/154.41 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ). % 154.32/154.41 % 154.32/154.41 fof(fact_com_Osimps_I15_J,axiom, % 154.32/154.41 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSKIP ). % 154.32/154.41 % 154.32/154.41 fof(fact_Sup__fin_Osingleton,axiom, % 154.32/154.41 ! [V_x_2,T_a] : % 154.32/154.41 ( class_Lattices_Olattice(T_a) % 154.32/154.41 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_finite,axiom, % 154.32/154.41 ! [V_A_2,T_a] : % 154.32/154.41 ( class_Finite__Set_Ofinite(T_a) % 154.32/154.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_finite__code,axiom, % 154.32/154.41 ! [V_A_2,T_a] : % 154.32/154.41 ( class_Finite__Set_Ofinite(T_a) % 154.32/154.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_Sup__fin_Oin__idem,axiom, % 154.32/154.41 ! [V_x_2,V_A_2,T_a] : % 154.32/154.41 ( class_Lattices_Olattice(T_a) % 154.32/154.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.32/154.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) ) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_Sup__fin_Oinsert__idem,axiom, % 154.32/154.41 ! [V_x_2,V_A_2,T_a] : % 154.32/154.41 ( class_Lattices_Olattice(T_a) % 154.32/154.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.32/154.41 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) ) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_Sup__fin_Ounion__idem,axiom, % 154.32/154.41 ! [V_B_2,V_A_2,T_a] : % 154.32/154.41 ( class_Lattices_Olattice(T_a) % 154.32/154.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.32/154.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.32/154.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.32/154.41 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) ) ) ) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_the__sym__eq__trivial,axiom, % 154.32/154.41 ! [V_x_2,T_a] : c_HOL_OThe(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 154.32/154.41 % 154.32/154.41 fof(fact_comm__monoid__big_OF__eq,axiom, % 154.32/154.41 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 154.32/154.41 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2) % 154.32/154.41 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 154.32/154.41 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2) ) % 154.32/154.41 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 154.32/154.41 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_Sup__fin_Oclosed,axiom, % 154.32/154.41 ! [V_A_2,T_a] : % 154.32/154.41 ( class_Lattices_Olattice(T_a) % 154.32/154.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.32/154.41 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 154.32/154.41 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_folding__one_Oinsert,axiom, % 154.32/154.41 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 154.32/154.41 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 154.32/154.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.32/154.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.32/154.41 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_folding__idem_Ounion__idem,axiom, % 154.32/154.41 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 154.32/154.41 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 154.32/154.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.32/154.41 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 154.32/154.41 % 154.32/154.41 fof(fact_folding__idem_Oinsert__idem,axiom, % 154.32/154.41 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 154.32/154.41 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 154.32/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.42 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_folding__idem_Oin__comp__idem,axiom, % 154.32/154.42 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 154.32/154.42 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 154.32/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.42 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.32/154.42 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_Sup__fin_Ohom__commute,axiom, % 154.32/154.42 ! [V_N_2,V_h_2,T_a] : % 154.32/154.42 ( class_Lattices_Olattice(T_a) % 154.32/154.42 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 154.32/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 154.32/154.42 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.32/154.42 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_a,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_folding__one__idem_Ounion__idem,axiom, % 154.32/154.42 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 154.32/154.42 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 154.32/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.32/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.32/154.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.32/154.42 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_folding__one__idem_Oinsert__idem,axiom, % 154.32/154.42 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 154.32/154.42 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 154.32/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.32/154.42 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_folding_Oinsert,axiom, % 154.32/154.42 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 154.32/154.42 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 154.32/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.32/154.42 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_Sup__fin_Oremove,axiom, % 154.32/154.42 ! [V_x_2,V_A_2,T_a] : % 154.32/154.42 ( class_Lattices_Olattice(T_a) % 154.32/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.42 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.32/154.42 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.32/154.42 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = V_x_2 ) % 154.32/154.42 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.32/154.42 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_DiffE,axiom, % 154.32/154.42 ! [V_B_2,V_A_2,V_c_2,T_a] : % 154.32/154.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.32/154.42 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 154.32/154.42 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_DiffI,axiom, % 154.32/154.42 ! [V_B_2,V_A_2,V_c_2,T_a] : % 154.32/154.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 154.32/154.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) % 154.32/154.42 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_finite__Diff,axiom, % 154.32/154.42 ! [V_B_2,V_A_2,T_a] : % 154.32/154.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.42 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_fun__diff__def,axiom, % 154.32/154.42 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] : % 154.32/154.42 ( class_Groups_Ominus(T_a) % 154.32/154.42 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_Diff__idemp,axiom, % 154.32/154.42 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 154.32/154.42 % 154.32/154.42 fof(fact_minus__apply,axiom, % 154.32/154.42 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] : % 154.32/154.42 ( class_Groups_Ominus(T_a) % 154.32/154.42 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_folding__one__idem_Oidem,axiom, % 154.32/154.42 ! [V_x_2,V_F_2,V_f_2,T_a] : % 154.32/154.42 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 154.32/154.42 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_DiffD2,axiom, % 154.32/154.42 ! [V_B_2,V_A_2,V_c_2,T_a] : % 154.32/154.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.32/154.42 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_DiffD1,axiom, % 154.32/154.42 ! [V_B_2,V_A_2,V_c_2,T_a] : % 154.32/154.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.32/154.42 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_Diff__iff,axiom, % 154.32/154.42 ! [V_B_2,V_A_2,V_c_2,T_a] : % 154.32/154.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.32/154.42 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 154.32/154.42 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_empty__Diff,axiom, % 154.32/154.42 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 154.32/154.42 % 154.32/154.42 fof(fact_Diff__empty,axiom, % 154.32/154.42 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ). % 154.32/154.42 % 154.32/154.42 fof(fact_Diff__cancel,axiom, % 154.32/154.42 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 154.32/154.42 % 154.32/154.42 fof(fact_finite__Diff2,axiom, % 154.32/154.42 ! [V_A_2,V_B_2,T_a] : % 154.32/154.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.32/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.32/154.42 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_Un__Diff__cancel,axiom, % 154.32/154.42 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 154.32/154.42 % 154.32/154.42 fof(fact_Un__Diff__cancel2,axiom, % 154.32/154.42 ! [V_A_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) ). % 154.32/154.42 % 154.32/154.42 fof(fact_Un__Diff,axiom, % 154.32/154.42 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 154.32/154.42 % 154.32/154.42 fof(fact_vimage__Diff,axiom, % 154.32/154.42 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ). % 154.32/154.42 % 154.32/154.42 fof(fact_folding_Ocommute__left__comp,axiom, % 154.32/154.42 ! [V_g_2,V_x_2,V_y_2,T_c,V_F_2,V_f_2,T_b,T_a] : % 154.32/154.42 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 154.32/154.42 => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_y_2)),V_g_2)) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_folding_Ocommute__comp,axiom, % 154.32/154.42 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_b,T_a] : % 154.32/154.42 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 154.32/154.42 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_folding_Ocommute__comps_I1_J,axiom, % 154.32/154.42 ! [V_h_2,V_g_2,T_f,V_f_2,T_c,T_d,T_e,V_F_2,V_fa_2,T_b,T_a] : % 154.32/154.42 ( c_Finite__Set_Ofolding(T_a,T_b,V_fa_2,V_F_2) % 154.32/154.42 => hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_f_2),hAPP(c_Fun_Ocomp(T_f,T_e,T_c,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_f,T_d,T_c,hAPP(c_Fun_Ocomp(T_e,T_d,T_f,V_f_2),V_g_2)),V_h_2) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_folding__one_Oinsert__remove,axiom, % 154.32/154.42 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 154.32/154.42 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 154.32/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.42 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.32/154.42 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 154.32/154.42 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.32/154.42 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_insert__Diff1,axiom, % 154.32/154.42 ! [V_A_2,V_B_2,V_x_2,T_a] : % 154.32/154.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 154.32/154.42 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_insert__Diff__if,axiom, % 154.32/154.42 ! [V_A_2,V_B_2,V_x_2,T_a] : % 154.32/154.42 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 154.32/154.42 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) % 154.32/154.42 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 154.32/154.42 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_Diff__insert,axiom, % 154.32/154.42 ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 154.32/154.42 % 154.32/154.42 fof(fact_Diff__insert2,axiom, % 154.32/154.42 ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2) ). % 154.32/154.42 % 154.32/154.42 fof(fact_insert__Diff__single,axiom, % 154.32/154.42 ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) ). % 154.32/154.42 % 154.32/154.42 fof(fact_finite__Diff__insert,axiom, % 154.32/154.42 ! [V_B_2,V_a_2,V_A_2,T_a] : % 154.32/154.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)))) % 154.32/154.42 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_folding_Oinsert__remove,axiom, % 154.32/154.42 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 154.32/154.42 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 154.32/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.42 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_folding__one_Oremove,axiom, % 154.32/154.42 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 154.32/154.42 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 154.32/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.42 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.32/154.42 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.32/154.42 => hAPP(V_F_2,V_A_2) = V_x_2 ) % 154.32/154.42 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.32/154.42 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_folding__idem_Oidem__left__comp,axiom, % 154.32/154.42 ! [V_g_2,V_x_2,T_c,V_F_2,V_f_2,T_b,T_a] : % 154.32/154.42 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 154.32/154.42 => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_folding__idem_Oidem__comp,axiom, % 154.32/154.42 ! [V_x_2,V_F_2,V_f_2,T_b,T_a] : % 154.32/154.42 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 154.32/154.42 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_folding_Oremove,axiom, % 154.32/154.42 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 154.32/154.42 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 154.32/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.42 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.32/154.42 => hAPP(V_F_2,V_A_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_Diff__insert__absorb,axiom, % 154.32/154.42 ! [V_A_2,V_x_2,T_a] : % 154.32/154.42 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.32/154.42 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_A_2 ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_insert__Diff,axiom, % 154.32/154.42 ! [V_A_2,V_a_2,T_a] : % 154.32/154.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.32/154.42 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = V_A_2 ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_folding_Ocommute__left__comp_H_H,axiom, % 154.32/154.42 ! [V_g_2,T_c,V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 154.32/154.42 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 154.32/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.32/154.42 => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_B_2)),V_g_2)) ) ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_folding_Ocommute__comp_H_H,axiom, % 154.32/154.42 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 154.32/154.42 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 154.32/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.32/154.42 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_folding_Ocommute__left__comp_H,axiom, % 154.32/154.42 ! [V_g_2,V_x_2,T_c,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 154.32/154.42 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 154.32/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.42 => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2)) ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_folding_Ocommute__comp_H,axiom, % 154.32/154.42 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 154.32/154.42 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 154.32/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.42 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_folding__one_Osingleton,axiom, % 154.32/154.42 ! [V_x_2,V_F_2,V_f_2,T_a] : % 154.32/154.42 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 154.32/154.42 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_folding__one__idem_Oin__idem,axiom, % 154.32/154.42 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 154.32/154.42 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 154.32/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.42 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.32/154.42 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_comm__monoid__big_Oinfinite,axiom, % 154.32/154.42 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 154.32/154.42 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2) % 154.32/154.42 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 154.32/154.42 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_Sup__fin_Oinsert__remove,axiom, % 154.32/154.42 ! [V_x_2,V_A_2,T_a] : % 154.32/154.42 ( class_Lattices_Olattice(T_a) % 154.32/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.32/154.42 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.32/154.42 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 154.32/154.42 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.32/154.42 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_folding__image__simple_Oremove,axiom, % 154.32/154.42 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 154.32/154.42 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 154.32/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 154.32/154.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 154.32/154.42 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_folding__image__simple_Oinsert__remove,axiom, % 154.32/154.42 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 154.32/154.42 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 154.32/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 154.32/154.42 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ). % 154.32/154.42 % 154.32/154.42 fof(fact_folding__one_Oclosed,axiom, % 154.32/154.42 ! [V_A_2,V_F_2,V_f_2,T_a] : % 154.32/154.42 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.42 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 154.47/154.42 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_fun__upd__image,axiom, % 154.47/154.42 ! [V_y_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 154.47/154.42 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.42 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) % 154.47/154.42 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.42 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_finite__empty__induct,axiom, % 154.47/154.42 ! [V_P_2,V_A_2,T_a] : % 154.47/154.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => ( hBOOL(hAPP(V_P_2,V_A_2)) % 154.47/154.42 => ( ! [B_a,B_A] : % 154.47/154.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_A)) % 154.47/154.42 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) % 154.47/154.42 => ( hBOOL(hAPP(V_P_2,B_A)) % 154.47/154.42 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_a),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) % 154.47/154.42 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_folding__one__idem_Ohom__commute,axiom, % 154.47/154.42 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_a] : % 154.47/154.42 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 154.47/154.42 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(V_f_2,B_x),B_y)) = hAPP(hAPP(V_f_2,hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 154.47/154.42 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.42 => hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_fun__left__comm__idem__remove,axiom, % 154.47/154.42 ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ). % 154.47/154.42 % 154.47/154.42 fof(fact_folding__image__simple_Oinsert,axiom, % 154.47/154.42 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 154.47/154.42 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 154.47/154.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 154.47/154.42 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_setsum__diff1__ring,axiom, % 154.47/154.42 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 154.47/154.42 ( class_Rings_Oring(T_b) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_setsum__diff1,axiom, % 154.47/154.42 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 154.47/154.42 ( class_Groups_Oab__group__add(T_b) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 154.47/154.42 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2) ) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_folding_Ounion,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 154.47/154.42 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.42 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.42 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf1E,axiom, % 154.47/154.42 ! [V_x_2,V_B_2,V_A_2,T_a] : % 154.47/154.42 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 154.47/154.42 => ~ ( hBOOL(hAPP(V_A_2,V_x_2)) % 154.47/154.42 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf1I,axiom, % 154.47/154.42 ! [T_a,V_B_2,V_x_2,V_A_2] : % 154.47/154.42 ( hBOOL(hAPP(V_A_2,V_x_2)) % 154.47/154.42 => ( hBOOL(hAPP(V_B_2,V_x_2)) % 154.47/154.42 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_fun__upd__triv,axiom, % 154.47/154.42 ! [V_x_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),hAPP(V_f_2,V_x_2)) = V_f_2 ). % 154.47/154.42 % 154.47/154.42 fof(fact_IntI,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,V_c_2,T_a] : % 154.47/154.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 154.47/154.42 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) % 154.47/154.42 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_IntE,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,V_c_2,T_a] : % 154.47/154.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.47/154.42 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 154.47/154.42 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_finite__Int,axiom, % 154.47/154.42 ! [V_Ga_2,V_F_2,T_a] : % 154.47/154.42 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 154.47/154.42 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2)) ) % 154.47/154.42 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_fun__upd__idem,axiom, % 154.47/154.42 ! [T_a,T_b,V_y_2,V_x_2,V_f_2] : % 154.47/154.42 ( hAPP(V_f_2,V_x_2) = V_y_2 % 154.47/154.42 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2) = V_f_2 ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_fun__upd__other,axiom, % 154.47/154.42 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] : % 154.47/154.42 ( V_z_2 != V_x_2 % 154.47/154.42 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_fun__upd__twist,axiom, % 154.47/154.42 ! [V_d_2,V_b_2,V_m_2,T_b,T_a,V_c_2,V_a_2] : % 154.47/154.42 ( V_a_2 != V_c_2 % 154.47/154.42 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_m_2),V_a_2),V_b_2)),V_c_2),V_d_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_m_2),V_c_2),V_d_2)),V_a_2),V_b_2) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_fun__upd__apply,axiom, % 154.47/154.42 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] : % 154.47/154.42 ( ( V_z_2 = V_x_2 % 154.47/154.42 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = V_y_2 ) % 154.47/154.42 & ( V_z_2 != V_x_2 % 154.47/154.42 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_fun__upd__same,axiom, % 154.47/154.42 ! [V_y_2,V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2),V_x_2) = V_y_2 ). % 154.47/154.42 % 154.47/154.42 fof(fact_fun__upd__upd,axiom, % 154.47/154.42 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_x_2),V_z_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_z_2) ). % 154.47/154.42 % 154.47/154.42 fof(fact_fun__upd__idem__iff,axiom, % 154.47/154.42 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 154.47/154.42 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 % 154.47/154.42 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Inf__fin_Oidem,axiom, % 154.47/154.42 ! [V_x,T_a] : % 154.47/154.42 ( class_Lattices_Olattice(T_a) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf1D2,axiom, % 154.47/154.42 ! [V_x_2,V_B_2,V_A_2,T_a] : % 154.47/154.42 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 154.47/154.42 => hBOOL(hAPP(V_B_2,V_x_2)) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf1D1,axiom, % 154.47/154.42 ! [V_x_2,V_B_2,V_A_2,T_a] : % 154.47/154.42 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 154.47/154.42 => hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf__apply,axiom, % 154.47/154.42 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 154.47/154.42 ( class_Lattices_Olattice(T_a) % 154.47/154.42 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf__assoc,axiom, % 154.47/154.42 ! [V_z,V_y,V_x,T_a] : % 154.47/154.42 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf__sup__aci_I2_J,axiom, % 154.47/154.42 ! [V_z,V_y,V_x,T_a] : % 154.47/154.42 ( class_Lattices_Olattice(T_a) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf_Oassoc,axiom, % 154.47/154.42 ! [V_c,V_b,V_a,T_a] : % 154.47/154.42 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Int__assoc,axiom, % 154.47/154.42 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf__left__commute,axiom, % 154.47/154.42 ! [V_z,V_y,V_x,T_a] : % 154.47/154.42 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf__sup__aci_I3_J,axiom, % 154.47/154.42 ! [V_z,V_y,V_x,T_a] : % 154.47/154.42 ( class_Lattices_Olattice(T_a) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf_Oleft__commute,axiom, % 154.47/154.42 ! [V_c,V_a,V_b,T_a] : % 154.47/154.42 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Int__left__commute,axiom, % 154.47/154.42 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf__left__idem,axiom, % 154.47/154.42 ! [V_y,V_x,T_a] : % 154.47/154.42 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf__sup__aci_I4_J,axiom, % 154.47/154.42 ! [V_y,V_x,T_a] : % 154.47/154.42 ( class_Lattices_Olattice(T_a) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf_Oleft__idem,axiom, % 154.47/154.42 ! [V_b,V_a,T_a] : % 154.47/154.42 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Int__left__absorb,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf__commute,axiom, % 154.47/154.42 ! [V_y,V_x,T_a] : % 154.47/154.42 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf__sup__aci_I1_J,axiom, % 154.47/154.42 ! [V_y,V_x,T_a] : % 154.47/154.42 ( class_Lattices_Olattice(T_a) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf_Ocommute,axiom, % 154.47/154.42 ! [V_b,V_a,T_a] : % 154.47/154.42 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_a) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Int__commute,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf__fun__def,axiom, % 154.47/154.42 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 154.47/154.42 ( class_Lattices_Olattice(T_a) % 154.47/154.42 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf__idem,axiom, % 154.47/154.42 ! [V_x,T_a] : % 154.47/154.42 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf_Oidem,axiom, % 154.47/154.42 ! [V_a,T_a] : % 154.47/154.42 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Int__absorb,axiom, % 154.47/154.42 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ). % 154.47/154.42 % 154.47/154.42 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom, % 154.47/154.42 ! [V_z_2,V_x_2,V_f_2,T_b,T_a] : % 154.47/154.42 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 154.47/154.42 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) = hAPP(hAPP(V_f_2,V_x_2),V_z_2) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_fun__left__comm__idem__inf,axiom, % 154.47/154.42 ! [T_a] : % 154.47/154.42 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.42 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_setsum__commute,axiom, % 154.47/154.42 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 154.47/154.42 ( class_Groups_Ocomm__monoid__add(T_a) % 154.47/154.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_a),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2))),V_A_2)),V_B_2) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_fun__upd__def,axiom, % 154.47/154.42 ! [V_b_2,V_f_2,T_b,T_a,V_a_2,V_x_2] : % 154.47/154.42 ( ( V_x_2 = V_a_2 % 154.47/154.42 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_a_2),V_b_2),V_x_2) = V_b_2 ) % 154.47/154.42 & ( V_x_2 != V_a_2 % 154.47/154.42 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_a_2),V_b_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom, % 154.47/154.42 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 154.47/154.42 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 154.47/154.42 => c_Finite__Set_Ofun__left__comm__idem(T_c,T_b,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf__bot__right,axiom, % 154.47/154.42 ! [V_x,T_a] : % 154.47/154.42 ( class_Lattices_Obounded__lattice__bot(T_a) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf__bot__left,axiom, % 154.47/154.42 ! [V_x,T_a] : % 154.47/154.42 ( class_Lattices_Obounded__lattice__bot(T_a) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_sup__inf__distrib2,axiom, % 154.47/154.42 ! [V_x,V_z,V_y,T_a] : % 154.47/154.42 ( class_Lattices_Odistrib__lattice(T_a) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_z),V_x)) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf__sup__distrib2,axiom, % 154.47/154.42 ! [V_x,V_z,V_y,T_a] : % 154.47/154.42 ( class_Lattices_Odistrib__lattice(T_a) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_z),V_x)) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_sup__inf__distrib1,axiom, % 154.47/154.42 ! [V_z,V_y,V_x,T_a] : % 154.47/154.42 ( class_Lattices_Odistrib__lattice(T_a) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf__sup__distrib1,axiom, % 154.47/154.42 ! [V_z,V_y,V_x,T_a] : % 154.47/154.42 ( class_Lattices_Odistrib__lattice(T_a) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_sup__inf__absorb,axiom, % 154.47/154.42 ! [V_y,V_x,T_a] : % 154.47/154.42 ( class_Lattices_Olattice(T_a) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = V_x ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf__sup__absorb,axiom, % 154.47/154.42 ! [V_y,V_x,T_a] : % 154.47/154.42 ( class_Lattices_Olattice(T_a) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = V_x ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Int__iff,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,V_c_2,T_a] : % 154.47/154.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.47/154.42 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 154.47/154.42 & hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_IntD1,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,V_c_2,T_a] : % 154.47/154.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.47/154.42 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_IntD2,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,V_c_2,T_a] : % 154.47/154.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.47/154.42 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_disjoint__iff__not__equal,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,T_a] : % 154.47/154.42 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.42 <=> ! [B_x] : % 154.47/154.42 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.47/154.42 => ! [B_xa] : % 154.47/154.42 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_B_2)) % 154.47/154.42 => B_x != B_xa ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Int__empty__right,axiom, % 154.47/154.42 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Int__empty__left,axiom, % 154.47/154.42 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 154.47/154.42 % 154.47/154.42 fof(fact_insert__inter__insert,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Un__Int__crazy,axiom, % 154.47/154.42 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Un__Int__distrib2,axiom, % 154.47/154.42 ! [V_A_2,V_C_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Int__Un__distrib2,axiom, % 154.47/154.42 ! [V_A_2,V_C_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Un__Int__distrib,axiom, % 154.47/154.42 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Int__Un__distrib,axiom, % 154.47/154.42 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Diff__Int2,axiom, % 154.47/154.42 ! [V_B_2,V_C_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Diff__Int__distrib2,axiom, % 154.47/154.42 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Int__Diff,axiom, % 154.47/154.42 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Diff__Int__distrib,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,V_C_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 154.47/154.42 % 154.47/154.42 fof(fact_vimage__Int,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ). % 154.47/154.42 % 154.47/154.42 fof(fact_folding__image__simple_Ounion__inter,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 154.47/154.42 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 154.47/154.42 => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_setsum__subtractf,axiom, % 154.47/154.42 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 154.47/154.42 ( class_Groups_Oab__group__add(T_a) % 154.47/154.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_g_2),V_A_2)) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf__Int__eq,axiom, % 154.47/154.42 ! [V_x_2,V_S_2,V_R_2,T_a] : % 154.47/154.42 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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)),V_x_2)) % 154.47/154.42 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_fun__upd__comp,axiom, % 154.47/154.42 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_c),V_g_2),V_x_2),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)),V_x_2),hAPP(V_f_2,V_y_2)) ). % 154.47/154.42 % 154.47/154.42 fof(fact_setsum__diff1__nat,axiom, % 154.47/154.42 ! [V_f_2,V_A_2,V_a_2,T_a] : % 154.47/154.42 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 154.47/154.42 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_folding__image__simple_Ounion__disjoint,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 154.47/154.42 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 154.47/154.42 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 154.47/154.42 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_fun__left__comm__idem__insert,axiom, % 154.47/154.42 ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)) ). % 154.47/154.42 % 154.47/154.42 fof(fact_fun__left__comm__idem__sup,axiom, % 154.47/154.42 ! [T_a] : % 154.47/154.42 ( class_Lattices_Osemilattice__sup(T_a) % 154.47/154.42 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom, % 154.47/154.42 ! [V_x_2,V_f_2,T_b,T_a] : % 154.47/154.42 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 154.47/154.42 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Int__insert__right,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,V_a_2,T_a] : % 154.47/154.42 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 154.47/154.42 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Int__insert__left,axiom, % 154.47/154.42 ! [V_B_2,V_C_2,V_a_2,T_a] : % 154.47/154.42 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ) % 154.47/154.42 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Int__insert__right__if0,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,V_a_2,T_a] : % 154.47/154.42 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Int__insert__left__if0,axiom, % 154.47/154.42 ! [V_B_2,V_C_2,V_a_2,T_a] : % 154.47/154.42 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Int__insert__right__if1,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,V_a_2,T_a] : % 154.47/154.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Int__insert__left__if1,axiom, % 154.47/154.42 ! [V_B_2,V_C_2,V_a_2,T_a] : % 154.47/154.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Diff__disjoint,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Diff__triv,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,T_a] : % 154.47/154.42 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.42 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_folding__image__simple_Oempty,axiom, % 154.47/154.42 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 154.47/154.42 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 154.47/154.42 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Diff__Int,axiom, % 154.47/154.42 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Diff__Un,axiom, % 154.47/154.42 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Un__Diff__Int,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = V_A_2 ). % 154.47/154.42 % 154.47/154.42 fof(fact_inf__Sup__absorb,axiom, % 154.47/154.42 ! [V_a_2,V_A_2,T_a] : % 154.47/154.42 ( class_Lattices_Olattice(T_a) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = V_a_2 ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_folding__image__simple_Oeq__fold__g,axiom, % 154.47/154.42 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 154.47/154.42 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 154.47/154.42 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_folding_Ounion__inter,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 154.47/154.42 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.42 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_folding__one_Ounion__disjoint,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 154.47/154.42 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.42 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.42 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_folding__one_Ounion__inter,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 154.47/154.42 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.42 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.42 => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Sup__fin_Ounion__disjoint,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,T_a] : % 154.47/154.42 ( class_Lattices_Olattice(T_a) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.42 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.42 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) ) ) ) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Sup__fin_Ounion__inter,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,T_a] : % 154.47/154.42 ( class_Lattices_Olattice(T_a) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.42 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) ) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Inf__fin_Oremove,axiom, % 154.47/154.42 ! [V_x_2,V_A_2,T_a] : % 154.47/154.42 ( class_Lattices_Olattice(T_a) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.42 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.42 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = V_x_2 ) % 154.47/154.42 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.42 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_setsum__diff1_H,axiom, % 154.47/154.42 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 154.47/154.42 ( class_Groups_Ocomm__monoid__add(T_b) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_setsum_Oremove,axiom, % 154.47/154.42 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 154.47/154.42 ( class_Groups_Ocomm__monoid__add(T_b) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Inf__fin_Ounion__disjoint,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,T_a] : % 154.47/154.42 ( class_Lattices_Olattice(T_a) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.42 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.42 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) ) ) ) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Inf__fin_Ounion__inter,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,T_a] : % 154.47/154.42 ( class_Lattices_Olattice(T_a) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.42 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) ) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Inf__fin_Oinsert__remove,axiom, % 154.47/154.42 ! [V_x_2,V_A_2,T_a] : % 154.47/154.42 ( class_Lattices_Olattice(T_a) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.42 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 154.47/154.42 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.42 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Inf__fin_Oinsert,axiom, % 154.47/154.42 ! [V_x_2,V_A_2,T_a] : % 154.47/154.42 ( class_Lattices_Olattice(T_a) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.42 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) ) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 154.47/154.42 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 154.47/154.42 => ( ! [B_x] : % 154.47/154.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.47/154.42 => hAPP(V_g_2,B_x) = V_z_2 ) % 154.47/154.42 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_folding__image__simple__idem_Ounion__idem,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 154.47/154.42 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 154.47/154.42 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Sup__fin_Oeq__fold_H,axiom, % 154.47/154.42 ! [V_x_2,V_A_2,T_a] : % 154.47/154.42 ( class_Lattices_Olattice(T_a) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.42 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_x_2),V_A_2) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_setsum__Un,axiom, % 154.47/154.42 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 154.47/154.42 ( class_Groups_Oab__group__add(T_b) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_folding__image__simple__idem_Oidem,axiom, % 154.47/154.42 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 154.47/154.42 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 154.47/154.42 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_fold__empty,axiom, % 154.47/154.42 ! [V_z_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_a,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ). % 154.47/154.42 % 154.47/154.42 fof(fact_setsum__addf,axiom, % 154.47/154.42 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 154.47/154.42 ( class_Groups_Ocomm__monoid__add(T_a) % 154.47/154.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Oplus__class_Oplus(T_a)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_g_2),V_A_2)) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom, % 154.47/154.42 ! [V_a_2,V_A_2,T_a] : % 154.47/154.42 ( class_Lattices_Olattice(T_a) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_a_2),V_A_2) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_fold__image__def,axiom, % 154.47/154.42 ! [V_g_2,V_f_2,T_b,T_a] : hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_b,T_a,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),V_f_2),V_g_2)) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Inf__fin_Oeq__fold_H,axiom, % 154.47/154.42 ! [V_x_2,V_A_2,T_a] : % 154.47/154.42 ( class_Lattices_Olattice(T_a) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.42 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_x_2),V_A_2) ) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_folding_Oeq__fold,axiom, % 154.47/154.42 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 154.47/154.42 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_s_2),V_A_2) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_Inf__fin_Osingleton,axiom, % 154.47/154.42 ! [V_x_2,T_a] : % 154.47/154.42 ( class_Lattices_Olattice(T_a) % 154.47/154.42 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_setsum_Odistrib,axiom, % 154.47/154.42 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 154.47/154.42 ( class_Groups_Ocomm__monoid__add(T_b) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Groups_Oplus__class_Oplus(T_b)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_h_2),V_A_2)) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_union__fold__insert,axiom, % 154.47/154.42 ! [V_B_2,V_A_2,T_a] : % 154.47/154.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)),V_B_2),V_A_2) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_fold__sup__insert,axiom, % 154.47/154.42 ! [V_a_2,V_b_2,V_A_2,T_a] : % 154.47/154.42 ( class_Lattices_Osemilattice__sup(T_a) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_b_2),V_A_2)) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_fold__inf__insert,axiom, % 154.47/154.42 ! [V_a_2,V_b_2,V_A_2,T_a] : % 154.47/154.42 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_b_2),V_A_2)) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_setsum__Un__nat,axiom, % 154.47/154.42 ! [V_f_2,V_B_2,V_A_2,T_a] : % 154.47/154.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.42 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 154.47/154.42 % 154.47/154.42 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom, % 154.47/154.42 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 154.47/154.42 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 154.47/154.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.42 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom, % 154.47/154.43 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 154.47/154.43 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom, % 154.47/154.43 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_a] : % 154.47/154.43 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,V_f_2),V_a_2),V_A_2) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_sup__Inf__absorb,axiom, % 154.47/154.43 ! [V_a_2,V_A_2,T_a] : % 154.47/154.43 ( class_Lattices_Olattice(T_a) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.43 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = V_a_2 ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Inf__fin_Oin__idem,axiom, % 154.47/154.43 ! [V_x_2,V_A_2,T_a] : % 154.47/154.43 ( class_Lattices_Olattice(T_a) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.43 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_setsum_Oinsert,axiom, % 154.47/154.43 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 154.47/154.43 ( class_Groups_Ocomm__monoid__add(T_b) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.43 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)) ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_setsum__insert,axiom, % 154.47/154.43 ! [V_f_2,V_a_2,V_F_2,T_a,T_b] : % 154.47/154.43 ( class_Groups_Ocomm__monoid__add(T_b) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 154.47/154.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_F_2)) % 154.47/154.43 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_F_2)) ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_setsum__Un__Int,axiom, % 154.47/154.43 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 154.47/154.43 ( class_Groups_Ocomm__monoid__add(T_b) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_B_2)) ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom, % 154.47/154.43 ! [V_a_2,V_A_2,T_a] : % 154.47/154.43 ( class_Lattices_Olattice(T_a) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_a_2),V_A_2) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_minus__fold__remove,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2),V_A_2) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_folding__one_Oeq__fold_H,axiom, % 154.47/154.43 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 154.47/154.43 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.43 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,V_f_2),V_x_2),V_A_2) ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Inf__fin_Oinsert__idem,axiom, % 154.47/154.43 ! [V_x_2,V_A_2,T_a] : % 154.47/154.43 ( class_Lattices_Olattice(T_a) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Inf__fin_Ounion__idem,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_a] : % 154.47/154.43 ( class_Lattices_Olattice(T_a) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.43 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) ) ) ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_folding__image__simple__idem_Oin__idem,axiom, % 154.47/154.43 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 154.47/154.43 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 154.47/154.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 154.47/154.43 => hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom, % 154.47/154.43 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 154.47/154.43 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 154.47/154.43 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_setsum_Oinsert__remove,axiom, % 154.47/154.43 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] : % 154.47/154.43 ( class_Groups_Ocomm__monoid__add(T_b) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_setsum__Un__disjoint,axiom, % 154.47/154.43 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 154.47/154.43 ( class_Groups_Ocomm__monoid__add(T_b) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.43 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_fun__left__comm_Ofold__rec,axiom, % 154.47/154.43 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 154.47/154.43 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.43 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_fun__left__comm_Ofold__insert__remove,axiom, % 154.47/154.43 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 154.47/154.43 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Inf__fin_Oclosed,axiom, % 154.47/154.43 ! [V_A_2,T_a] : % 154.47/154.43 ( class_Lattices_Olattice(T_a) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 154.47/154.43 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_add__diff__cancel,axiom, % 154.47/154.43 ! [V_b,V_a,T_a] : % 154.47/154.43 ( class_Groups_Ogroup__add(T_a) % 154.47/154.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = V_a ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_diff__add__cancel,axiom, % 154.47/154.43 ! [V_b,V_a,T_a] : % 154.47/154.43 ( class_Groups_Ogroup__add(T_a) % 154.47/154.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_b) = V_a ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Inf__fin_Ohom__commute,axiom, % 154.47/154.43 ! [V_N_2,V_h_2,T_a] : % 154.47/154.43 ( class_Lattices_Olattice(T_a) % 154.47/154.43 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 154.47/154.43 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_a,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_SUPR__fold__sup,axiom, % 154.47/154.43 ! [V_f_2,V_A_2,T_a,T_b] : % 154.47/154.43 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(T_b)),V_A_2) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_fun__left__comm_Ofold__insert2,axiom, % 154.47/154.43 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 154.47/154.43 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.43 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_fun__left__comm_Ofold__insert,axiom, % 154.47/154.43 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 154.47/154.43 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.43 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2)) ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Sup__fold__sup,axiom, % 154.47/154.43 ! [V_A_2,T_a] : % 154.47/154.43 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),c_Orderings_Obot__class_Obot(T_a)),V_A_2) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_SUP1__I,axiom, % 154.47/154.43 ! [T_b,V_b_2,V_B_2,V_A_2,V_a_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.43 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 154.47/154.43 => hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_SUP2__I,axiom, % 154.47/154.43 ! [T_c,T_b,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.43 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) % 154.47/154.43 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_fun__left__comm_Ofun__left__comm,axiom, % 154.47/154.43 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] : % 154.47/154.43 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 154.47/154.43 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_y_2),V_z_2)) = hAPP(hAPP(V_f_2,V_y_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom, % 154.47/154.43 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 154.47/154.43 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 154.47/154.43 => c_Finite__Set_Ofun__left__comm(T_c,T_b,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_finite__UN,axiom, % 154.47/154.43 ! [V_B_2,T_b,V_A_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.47/154.43 <=> ! [B_x] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.47/154.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__o,axiom, % 154.47/154.43 ! [V_f_2,V_g_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_c,tc_fun(T_a,tc_HOL_Obool),T_b,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_g_2) ). % 154.47/154.43 % 154.47/154.43 fof(fact_finite__UnionD,axiom, % 154.47/154.43 ! [V_A_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) % 154.47/154.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_fun__left__comm_Ofun__comp__comm,axiom, % 154.47/154.43 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 154.47/154.43 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 154.47/154.43 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 154.47/154.43 ! [V_c,V_b,V_a,T_a] : % 154.47/154.43 ( class_Groups_Oab__semigroup__add(T_a) % 154.47/154.43 => 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)) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_add__left__cancel,axiom, % 154.47/154.43 ! [V_c_2,V_b_2,V_a_2,T_a] : % 154.47/154.43 ( class_Groups_Ocancel__semigroup__add(T_a) % 154.47/154.43 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2) % 154.47/154.43 <=> V_b_2 = V_c_2 ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_add__right__cancel,axiom, % 154.47/154.43 ! [V_c_2,V_a_2,V_b_2,T_a] : % 154.47/154.43 ( class_Groups_Ocancel__semigroup__add(T_a) % 154.47/154.43 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2) % 154.47/154.43 <=> V_b_2 = V_c_2 ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_add__left__imp__eq,axiom, % 154.47/154.43 ! [V_c,V_b,V_a,T_a] : % 154.47/154.43 ( class_Groups_Ocancel__semigroup__add(T_a) % 154.47/154.43 => ( 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) % 154.47/154.43 => V_b = V_c ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_add__imp__eq,axiom, % 154.47/154.43 ! [V_c,V_b,V_a,T_a] : % 154.47/154.43 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 154.47/154.43 => ( 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) % 154.47/154.43 => V_b = V_c ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_add__right__imp__eq,axiom, % 154.47/154.43 ! [V_c,V_a,V_b,T_a] : % 154.47/154.43 ( class_Groups_Ocancel__semigroup__add(T_a) % 154.47/154.43 => ( 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) % 154.47/154.43 => V_b = V_c ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_diff__eq__diff__eq,axiom, % 154.47/154.43 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 154.47/154.43 ( class_Groups_Oab__group__add(T_a) % 154.47/154.43 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2) % 154.47/154.43 => ( V_a_2 = V_b_2 % 154.47/154.43 <=> V_c_2 = V_d_2 ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_fun__left__comm_Ofold__fun__comm,axiom, % 154.47/154.43 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 154.47/154.43 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_sup__Sup__fold__sup,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_a] : % 154.47/154.43 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_B_2),V_A_2) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Sup__fin__Sup,axiom, % 154.47/154.43 ! [V_A_2,T_a] : % 154.47/154.43 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_sup__SUPR__fold__sup,axiom, % 154.47/154.43 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 154.47/154.43 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),V_B_2),V_A_2) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Sup__binary,axiom, % 154.47/154.43 ! [V_b_2,V_a_2,T_a] : % 154.47/154.43 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.43 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),V_b_2) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_vimage__eq__UN,axiom, % 154.47/154.43 ! [V_B_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_Ovimage(T_a,T_b,V_f_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ). % 154.47/154.43 % 154.47/154.43 fof(fact_image__eq__UN,axiom, % 154.47/154.43 ! [V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Set_Oinsert(T_a)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__I,axiom, % 154.47/154.43 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 154.47/154.43 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Sup__insert,axiom, % 154.47/154.43 ! [V_A_2,V_a_2,T_a] : % 154.47/154.43 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.43 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Sup__singleton,axiom, % 154.47/154.43 ! [V_a_2,T_a] : % 154.47/154.43 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.43 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Sup__empty,axiom, % 154.47/154.43 ! [T_a] : % 154.47/154.43 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.43 => c_Complete__Lattice_OSup__class_OSup(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_a) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_SUP__const,axiom, % 154.47/154.43 ! [V_M_2,T_a,V_A_2,T_b] : % 154.47/154.43 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 154.47/154.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),hAPP(c_COMBK(T_b,T_a),V_M_2)) = V_M_2 ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UnionI,axiom, % 154.47/154.43 ! [V_A_2,V_C_2,V_X_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 154.47/154.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) % 154.47/154.43 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__insert,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,V_a_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_SUP1__iff,axiom, % 154.47/154.43 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 154.47/154.43 <=> ? [B_x] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.47/154.43 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Union__image__eq,axiom, % 154.47/154.43 ! [V_A_2,V_B_2,T_b,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UNION__eq__Union__image,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Union__def,axiom, % 154.47/154.43 ! [V_S_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_a,tc_HOL_Obool))) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__extend__simps_I8_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__extend__simps_I9_J,axiom, % 154.47/154.43 ! [V_C_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__simps_I8_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_ball__UN,axiom, % 154.47/154.43 ! [V_P_2,V_B_2,V_A_2,T_b,T_a] : % 154.47/154.43 ( ! [B_x] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.47/154.43 => hBOOL(hAPP(V_P_2,B_x)) ) % 154.47/154.43 <=> ! [B_x] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 154.47/154.43 => ! [B_xa] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(V_B_2,B_x))) % 154.47/154.43 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__simps_I9_J,axiom, % 154.47/154.43 ! [V_C_2,V_B_2,V_A_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__UN__flatten,axiom, % 154.47/154.43 ! [V_C_2,V_B_2,V_A_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_SUP2__iff,axiom, % 154.47/154.43 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 154.47/154.43 <=> ? [B_x] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.47/154.43 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Union__empty,axiom, % 154.47/154.43 ! [T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Union__Un__distrib,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Un__eq__Union,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))))) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Union__insert,axiom, % 154.47/154.43 ! [V_B_2,V_a_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__iff,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.47/154.43 <=> ? [B_x] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 154.47/154.43 & hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UNION__empty__conv_I1_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_b,T_a] : % 154.47/154.43 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) % 154.47/154.43 <=> ! [B_x] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 154.47/154.43 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__empty2,axiom, % 154.47/154.43 ! [V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__constant,axiom, % 154.47/154.43 ! [V_c_2,T_b,T_a,V_A_2] : % 154.47/154.43 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 154.47/154.43 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_c_2)) = V_c_2 ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UNION__empty__conv_I2_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_a,T_b] : % 154.47/154.43 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 <=> ! [B_x] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 154.47/154.43 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__extend__simps_I10_J,axiom, % 154.47/154.43 ! [V_f_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2) ). % 154.47/154.43 % 154.47/154.43 fof(fact_image__UN,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_c,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Oimage(T_b,T_a,V_f_2)),V_B_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__simps_I10_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),V_B_2),V_f_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_image__Union,axiom, % 154.47/154.43 ! [V_S_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_b,T_a,V_f_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__Un__distrib,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,V_I_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_B_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__Un,axiom, % 154.47/154.43 ! [V_M_2,V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_M_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Un__Union__image,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2))) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Int__UN__distrib2,axiom, % 154.47/154.43 ! [V_B_2,V_J_2,T_c,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2))),V_B_2))) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__extend__simps_I4_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,V_C_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Int__UN__distrib,axiom, % 154.47/154.43 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),V_A_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__extend__simps_I5_J,axiom, % 154.47/154.43 ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__simps_I4_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__simps_I5_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Int__Union2,axiom, % 154.47/154.43 ! [V_A_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Int__Union,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_SUPR__apply,axiom, % 154.47/154.43 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] : % 154.47/154.43 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.43 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,T_a)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_f_2),V_x_2)) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_SUP__commute,axiom, % 154.47/154.43 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] : % 154.47/154.43 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.43 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),T_a,T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_a),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_a),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),T_a,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2))) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__extend__simps_I6_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,V_C_2,T_b,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__simps_I6_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 154.47/154.43 % 154.47/154.43 fof(fact_vimage__UN,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_c,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Ovimage(T_a,T_b,V_f_2)),V_B_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_vimage__Union,axiom, % 154.47/154.43 ! [V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_a,T_b,V_f_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Union__disjoint,axiom, % 154.47/154.43 ! [V_A_2,V_C_2,T_a] : % 154.47/154.43 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 <=> ! [B_x] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_C_2)) % 154.47/154.43 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__insert__distrib,axiom, % 154.47/154.43 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2)) % 154.47/154.43 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__absorb,axiom, % 154.47/154.43 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2)) % 154.47/154.43 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__simps_I1_J,axiom, % 154.47/154.43 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] : % 154.47/154.43 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 154.47/154.43 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__singleton,axiom, % 154.47/154.43 ! [V_A_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_A_2 ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__extend__simps_I1_J,axiom, % 154.47/154.43 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] : % 154.47/154.43 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) % 154.47/154.43 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__simps_I3_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 154.47/154.43 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 154.47/154.43 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__simps_I2_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 154.47/154.43 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 154.47/154.43 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__extend__simps_I3_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 154.47/154.43 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 154.47/154.43 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__extend__simps_I2_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 154.47/154.43 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) % 154.47/154.43 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_finite__Union,axiom, % 154.47/154.43 ! [V_A_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) % 154.47/154.43 => ( ! [B_M] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_M),V_A_2)) % 154.47/154.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_M)) ) % 154.47/154.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_diff__cancel2,axiom, % 154.47/154.43 ! [V_n,V_k,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ). % 154.47/154.43 % 154.47/154.43 fof(fact_diff__cancel,axiom, % 154.47/154.43 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ). % 154.47/154.43 % 154.47/154.43 fof(fact_diff__diff__left,axiom, % 154.47/154.43 ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_diff__add__inverse,axiom, % 154.47/154.43 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_n) = V_m ). % 154.47/154.43 % 154.47/154.43 fof(fact_diff__add__inverse2,axiom, % 154.47/154.43 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ). % 154.47/154.43 % 154.47/154.43 fof(fact_finite__UN__I,axiom, % 154.47/154.43 ! [V_B_2,T_b,V_A_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => ( ! [B_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 154.47/154.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) ) % 154.47/154.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_insert__partition,axiom, % 154.47/154.43 ! [V_F_2,V_x_2,T_a] : % 154.47/154.43 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2)) % 154.47/154.43 => ( ! [B_x] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2))) % 154.47/154.43 => ! [B_xa] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2))) % 154.47/154.43 => ( B_x != B_xa % 154.47/154.43 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_x),B_xa) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) % 154.47/154.43 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_inf__INFI__fold__inf,axiom, % 154.47/154.43 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 154.47/154.43 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),V_B_2),V_A_2) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UnionE,axiom, % 154.47/154.43 ! [V_C_2,V_A_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))) % 154.47/154.43 => ~ ! [B_X] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) % 154.47/154.43 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INF1__D,axiom, % 154.47/154.43 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 154.47/154.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.43 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INF1__E,axiom, % 154.47/154.43 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 154.47/154.43 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 154.47/154.43 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__D,axiom, % 154.47/154.43 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.47/154.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 154.47/154.43 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__E,axiom, % 154.47/154.43 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.47/154.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) % 154.47/154.43 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INF2__D,axiom, % 154.47/154.43 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 154.47/154.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.43 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INF2__E,axiom, % 154.47/154.43 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 154.47/154.43 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) % 154.47/154.43 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_finite__INT,axiom, % 154.47/154.43 ! [V_A_2,T_b,V_I_2,T_a] : % 154.47/154.43 ( ? [B_x] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_I_2)) % 154.47/154.43 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_A_2,B_x))) ) % 154.47/154.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INFI__apply,axiom, % 154.47/154.43 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] : % 154.47/154.43 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.43 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,T_a)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_f_2),V_x_2)) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__simps_I8_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__extend__simps_I8_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INF__commute,axiom, % 154.47/154.43 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] : % 154.47/154.43 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.43 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),T_a,T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_a),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_a),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),T_a,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2))) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__iff,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.47/154.43 <=> ! [B_x] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 154.47/154.43 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__extend__simps_I5_J,axiom, % 154.47/154.43 ! [V_B_2,V_C_2,T_b,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_a),V_a_2)),V_B_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__simps_I5_J,axiom, % 154.47/154.43 ! [V_B_2,V_a_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_a),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__simps_I10_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),V_B_2),V_f_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__extend__simps_I10_J,axiom, % 154.47/154.43 ! [V_f_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Un__INT__distrib2,axiom, % 154.47/154.43 ! [V_B_2,V_J_2,T_c,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2))),V_B_2))) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__extend__simps_I6_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,V_C_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Un__INT__distrib,axiom, % 154.47/154.43 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),V_A_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__extend__simps_I7_J,axiom, % 154.47/154.43 ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__simps_I6_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__simps_I7_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__Int__distrib,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,V_I_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_B_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__simps_I9_J,axiom, % 154.47/154.43 ! [V_C_2,V_B_2,V_A_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__extend__simps_I9_J,axiom, % 154.47/154.43 ! [V_C_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ). % 154.47/154.43 % 154.47/154.43 fof(fact_vimage__INT,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_c,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Ovimage(T_a,T_b,V_f_2)),V_B_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__insert__distrib,axiom, % 154.47/154.43 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2)) % 154.47/154.43 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__absorb,axiom, % 154.47/154.43 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2)) % 154.47/154.43 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INF__const,axiom, % 154.47/154.43 ! [V_M_2,T_a,V_A_2,T_b] : % 154.47/154.43 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 154.47/154.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),hAPP(c_COMBK(T_b,T_a),V_M_2)) = V_M_2 ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__extend__simps_I1_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 154.47/154.43 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) % 154.47/154.43 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__extend__simps_I2_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 154.47/154.43 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 154.47/154.43 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__insert,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,V_a_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__Un,axiom, % 154.47/154.43 ! [V_M_2,V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_M_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__extend__simps_I7_J,axiom, % 154.47/154.43 ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UN__simps_I7_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__extend__simps_I4_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 154.47/154.43 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 154.47/154.43 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_nat__add__right__cancel,axiom, % 154.47/154.43 ! [V_n_2,V_k_2,V_m_2] : % 154.47/154.43 ( 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) % 154.47/154.43 <=> V_m_2 = V_n_2 ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_nat__add__left__cancel,axiom, % 154.47/154.43 ! [V_n_2,V_m_2,V_k_2] : % 154.47/154.43 ( 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) % 154.47/154.43 <=> V_m_2 = V_n_2 ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_nat__add__assoc,axiom, % 154.47/154.43 ! [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)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_nat__add__left__commute,axiom, % 154.47/154.43 ! [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)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_nat__add__commute,axiom, % 154.47/154.43 ! [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) ). % 154.47/154.43 % 154.47/154.43 fof(fact_diff__commute,axiom, % 154.47/154.43 ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_k)),V_j) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INFI__fold__inf,axiom, % 154.47/154.43 ! [V_f_2,V_A_2,T_a,T_b] : % 154.47/154.43 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),c_Orderings_Otop__class_Otop(T_b)),V_A_2) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_finite__induct,axiom, % 154.47/154.43 ! [V_P_2,V_F_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 154.47/154.43 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 154.47/154.43 => ( ! [B_x,B_F] : % 154.47/154.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F)) % 154.47/154.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_F)) % 154.47/154.43 => ( hBOOL(hAPP(V_P_2,B_F)) % 154.47/154.43 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_x),B_F))) ) ) ) % 154.47/154.43 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_fold__graph_H_Ointros_I2_J,axiom, % 154.47/154.43 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.43 => ( c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_y_2) % 154.47/154.43 => c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_K__record__comp,axiom, % 154.47/154.43 ! [V_x_2,V_f_2,V_c_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,hAPP(c_COMBK(T_a,T_b),V_c_2)),V_f_2),V_x_2) = V_c_2 ). % 154.47/154.43 % 154.47/154.43 fof(fact_Diff1__fold__graph,axiom, % 154.47/154.43 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 154.47/154.43 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_y_2)) % 154.47/154.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.43 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_SUP2__E,axiom, % 154.47/154.43 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 154.47/154.43 => ~ ! [B_x] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.47/154.43 => ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_card__Un__disjoint,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.43 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_setsum__restrict__set,axiom, % 154.47/154.43 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] : % 154.47/154.43 ( class_Groups_Ocomm__monoid__add(T_b) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(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,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Inf__fin__Inf,axiom, % 154.47/154.43 ! [V_A_2,T_a] : % 154.47/154.43 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UNIV__I,axiom, % 154.47/154.43 ! [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)))) ). % 154.47/154.43 % 154.47/154.43 fof(fact_finite__Inter,axiom, % 154.47/154.43 ! [V_M_2,T_a] : % 154.47/154.43 ( ? [B_x] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_M_2)) % 154.47/154.43 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_x)) ) % 154.47/154.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_M_2))) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_InterE,axiom, % 154.47/154.43 ! [V_X_2,V_C_2,V_A_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2))) % 154.47/154.43 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 154.47/154.43 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_InterD,axiom, % 154.47/154.43 ! [V_X_2,V_C_2,V_A_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2))) % 154.47/154.43 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 154.47/154.43 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Inter__UNIV,axiom, % 154.47/154.43 ! [T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INF1__iff,axiom, % 154.47/154.43 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 154.47/154.43 <=> ! [B_x] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.47/154.43 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_card_Oempty,axiom, % 154.47/154.43 ! [T_a] : hAPP(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) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INF2__iff,axiom, % 154.47/154.43 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 154.47/154.43 <=> ! [B_x] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.47/154.43 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_zero__reorient,axiom, % 154.47/154.43 ! [V_x_2,T_a] : % 154.47/154.43 ( class_Groups_Ozero(T_a) % 154.47/154.43 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2 % 154.47/154.43 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_top__apply,axiom, % 154.47/154.43 ! [V_x_2,T_b,T_a] : % 154.47/154.43 ( class_Orderings_Otop(T_a) % 154.47/154.43 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom, % 154.47/154.43 ! [V_A_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 154.47/154.43 => ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 154.47/154.43 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_card__infinite,axiom, % 154.47/154.43 ! [V_A_2,T_a] : % 154.47/154.43 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_finite__option__UNIV,axiom, % 154.47/154.43 ! [T_a] : % 154.47/154.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool)))) % 154.47/154.43 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_finite__Plus__UNIV__iff,axiom, % 154.47/154.43 ! [T_b,T_a] : % 154.47/154.43 ( hBOOL(hAPP(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)))) % 154.47/154.43 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 154.47/154.43 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_finite__Prod__UNIV,axiom, % 154.47/154.43 ! [T_b,T_a] : % 154.47/154.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 154.47/154.43 => hBOOL(hAPP(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)))) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_iso__tuple__UNIV__I,axiom, % 154.47/154.43 ! [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)))) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Union__UNIV,axiom, % 154.47/154.43 ! [T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INTER__UNIV__conv_I1_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_b,T_a] : % 154.47/154.43 ( c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) % 154.47/154.43 <=> ! [B_x] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 154.47/154.43 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INTER__UNIV__conv_I2_J,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_a,T_b] : % 154.47/154.43 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 <=> ! [B_x] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 154.47/154.43 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Inf__UNIV,axiom, % 154.47/154.43 ! [T_a] : % 154.47/154.43 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.43 => c_Complete__Lattice_OInf__class_OInf(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_a) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Inter__def,axiom, % 154.47/154.43 ! [V_S_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_a,tc_HOL_Obool))) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Sup__UNIV,axiom, % 154.47/154.43 ! [T_a] : % 154.47/154.43 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.43 => c_Complete__Lattice_OSup__class_OSup(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_a) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Inter__empty,axiom, % 154.47/154.43 ! [T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Inf__empty,axiom, % 154.47/154.43 ! [T_a] : % 154.47/154.43 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.43 => c_Complete__Lattice_OInf__class_OInf(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_a) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_card__eq__0__iff,axiom, % 154.47/154.43 ! [V_A_2,T_a] : % 154.47/154.43 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.47/154.43 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_fold__graph_H_Oequations_I1_J,axiom, % 154.47/154.43 ! [V_a2_2,V_a1_2,T_b,T_a] : c_Nitpick_Ofold__graph_H(T_a,T_b,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_a2_2) ). % 154.47/154.43 % 154.47/154.43 fof(fact_fold__graph_H_Ointros_I1_J,axiom, % 154.47/154.43 ! [V_z_2,V_f_2,T_b,T_a] : c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_z_2) ). % 154.47/154.43 % 154.47/154.43 fof(fact_finite__fun__UNIVD2,axiom, % 154.47/154.43 ! [T_b,T_a] : % 154.47/154.43 ( hBOOL(hAPP(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)))) % 154.47/154.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_UNIV__not__empty,axiom, % 154.47/154.43 ! [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)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_finite__UNIV,axiom, % 154.47/154.43 ! [T_a] : % 154.47/154.43 ( class_Finite__Set_Ofinite(T_a) % 154.47/154.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_add_Ocomm__neutral,axiom, % 154.47/154.43 ! [V_a,T_a] : % 154.47/154.43 ( class_Groups_Ocomm__monoid__add(T_a) % 154.47/154.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_add__0__right,axiom, % 154.47/154.43 ! [V_a,T_a] : % 154.47/154.43 ( class_Groups_Omonoid__add(T_a) % 154.47/154.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_double__zero__sym,axiom, % 154.47/154.43 ! [V_a_2,T_a] : % 154.47/154.43 ( class_Groups_Olinordered__ab__group__add(T_a) % 154.47/154.43 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) % 154.47/154.43 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_add__0,axiom, % 154.47/154.43 ! [V_a,T_a] : % 154.47/154.43 ( class_Groups_Ocomm__monoid__add(T_a) % 154.47/154.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_add__0__left,axiom, % 154.47/154.43 ! [V_a,T_a] : % 154.47/154.43 ( class_Groups_Omonoid__add(T_a) % 154.47/154.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Un__UNIV__left,axiom, % 154.47/154.43 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Un__UNIV__right,axiom, % 154.47/154.43 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_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)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Int__UNIV__left,axiom, % 154.47/154.43 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = V_B_2 ). % 154.47/154.43 % 154.47/154.43 fof(fact_Int__UNIV__right,axiom, % 154.47/154.43 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ). % 154.47/154.43 % 154.47/154.43 fof(fact_right__minus__eq,axiom, % 154.47/154.43 ! [V_b_2,V_a_2,T_a] : % 154.47/154.43 ( class_Groups_Ogroup__add(T_a) % 154.47/154.43 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) % 154.47/154.43 <=> V_a_2 = V_b_2 ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_eq__iff__diff__eq__0,axiom, % 154.47/154.43 ! [V_b_2,V_a_2,T_a] : % 154.47/154.43 ( class_Groups_Oab__group__add(T_a) % 154.47/154.43 => ( V_a_2 = V_b_2 % 154.47/154.43 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_diff__self,axiom, % 154.47/154.43 ! [V_a,T_a] : % 154.47/154.43 ( class_Groups_Ogroup__add(T_a) % 154.47/154.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_diff__0__right,axiom, % 154.47/154.43 ! [V_a,T_a] : % 154.47/154.43 ( class_Groups_Ogroup__add(T_a) % 154.47/154.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_plus__nat_Oadd__0,axiom, % 154.47/154.43 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 154.47/154.43 % 154.47/154.43 fof(fact_Nat_Oadd__0__right,axiom, % 154.47/154.43 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 154.47/154.43 % 154.47/154.43 fof(fact_add__is__0,axiom, % 154.47/154.43 ! [V_n_2,V_m_2] : % 154.47/154.43 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.47/154.43 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.47/154.43 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_add__eq__self__zero,axiom, % 154.47/154.43 ! [V_n,V_m] : % 154.47/154.43 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 154.47/154.43 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_diffs0__imp__equal,axiom, % 154.47/154.43 ! [V_n,V_m] : % 154.47/154.43 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.47/154.43 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.47/154.43 => V_m = V_n ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_diff__self__eq__0,axiom, % 154.47/154.43 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.47/154.43 % 154.47/154.43 fof(fact_minus__nat_Odiff__0,axiom, % 154.47/154.43 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 154.47/154.43 % 154.47/154.43 fof(fact_diff__0__eq__0,axiom, % 154.47/154.43 ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.47/154.43 % 154.47/154.43 fof(fact_vimage__UNIV,axiom, % 154.47/154.43 ! [V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_fold__graph_Oequations_I1_J,axiom, % 154.47/154.43 ! [V_z_2,V_f_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_z_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_fold__graph_OemptyI,axiom, % 154.47/154.43 ! [V_z_2,V_f_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_z_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_empty__fold__graphE,axiom, % 154.47/154.43 ! [V_x_2,V_z_2,V_f_2,T_b,T_a] : % 154.47/154.43 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_x_2)) % 154.47/154.43 => V_x_2 = V_z_2 ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_fold__graph__imp__finite,axiom, % 154.47/154.43 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 154.47/154.43 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2)) % 154.47/154.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INF__INT__eq,axiom, % 154.47/154.43 ! [V_x_2,V_r_2,T_b,T_a] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b))),V_r_2)),V_x_2)) % 154.47/154.43 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__constant,axiom, % 154.47/154.43 ! [V_c_2,T_b,T_a,V_A_2] : % 154.47/154.43 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 154.47/154.43 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_c_2)) = V_c_2 ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INT__empty,axiom, % 154.47/154.43 ! [V_B_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_range__composition,axiom, % 154.47/154.43 ! [V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(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))) = hAPP(c_Set_Oimage(T_c,T_a,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 154.47/154.43 % 154.47/154.43 fof(fact_setsum__0,axiom, % 154.47/154.43 ! [V_A_2,T_b,T_a] : % 154.47/154.43 ( class_Groups_Ocomm__monoid__add(T_a) % 154.47/154.43 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Ozero__class_Ozero(T_a))),V_A_2) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Un__Inter,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_fun__left__comm_Ofold__graph__determ,axiom, % 154.47/154.43 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 154.47/154.43 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2)) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 154.47/154.43 => V_y_2 = V_x_2 ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_sup__top__left,axiom, % 154.47/154.43 ! [V_x,T_a] : % 154.47/154.43 ( class_Lattices_Obounded__lattice__top(T_a) % 154.47/154.43 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = c_Orderings_Otop__class_Otop(T_a) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_sup__top__right,axiom, % 154.47/154.43 ! [V_x,T_a] : % 154.47/154.43 ( class_Lattices_Obounded__lattice__top(T_a) % 154.47/154.43 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_inf__top__left,axiom, % 154.47/154.43 ! [V_x,T_a] : % 154.47/154.43 ( class_Lattices_Obounded__lattice__top(T_a) % 154.47/154.43 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_inf__top__right,axiom, % 154.47/154.43 ! [V_x,T_a] : % 154.47/154.43 ( class_Lattices_Obounded__lattice__top(T_a) % 154.47/154.43 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_inf__eq__top__iff,axiom, % 154.47/154.43 ! [V_y_2,V_x_2,T_a] : % 154.47/154.43 ( class_Lattices_Obounded__lattice__top(T_a) % 154.47/154.43 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_a) % 154.47/154.43 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_a) % 154.47/154.43 & V_y_2 = c_Orderings_Otop__class_Otop(T_a) ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Inter__image__eq,axiom, % 154.47/154.43 ! [V_A_2,V_B_2,T_b,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 154.47/154.43 % 154.47/154.43 fof(fact_INTER__eq__Inter__image,axiom, % 154.47/154.43 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_range__eqI,axiom, % 154.47/154.43 ! [T_b,T_a,V_x_2,V_f_2,V_b_2] : % 154.47/154.43 ( V_b_2 = hAPP(V_f_2,V_x_2) % 154.47/154.43 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_rangeI,axiom, % 154.47/154.43 ! [T_b,V_x_2,V_f_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Inf__fold__inf,axiom, % 154.47/154.43 ! [V_A_2,T_a] : % 154.47/154.43 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),c_Orderings_Otop__class_Otop(T_a)),V_A_2) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_Diff__UNIV,axiom, % 154.47/154.43 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 154.47/154.43 % 154.47/154.43 fof(fact_comp__surj,axiom, % 154.47/154.43 ! [V_g_2,T_c,V_f_2,T_a,T_b] : % 154.47/154.43 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => ( hAPP(c_Set_Oimage(T_a,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) % 154.47/154.43 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_Fun_Ocomp(T_a,T_c,T_b,V_g_2),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_setsum__empty,axiom, % 154.47/154.43 ! [V_f_2,T_b,T_a] : % 154.47/154.43 ( class_Groups_Ocomm__monoid__add(T_a) % 154.47/154.43 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_setsum_Oempty,axiom, % 154.47/154.43 ! [V_g_2,T_b,T_a] : % 154.47/154.43 ( class_Groups_Ocomm__monoid__add(T_a) % 154.47/154.43 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_setsum_Oinfinite,axiom, % 154.47/154.43 ! [V_g_2,V_A_2,T_a,T_b] : % 154.47/154.43 ( class_Groups_Ocomm__monoid__add(T_b) % 154.47/154.43 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_setsum__infinite,axiom, % 154.47/154.43 ! [V_f_2,V_A_2,T_a,T_b] : % 154.47/154.43 ( class_Groups_Ocomm__monoid__add(T_b) % 154.47/154.43 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.43 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_surj__image__vimage__eq,axiom, % 154.47/154.43 ! [V_A_2,V_f_2,T_a,T_b] : % 154.47/154.43 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.43 => hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)) = V_A_2 ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_diff__add__0,axiom, % 154.47/154.43 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.47/154.43 % 154.47/154.43 fof(fact_fold__graph_OinsertI,axiom, % 154.47/154.43 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 154.47/154.43 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.43 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 154.47/154.43 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_setsum__eq__0__iff,axiom, % 154.47/154.43 ! [V_f_2,V_F_2,T_a] : % 154.47/154.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 154.47/154.43 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.47/154.43 <=> ! [B_x] : % 154.47/154.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2)) % 154.47/154.43 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 154.47/154.43 % 154.47/154.43 fof(fact_SUP__UN__eq,axiom, % 154.47/154.43 ! [V_x_2,V_r_2,T_b,T_a] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b))),V_r_2)),V_x_2)) % 154.47/154.44 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_finite__range__imageI,axiom, % 154.47/154.44 ! [V_f_2,T_c,V_g_2,T_b,T_a] : % 154.47/154.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) % 154.47/154.44 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,hAPP(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))))) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_INT__simps_I2_J,axiom, % 154.47/154.44 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 154.47/154.44 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.44 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 154.47/154.44 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.44 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_INT__simps_I1_J,axiom, % 154.47/154.44 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 154.47/154.44 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.44 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 154.47/154.44 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.44 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_INT__simps_I3_J,axiom, % 154.47/154.44 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 154.47/154.44 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.44 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 154.47/154.44 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.44 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_INT__extend__simps_I3_J,axiom, % 154.47/154.44 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 154.47/154.44 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.44 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) ) % 154.47/154.44 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.44 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Inter__insert,axiom, % 154.47/154.44 ! [V_B_2,V_a_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Inter__Un__distrib,axiom, % 154.47/154.44 ! [V_B_2,V_A_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ). % 154.47/154.44 % 154.47/154.44 fof(fact_fun__left__comm_Ofold__equality,axiom, % 154.47/154.44 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 154.47/154.44 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 154.47/154.44 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 154.47/154.44 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Int__Inter__image,axiom, % 154.47/154.44 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2))) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Inf__singleton,axiom, % 154.47/154.44 ! [V_a_2,T_a] : % 154.47/154.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.44 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Inf__insert,axiom, % 154.47/154.44 ! [V_A_2,V_a_2,T_a] : % 154.47/154.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.44 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_finite__vimageD,axiom, % 154.47/154.44 ! [V_F_2,V_h_2,T_b,T_a] : % 154.47/154.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Ovimage(T_a,T_b,V_h_2),V_F_2))) % 154.47/154.44 => ( hAPP(c_Set_Oimage(T_a,T_b,V_h_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 154.47/154.44 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_fold__def,axiom, % 154.47/154.44 ! [V_A_2,V_z_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_a,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_a,c_Finite__Set_Ofold__graph(T_b,T_a,V_f_2,V_z_2,V_A_2)) ). % 154.47/154.44 % 154.47/154.44 fof(fact_image__vimage__eq,axiom, % 154.47/154.44 ! [V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 154.47/154.44 % 154.47/154.44 fof(fact_o__eq__dest__lhs,axiom, % 154.47/154.44 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_a,T_b,T_c] : % 154.47/154.44 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = V_c_2 % 154.47/154.44 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_INT__simps_I4_J,axiom, % 154.47/154.44 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 154.47/154.44 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.44 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 154.47/154.44 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.44 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_vimage__const,axiom, % 154.47/154.44 ! [T_b,V_A_2,V_c_2,T_a] : % 154.47/154.44 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 154.47/154.44 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(c_COMBK(T_a,T_b),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 154.47/154.44 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 154.47/154.44 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(c_COMBK(T_a,T_b),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_setsum__delta,axiom, % 154.47/154.44 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 154.47/154.44 ( class_Groups_Ocomm__monoid__add(T_b) % 154.47/154.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 154.47/154.44 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 154.47/154.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(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_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 154.47/154.44 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 154.47/154.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(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_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_setsum__delta_H,axiom, % 154.47/154.44 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 154.47/154.44 ( class_Groups_Ocomm__monoid__add(T_b) % 154.47/154.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 154.47/154.44 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 154.47/154.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(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_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 154.47/154.44 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 154.47/154.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(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_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_card_Ounion__inter,axiom, % 154.47/154.44 ! [V_B_2,V_A_2,T_a] : % 154.47/154.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.44 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_card__Un__Int,axiom, % 154.47/154.44 ! [V_B_2,V_A_2,T_a] : % 154.47/154.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.44 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_card__Diff__subset__Int,axiom, % 154.47/154.44 ! [V_B_2,V_A_2,T_a] : % 154.47/154.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.47/154.44 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Int__eq__Inter,axiom, % 154.47/154.44 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))))) ). % 154.47/154.44 % 154.47/154.44 fof(fact_fun__left__comm_Ofold__graph__fold,axiom, % 154.47/154.44 ! [V_z_2,V_A_2,V_f_2,T_b,T_a] : % 154.47/154.44 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 154.47/154.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2))) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Inf__binary,axiom, % 154.47/154.44 ! [V_b_2,V_a_2,T_a] : % 154.47/154.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.44 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),V_b_2) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_setsum_OF__eq,axiom, % 154.47/154.44 ! [V_g_2,V_A_2,T_a,T_b] : % 154.47/154.44 ( class_Groups_Ocomm__monoid__add(T_b) % 154.47/154.44 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Oplus__class_Oplus(T_b)),V_g_2),c_Groups_Ozero__class_Ozero(T_b)),V_A_2) ) % 154.47/154.44 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_setsum_Oeq__fold,axiom, % 154.47/154.44 ! [V_g_2,V_A_2,T_a,T_b] : % 154.47/154.44 ( class_Groups_Ocomm__monoid__add(T_b) % 154.47/154.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Oplus__class_Oplus(T_b)),V_g_2),c_Groups_Ozero__class_Ozero(T_b)),V_A_2) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_inf__Inf__fold__inf,axiom, % 154.47/154.44 ! [V_B_2,V_A_2,T_a] : % 154.47/154.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_B_2),V_A_2) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_triple_Osize_I1_J,axiom, % 154.47/154.44 ! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_a] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_a,V_fa_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.47/154.44 % 154.47/154.44 fof(fact_fold1Set_Ointros,axiom, % 154.47/154.44 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_a] : % 154.47/154.44 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,V_a_2,V_A_2),V_x_2)) % 154.47/154.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.44 => hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),V_x_2)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom, % 154.47/154.44 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 154.47/154.44 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 154.47/154.44 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.44 => ? [B_y_H] : % 154.47/154.44 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) % 154.47/154.44 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),B_y_H)) ) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_setsum_Ounion__inter__neutral,axiom, % 154.47/154.44 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 154.47/154.44 ( class_Groups_Ocomm__monoid__add(T_b) % 154.47/154.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.44 => ( ! [B_x] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.47/154.44 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 154.47/154.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_setsum__Un__zero,axiom, % 154.47/154.44 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 154.47/154.44 ( class_Groups_Ocomm__monoid__add(T_b) % 154.47/154.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 154.47/154.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 154.47/154.44 => ( ! [B_x] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))) % 154.47/154.44 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 154.47/154.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_T_2)) ) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_setsum__reindex__nonzero,axiom, % 154.47/154.44 ! [T_b,V_h_2,V_f_2,V_S_2,T_a,T_c] : % 154.47/154.44 ( class_Groups_Ocomm__monoid__add(T_c) % 154.47/154.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 154.47/154.44 => ( ! [B_x] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 154.47/154.44 => ! [B_y] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_S_2)) % 154.47/154.44 => ( B_x != B_y % 154.47/154.44 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 154.47/154.44 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) % 154.47/154.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)),V_S_2) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_card__Diff__singleton,axiom, % 154.47/154.44 ! [V_x_2,V_A_2,T_a] : % 154.47/154.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.44 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_card__Diff__singleton__if,axiom, % 154.47/154.44 ! [V_x_2,V_A_2,T_a] : % 154.47/154.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.44 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) % 154.47/154.44 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.44 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_card_Oremove,axiom, % 154.47/154.44 ! [V_x_2,V_A_2,T_a] : % 154.47/154.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.44 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_top1I,axiom, % 154.47/154.44 ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ). % 154.47/154.44 % 154.47/154.44 fof(fact_bot__nat__def,axiom, % 154.47/154.44 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.47/154.44 % 154.47/154.44 fof(fact_card__UNIV__unit,axiom, % 154.47/154.44 hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 154.47/154.44 % 154.47/154.44 fof(fact_one__reorient,axiom, % 154.47/154.44 ! [V_x_2,T_a] : % 154.47/154.44 ( class_Groups_Oone(T_a) % 154.47/154.44 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2 % 154.47/154.44 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_fold1Set__nonempty,axiom, % 154.47/154.44 ! [V_x_2,V_A_2,V_f_2,T_a] : % 154.47/154.44 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2),V_x_2)) % 154.47/154.44 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_empty__fold1SetE,axiom, % 154.47/154.44 ! [V_x_2,V_f_2,T_a] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_x_2)) ). % 154.47/154.44 % 154.47/154.44 fof(fact_setsum__eq__1__iff,axiom, % 154.47/154.44 ! [V_f_2,V_A_2,T_a] : % 154.47/154.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 154.47/154.44 <=> ? [B_x] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.47/154.44 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 154.47/154.44 & ! [B_xa] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 154.47/154.44 => ( B_x != B_xa % 154.47/154.44 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_card__eq__setsum,axiom, % 154.47/154.44 ! [V_A_2,T_a] : hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2) ). % 154.47/154.44 % 154.47/154.44 fof(fact_card__def,axiom, % 154.47/154.44 ! [V_A_2,T_a] : % 154.47/154.44 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) % 154.47/154.44 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_card_Oeq__fold__g,axiom, % 154.47/154.44 ! [V_A_2,T_a] : % 154.47/154.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_fold1Set__sing,axiom, % 154.47/154.44 ! [V_b_2,V_a_2,V_f_2,T_a] : % 154.47/154.44 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_b_2)) % 154.47/154.44 <=> V_a_2 = V_b_2 ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_card_Oinsert,axiom, % 154.47/154.44 ! [V_x_2,V_A_2,T_a] : % 154.47/154.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.44 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_card__Diff__insert,axiom, % 154.47/154.44 ! [V_B_2,V_a_2,V_A_2,T_a] : % 154.47/154.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 154.47/154.44 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_card_Oinsert__remove,axiom, % 154.47/154.44 ! [V_x_2,V_A_2,T_a] : % 154.47/154.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_triple_Osize_I2_J,axiom, % 154.47/154.44 ! [V_fun2_2,V_com_2,V_fun1_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.47/154.44 % 154.47/154.44 fof(fact_card_Ounion__inter__neutral,axiom, % 154.47/154.44 ! [V_B_2,V_A_2,T_a] : % 154.47/154.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.44 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.47/154.44 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 154.47/154.44 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_fold__graph_H_Oequations_I2_J,axiom, % 154.47/154.44 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a] : % 154.47/154.44 ( c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)) % 154.47/154.44 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.44 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 ) % 154.47/154.44 | ? [B_x,B_y] : % 154.47/154.44 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) % 154.47/154.44 & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a2_2)) % 154.47/154.44 & c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),B_y) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_zero__neq__one,axiom, % 154.47/154.44 ! [T_a] : % 154.47/154.44 ( class_Rings_Ozero__neq__one(T_a) % 154.47/154.44 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_one__neq__zero,axiom, % 154.47/154.44 ! [T_a] : % 154.47/154.44 ( class_Rings_Ozero__neq__one(T_a) % 154.47/154.44 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 154.47/154.44 ! [V_a,T_a] : % 154.47/154.44 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 154.47/154.44 ! [V_a,T_a] : % 154.47/154.44 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_add__0__iff,axiom, % 154.47/154.44 ! [V_a_2,V_b_2,T_a] : % 154.47/154.44 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 154.47/154.44 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) % 154.47/154.44 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_double__eq__0__iff,axiom, % 154.47/154.44 ! [V_a_2,T_a] : % 154.47/154.44 ( class_Groups_Olinordered__ab__group__add(T_a) % 154.47/154.44 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 154.47/154.44 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 154.47/154.44 ! [V_d,V_c,V_b,V_a,T_a] : % 154.47/154.44 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.44 => 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)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 154.47/154.44 ! [V_c,V_b,V_a,T_a] : % 154.47/154.44 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.44 => 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) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 154.47/154.44 ! [V_c,V_b,V_a,T_a] : % 154.47/154.44 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.44 => 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)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 154.47/154.44 ! [V_d,V_c,V_a,T_a] : % 154.47/154.44 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.44 => 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) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 154.47/154.44 ! [V_d,V_c,V_a,T_a] : % 154.47/154.44 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.44 => 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)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 154.47/154.44 ! [V_c,V_a,T_a] : % 154.47/154.44 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.44 => 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) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_card__Plus__conv__if,axiom, % 154.47/154.44 ! [V_B_2,T_b,V_A_2,T_a] : % 154.47/154.44 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) % 154.47/154.44 => hAPP(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),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) % 154.47/154.44 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) % 154.47/154.44 => hAPP(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) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_fold__Un__disjoint,axiom, % 154.47/154.44 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 154.47/154.44 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.47/154.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.44 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.44 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_B_2)) ) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_card__Diff2__less,axiom, % 154.47/154.44 ! [V_y_2,V_x_2,V_A_2,T_a] : % 154.47/154.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_card__Diff1__less,axiom, % 154.47/154.44 ! [V_x_2,V_A_2,T_a] : % 154.47/154.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_card__Suc__Diff1,axiom, % 154.47/154.44 ! [V_x_2,V_A_2,T_a] : % 154.47/154.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.44 => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Body__triple__valid__0,axiom, % 154.47/154.44 ! [V_Q_2,V_pn_2,V_P_2,T_a] : c_Hoare__Mirabelle_Otriple__valid(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ). % 154.47/154.44 % 154.47/154.44 fof(fact_insert__fold1SetE,axiom, % 154.47/154.44 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_a] : % 154.47/154.44 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2)),V_x_2)) % 154.47/154.44 => ~ ! [B_a,B_A] : % 154.47/154.44 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) % 154.47/154.44 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_x_2)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_fold1Set_Oequations,axiom, % 154.47/154.44 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_a] : % 154.47/154.44 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2)),V_a3_2)) % 154.47/154.44 <=> ? [B_a,B_A] : % 154.47/154.44 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) % 154.47/154.44 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_a3_2)) % 154.47/154.44 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Ints__odd__nonzero,axiom, % 154.47/154.44 ! [V_a_2,T_a] : % 154.47/154.44 ( class_Int_Oring__char__0(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 154.47/154.44 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__zeroE,axiom, % 154.47/154.44 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Suc__mono,axiom, % 154.47/154.44 ! [V_n,V_m] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_lessI,axiom, % 154.47/154.44 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ). % 154.47/154.44 % 154.47/154.44 fof(fact_zero__less__Suc,axiom, % 154.47/154.44 ! [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))) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__strict__left__mono__neg,axiom, % 154.47/154.44 ! [V_c,V_a,V_b,T_a] : % 154.47/154.44 ( class_Rings_Olinordered__ring__strict(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__strict__right__mono__neg,axiom, % 154.47/154.44 ! [V_c,V_a,V_b,T_a] : % 154.47/154.44 ( class_Rings_Olinordered__ring__strict(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__mult__strict__left__mono,axiom, % 154.47/154.44 ! [V_c,V_b,V_a,T_a] : % 154.47/154.44 ( class_Rings_Olinordered__comm__semiring__strict(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__strict__left__mono,axiom, % 154.47/154.44 ! [V_c,V_b,V_a,T_a] : % 154.47/154.44 ( class_Rings_Olinordered__semiring__strict(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__strict__right__mono,axiom, % 154.47/154.44 ! [V_c,V_b,V_a,T_a] : % 154.47/154.44 ( class_Rings_Olinordered__semiring__strict(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__neg__neg,axiom, % 154.47/154.44 ! [V_b,V_a,T_a] : % 154.47/154.44 ( class_Rings_Olinordered__ring__strict(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__neg__pos,axiom, % 154.47/154.44 ! [V_b,V_a,T_a] : % 154.47/154.44 ( class_Rings_Olinordered__semiring__strict(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__less__cancel__left__neg,axiom, % 154.47/154.44 ! [V_b_2,V_a_2,V_c_2,T_a] : % 154.47/154.44 ( class_Rings_Olinordered__ring__strict(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) % 154.47/154.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_zero__less__mult__pos2,axiom, % 154.47/154.44 ! [V_a,V_b,T_a] : % 154.47/154.44 ( class_Rings_Olinordered__semiring__strict(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_zero__less__mult__pos,axiom, % 154.47/154.44 ! [V_b,V_a,T_a] : % 154.47/154.44 ( class_Rings_Olinordered__semiring__strict(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__pos__neg2,axiom, % 154.47/154.44 ! [V_b,V_a,T_a] : % 154.47/154.44 ( class_Rings_Olinordered__semiring__strict(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__pos__neg,axiom, % 154.47/154.44 ! [V_b,V_a,T_a] : % 154.47/154.44 ( class_Rings_Olinordered__semiring__strict(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__pos__pos,axiom, % 154.47/154.44 ! [V_b,V_a,T_a] : % 154.47/154.44 ( class_Rings_Olinordered__semiring__strict(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__less__cancel__left__pos,axiom, % 154.47/154.44 ! [V_b_2,V_a_2,V_c_2,T_a] : % 154.47/154.44 ( class_Rings_Olinordered__ring__strict(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) % 154.47/154.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__less__cancel__left__disj,axiom, % 154.47/154.44 ! [V_b_2,V_a_2,V_c_2,T_a] : % 154.47/154.44 ( class_Rings_Olinordered__ring__strict(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) % 154.47/154.44 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 154.47/154.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) % 154.47/154.44 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__less__cancel__right__disj,axiom, % 154.47/154.44 ! [V_b_2,V_c_2,V_a_2,T_a] : % 154.47/154.44 ( class_Rings_Olinordered__ring__strict(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))) % 154.47/154.44 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 154.47/154.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) % 154.47/154.44 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_not__square__less__zero,axiom, % 154.47/154.44 ! [V_a,T_a] : % 154.47/154.44 ( class_Rings_Olinordered__ring(T_a) % 154.47/154.44 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__1__mult,axiom, % 154.47/154.44 ! [V_n,V_m,T_a] : % 154.47/154.44 ( class_Rings_Olinordered__semidom(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_linorder__neqE__linordered__idom,axiom, % 154.47/154.44 ! [V_y,V_x,T_a] : % 154.47/154.44 ( class_Rings_Olinordered__idom(T_a) % 154.47/154.44 => ( V_x != V_y % 154.47/154.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom, % 154.47/154.44 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 154.47/154.44 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom, % 154.47/154.44 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 154.47/154.44 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom, % 154.47/154.44 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 154.47/154.44 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom, % 154.47/154.44 ! [V_rx,V_ly,V_lx,T_a] : % 154.47/154.44 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom, % 154.47/154.44 ! [V_rx,V_ly,V_lx,T_a] : % 154.47/154.44 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom, % 154.47/154.44 ! [V_ry,V_rx,V_lx,T_a] : % 154.47/154.44 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom, % 154.47/154.44 ! [V_ry,V_rx,V_lx,T_a] : % 154.47/154.44 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom, % 154.47/154.44 ! [V_b,V_a,T_a] : % 154.47/154.44 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Ints__mult,axiom, % 154.47/154.44 ! [V_b_2,V_a_2,T_a] : % 154.47/154.44 ( class_Rings_Oring__1(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_triple__valid__Suc,axiom, % 154.47/154.44 ! [V_t,V_n,T_a] : % 154.47/154.44 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t) % 154.47/154.44 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_linorder__cases,axiom, % 154.47/154.44 ! [V_y,V_x,T_a] : % 154.47/154.44 ( class_Orderings_Olinorder(T_a) % 154.47/154.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 154.47/154.44 => ( V_x != V_y % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_order__less__asym,axiom, % 154.47/154.44 ! [V_y,V_x,T_a] : % 154.47/154.44 ( class_Orderings_Opreorder(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 154.47/154.44 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_xt1_I10_J,axiom, % 154.47/154.44 ! [V_z,V_x,V_y,T_a] : % 154.47/154.44 ( class_Orderings_Oorder(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_order__less__trans,axiom, % 154.47/154.44 ! [V_z,V_y,V_x,T_a] : % 154.47/154.44 ( class_Orderings_Opreorder(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_xt1_I2_J,axiom, % 154.47/154.44 ! [V_c,V_a,V_b,T_a] : % 154.47/154.44 ( class_Orderings_Oorder(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 154.47/154.44 => ( V_b = V_c % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_ord__less__eq__trans,axiom, % 154.47/154.44 ! [V_c,V_b,V_a,T_a] : % 154.47/154.44 ( class_Orderings_Oord(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 154.47/154.44 => ( V_b = V_c % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_xt1_I1_J,axiom, % 154.47/154.44 ! [V_c,V_b,V_a,T_a] : % 154.47/154.44 ( class_Orderings_Oorder(T_a) % 154.47/154.44 => ( V_a = V_b % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_ord__eq__less__trans,axiom, % 154.47/154.44 ! [V_c,V_b,V_a,T_a] : % 154.47/154.44 ( class_Orderings_Oord(T_a) % 154.47/154.44 => ( V_a = V_b % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_xt1_I9_J,axiom, % 154.47/154.44 ! [V_a,V_b,T_a] : % 154.47/154.44 ( class_Orderings_Oorder(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 154.47/154.44 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_order__less__asym_H,axiom, % 154.47/154.44 ! [V_b,V_a,T_a] : % 154.47/154.44 ( class_Orderings_Opreorder(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 154.47/154.44 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_order__less__imp__not__eq2,axiom, % 154.47/154.44 ! [V_y,V_x,T_a] : % 154.47/154.44 ( class_Orderings_Oorder(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 154.47/154.44 => V_y != V_x ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_order__less__imp__not__eq,axiom, % 154.47/154.44 ! [V_y,V_x,T_a] : % 154.47/154.44 ( class_Orderings_Oorder(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 154.47/154.44 => V_x != V_y ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_order__less__imp__not__less,axiom, % 154.47/154.44 ! [V_y,V_x,T_a] : % 154.47/154.44 ( class_Orderings_Opreorder(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 154.47/154.44 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_order__less__not__sym,axiom, % 154.47/154.44 ! [V_y,V_x,T_a] : % 154.47/154.44 ( class_Orderings_Opreorder(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 154.47/154.44 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__imp__neq,axiom, % 154.47/154.44 ! [V_y,V_x,T_a] : % 154.47/154.44 ( class_Orderings_Oorder(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 154.47/154.44 => V_x != V_y ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_linorder__neqE,axiom, % 154.47/154.44 ! [V_y,V_x,T_a] : % 154.47/154.44 ( class_Orderings_Olinorder(T_a) % 154.47/154.44 => ( V_x != V_y % 154.47/154.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_linorder__antisym__conv3,axiom, % 154.47/154.44 ! [V_x_2,V_y_2,T_a] : % 154.47/154.44 ( class_Orderings_Olinorder(T_a) % 154.47/154.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 154.47/154.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 154.47/154.44 <=> V_x_2 = V_y_2 ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__left__idem,axiom, % 154.47/154.44 ! [V_b,V_a,T_a] : % 154.47/154.44 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_linorder__less__linear,axiom, % 154.47/154.44 ! [V_y,V_x,T_a] : % 154.47/154.44 ( class_Orderings_Olinorder(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 154.47/154.44 | V_x = V_y % 154.47/154.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__idem,axiom, % 154.47/154.44 ! [V_x,T_a] : % 154.47/154.44 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_times_Oidem,axiom, % 154.47/154.44 ! [V_a,T_a] : % 154.47/154.44 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_not__less__iff__gr__or__eq,axiom, % 154.47/154.44 ! [V_y_2,V_x_2,T_a] : % 154.47/154.44 ( class_Orderings_Olinorder(T_a) % 154.47/154.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 154.47/154.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 154.47/154.44 | V_x_2 = V_y_2 ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_linorder__neq__iff,axiom, % 154.47/154.44 ! [V_y_2,V_x_2,T_a] : % 154.47/154.44 ( class_Orderings_Olinorder(T_a) % 154.47/154.44 => ( V_x_2 != V_y_2 % 154.47/154.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 154.47/154.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_order__less__irrefl,axiom, % 154.47/154.44 ! [V_x,T_a] : % 154.47/154.44 ( class_Orderings_Opreorder(T_a) % 154.47/154.44 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom, % 154.47/154.44 ! [V_c,V_b,V_a,T_a] : % 154.47/154.44 ( class_Groups_Oab__semigroup__mult(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__Suc,axiom, % 154.47/154.44 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__Suc__right,axiom, % 154.47/154.44 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__iff__Suc__add,axiom, % 154.47/154.44 ! [V_n_2,V_m_2] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 154.47/154.44 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__add__Suc2,axiom, % 154.47/154.44 ! [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)))) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__add__Suc1,axiom, % 154.47/154.44 ! [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)))) ). % 154.47/154.44 % 154.47/154.44 fof(fact_nat__less__cases,axiom, % 154.47/154.44 ! [V_P_2,V_n_2,V_m_2] : % 154.47/154.44 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 154.47/154.44 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 154.47/154.44 => ( ( V_m_2 = V_n_2 % 154.47/154.44 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 154.47/154.44 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 154.47/154.44 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 154.47/154.44 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Suc__less__SucD,axiom, % 154.47/154.44 ! [V_n,V_m] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Suc__inject,axiom, % 154.47/154.44 ! [V_y,V_x] : % 154.47/154.44 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) % 154.47/154.44 => V_x = V_y ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Suc__lessD,axiom, % 154.47/154.44 ! [V_n,V_m] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__SucE,axiom, % 154.47/154.44 ! [V_n,V_m] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 154.47/154.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 154.47/154.44 => V_m = V_n ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__trans__Suc,axiom, % 154.47/154.44 ! [V_k,V_j,V_i] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Suc__lessI,axiom, % 154.47/154.44 ! [V_n,V_m] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 154.47/154.44 => ( hAPP(c_Nat_OSuc,V_m) != V_n % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__SucI,axiom, % 154.47/154.44 ! [V_n,V_m] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__not__refl3,axiom, % 154.47/154.44 ! [V_t,V_s] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) % 154.47/154.44 => V_s != V_t ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__not__refl2,axiom, % 154.47/154.44 ! [V_m,V_n] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 154.47/154.44 => V_m != V_n ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__irrefl__nat,axiom, % 154.47/154.44 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 154.47/154.44 % 154.47/154.44 fof(fact_linorder__neqE__nat,axiom, % 154.47/154.44 ! [V_y,V_x] : % 154.47/154.44 ( V_x != V_y % 154.47/154.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__antisym,axiom, % 154.47/154.44 ! [V_m,V_n] : % 154.47/154.44 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) % 154.47/154.44 => V_m = V_n ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_not__less__less__Suc__eq,axiom, % 154.47/154.44 ! [V_m_2,V_n_2] : % 154.47/154.44 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 154.47/154.44 <=> V_n_2 = V_m_2 ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Suc__mult__less__cancel1,axiom, % 154.47/154.44 ! [V_n_2,V_m_2,V_k_2] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2))) % 154.47/154.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Suc__mult__cancel1,axiom, % 154.47/154.44 ! [V_n_2,V_m_2,V_k_2] : % 154.47/154.44 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2) % 154.47/154.44 <=> V_m_2 = V_n_2 ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Suc__less__eq,axiom, % 154.47/154.44 ! [V_n_2,V_m_2] : % 154.47/154.44 ( 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))) % 154.47/154.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_nat_Oinject,axiom, % 154.47/154.44 ! [V_nat_H_2,V_nat_2] : % 154.47/154.44 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) % 154.47/154.44 <=> V_nat_2 = V_nat_H_2 ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__Suc__eq,axiom, % 154.47/154.44 ! [V_n_2,V_m_2] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 154.47/154.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 154.47/154.44 | V_m_2 = V_n_2 ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_nat__neq__iff,axiom, % 154.47/154.44 ! [V_n_2,V_m_2] : % 154.47/154.44 ( V_m_2 != V_n_2 % 154.47/154.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 154.47/154.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_not__less__eq,axiom, % 154.47/154.44 ! [V_n_2,V_m_2] : % 154.47/154.44 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 154.47/154.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Suc__n__not__n,axiom, % 154.47/154.44 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ). % 154.47/154.44 % 154.47/154.44 fof(fact_n__not__Suc__n,axiom, % 154.47/154.44 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__not__refl,axiom, % 154.47/154.44 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 154.47/154.44 % 154.47/154.44 fof(fact_diff__less__Suc,axiom, % 154.47/154.44 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(c_Nat_OSuc,V_m))) ). % 154.47/154.44 % 154.47/154.44 fof(fact_one__less__mult,axiom, % 154.47/154.44 ! [V_m,V_n] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_n__less__n__mult__m,axiom, % 154.47/154.44 ! [V_m,V_n] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m))) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_n__less__m__mult__n,axiom, % 154.47/154.44 ! [V_m,V_n] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__less__mono2,axiom, % 154.47/154.44 ! [V_k,V_j,V_i] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__less__mono1,axiom, % 154.47/154.44 ! [V_k,V_j,V_i] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__less__cancel2,axiom, % 154.47/154.44 ! [V_n_2,V_k_2,V_m_2] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) % 154.47/154.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 154.47/154.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__less__cancel1,axiom, % 154.47/154.44 ! [V_n_2,V_m_2,V_k_2] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 154.47/154.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 154.47/154.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__eq__1__iff,axiom, % 154.47/154.44 ! [V_n_2,V_m_2] : % 154.47/154.44 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 154.47/154.44 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 154.47/154.44 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__Suc__eq__0__disj,axiom, % 154.47/154.44 ! [V_n_2,V_m_2] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 154.47/154.44 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.47/154.44 | ? [B_j] : % 154.47/154.44 ( V_m_2 = hAPP(c_Nat_OSuc,B_j) % 154.47/154.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__Suc0,axiom, % 154.47/154.44 ! [V_n_2] : % 154.47/154.44 ( 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)))) % 154.47/154.44 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_nat__0__less__mult__iff,axiom, % 154.47/154.44 ! [V_n_2,V_m_2] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))) % 154.47/154.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 154.47/154.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_gr0__conv__Suc,axiom, % 154.47/154.44 ! [V_n_2] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 154.47/154.44 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__add__iff2,axiom, % 154.47/154.44 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] : % 154.47/154.44 ( class_Rings_Oordered__ring(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) % 154.47/154.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__add__iff1,axiom, % 154.47/154.44 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] : % 154.47/154.44 ( class_Rings_Oordered__ring(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) % 154.47/154.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_diff__Suc__less,axiom, % 154.47/154.44 ! [V_i,V_n] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_i))),V_n)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Suc__pred,axiom, % 154.47/154.44 ! [V_n] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 154.47/154.44 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__zero__left,axiom, % 154.47/154.44 ! [V_a,T_a] : % 154.47/154.44 ( class_Rings_Omult__zero(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom, % 154.47/154.44 ! [V_a,T_a] : % 154.47/154.44 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__zero__right,axiom, % 154.47/154.44 ! [V_a,T_a] : % 154.47/154.44 ( class_Rings_Omult__zero(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom, % 154.47/154.44 ! [V_a,T_a] : % 154.47/154.44 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__eq__0__iff,axiom, % 154.47/154.44 ! [V_b_2,V_a_2,T_a] : % 154.47/154.44 ( class_Rings_Oring__no__zero__divisors(T_a) % 154.47/154.44 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) % 154.47/154.44 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) % 154.47/154.44 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_no__zero__divisors,axiom, % 154.47/154.44 ! [V_b,V_a,T_a] : % 154.47/154.44 ( class_Rings_Ono__zero__divisors(T_a) % 154.47/154.44 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 154.47/154.44 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_divisors__zero,axiom, % 154.47/154.44 ! [V_b,V_a,T_a] : % 154.47/154.44 ( class_Rings_Ono__zero__divisors(T_a) % 154.47/154.44 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 154.47/154.44 => ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 154.47/154.44 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_crossproduct__eq,axiom, % 154.47/154.44 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] : % 154.47/154.44 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 154.47/154.44 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2)) % 154.47/154.44 <=> ( V_w_2 = V_x_2 % 154.47/154.44 | V_y_2 = V_z_2 ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_combine__common__factor,axiom, % 154.47/154.44 ! [V_c,V_b,V_e,V_a,T_a] : % 154.47/154.44 ( class_Rings_Osemiring(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom, % 154.47/154.44 ! [V_b,V_m,V_a,T_a] : % 154.47/154.44 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom, % 154.47/154.44 ! [V_c,V_b,V_a,T_a] : % 154.47/154.44 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__semiring__class_Odistrib,axiom, % 154.47/154.44 ! [V_c,V_b,V_a,T_a] : % 154.47/154.44 ( class_Rings_Ocomm__semiring(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_crossproduct__noteq,axiom, % 154.47/154.44 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 154.47/154.44 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 154.47/154.44 => ( ( V_a_2 != V_b_2 % 154.47/154.44 & V_c_2 != V_d_2 ) % 154.47/154.44 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom, % 154.47/154.44 ! [V_z,V_y,V_x,T_a] : % 154.47/154.44 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_add__less__cancel__right,axiom, % 154.47/154.44 ! [V_b_2,V_c_2,V_a_2,T_a] : % 154.47/154.44 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2))) % 154.47/154.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_add__less__cancel__left,axiom, % 154.47/154.44 ! [V_b_2,V_a_2,V_c_2,T_a] : % 154.47/154.44 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2))) % 154.47/154.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_add__strict__right__mono,axiom, % 154.47/154.44 ! [V_c,V_b,V_a,T_a] : % 154.47/154.44 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 154.47/154.44 => 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))) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_add__strict__left__mono,axiom, % 154.47/154.44 ! [V_c,V_b,V_a,T_a] : % 154.47/154.44 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 154.47/154.44 => 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))) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_add__strict__mono,axiom, % 154.47/154.44 ! [V_d,V_c,V_b,V_a,T_a] : % 154.47/154.44 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 154.47/154.44 => 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))) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_add__less__imp__less__right,axiom, % 154.47/154.44 ! [V_b,V_c,V_a,T_a] : % 154.47/154.44 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 154.47/154.44 => ( 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))) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_add__less__imp__less__left,axiom, % 154.47/154.44 ! [V_b,V_a,V_c,T_a] : % 154.47/154.44 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 154.47/154.44 => ( 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))) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Zero__not__Suc,axiom, % 154.47/154.44 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 154.47/154.44 % 154.47/154.44 fof(fact_nat_Osimps_I2_J,axiom, % 154.47/154.44 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Suc__not__Zero,axiom, % 154.47/154.44 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.47/154.44 % 154.47/154.44 fof(fact_nat_Osimps_I3_J,axiom, % 154.47/154.44 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Zero__neq__Suc,axiom, % 154.47/154.44 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Suc__neq__Zero,axiom, % 154.47/154.44 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.47/154.44 % 154.47/154.44 fof(fact_diff__eq__diff__less,axiom, % 154.47/154.44 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 154.47/154.44 ( class_Groups_Oordered__ab__group__add(T_a) % 154.47/154.44 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 154.47/154.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2)) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult_Ocomm__neutral,axiom, % 154.47/154.44 ! [V_a,T_a] : % 154.47/154.44 ( class_Groups_Ocomm__monoid__mult(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__1__right,axiom, % 154.47/154.44 ! [V_a,T_a] : % 154.47/154.44 ( class_Groups_Omonoid__mult(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__1,axiom, % 154.47/154.44 ! [V_a,T_a] : % 154.47/154.44 ( class_Groups_Ocomm__monoid__mult(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__1__left,axiom, % 154.47/154.44 ! [V_a,T_a] : % 154.47/154.44 ( class_Groups_Omonoid__mult(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom, % 154.47/154.44 ! [V_a,T_a] : % 154.47/154.44 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom, % 154.47/154.44 ! [V_a,T_a] : % 154.47/154.44 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_add__Suc__shift,axiom, % 154.47/154.44 ! [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)) ). % 154.47/154.44 % 154.47/154.44 fof(fact_add__Suc,axiom, % 154.47/154.44 ! [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)) ). % 154.47/154.44 % 154.47/154.44 fof(fact_add__Suc__right,axiom, % 154.47/154.44 ! [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)) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__supI2,axiom, % 154.47/154.44 ! [V_a,V_b,V_x,T_a] : % 154.47/154.44 ( class_Lattices_Osemilattice__sup(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__supI1,axiom, % 154.47/154.44 ! [V_b,V_a,V_x,T_a] : % 154.47/154.44 ( class_Lattices_Osemilattice__sup(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__0,axiom, % 154.47/154.44 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__0__right,axiom, % 154.47/154.44 ! [V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__is__0,axiom, % 154.47/154.44 ! [V_n_2,V_m_2] : % 154.47/154.44 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.47/154.44 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.47/154.44 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__cancel1,axiom, % 154.47/154.44 ! [V_n_2,V_m_2,V_k_2] : % 154.47/154.44 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) % 154.47/154.44 <=> ( V_m_2 = V_n_2 % 154.47/154.44 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_mult__cancel2,axiom, % 154.47/154.44 ! [V_n_2,V_k_2,V_m_2] : % 154.47/154.44 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2) % 154.47/154.44 <=> ( V_m_2 = V_n_2 % 154.47/154.44 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__infI2,axiom, % 154.47/154.44 ! [V_a,V_x,V_b,T_a] : % 154.47/154.44 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__infI1,axiom, % 154.47/154.44 ! [V_b,V_x,V_a,T_a] : % 154.47/154.44 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_not__less0,axiom, % 154.47/154.44 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 154.47/154.44 % 154.47/154.44 fof(fact_neq0__conv,axiom, % 154.47/154.44 ! [V_n_2] : % 154.47/154.44 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.47/154.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__nat__zero__code,axiom, % 154.47/154.44 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 154.47/154.44 % 154.47/154.44 fof(fact_gr__implies__not0,axiom, % 154.47/154.44 ! [V_n,V_m] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 154.47/154.44 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_gr0I,axiom, % 154.47/154.44 ! [V_n] : % 154.47/154.44 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_diff__Suc__Suc,axiom, % 154.47/154.44 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Suc__diff__diff,axiom, % 154.47/154.44 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)),hAPP(c_Nat_OSuc,V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k) ). % 154.47/154.44 % 154.47/154.44 fof(fact_add__mult__distrib,axiom, % 154.47/154.44 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ). % 154.47/154.44 % 154.47/154.44 fof(fact_add__mult__distrib2,axiom, % 154.47/154.44 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ). % 154.47/154.44 % 154.47/154.44 fof(fact_add__lessD1,axiom, % 154.47/154.44 ! [V_k,V_j,V_i] : % 154.47/154.44 ( 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)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__add__eq__less,axiom, % 154.47/154.44 ! [V_n,V_m,V_l,V_k] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 154.47/154.44 => ( 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) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_add__less__mono,axiom, % 154.47/154.44 ! [V_l,V_k,V_j,V_i] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 154.47/154.44 => 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))) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_add__less__mono1,axiom, % 154.47/154.44 ! [V_k,V_j,V_i] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 154.47/154.44 => 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))) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_trans__less__add2,axiom, % 154.47/154.44 ! [V_m,V_j,V_i] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 154.47/154.44 => 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))) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_trans__less__add1,axiom, % 154.47/154.44 ! [V_m,V_j,V_i] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 154.47/154.44 => 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))) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_nat__add__left__cancel__less,axiom, % 154.47/154.44 ! [V_n_2,V_m_2,V_k_2] : % 154.47/154.44 ( 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))) % 154.47/154.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_not__add__less2,axiom, % 154.47/154.44 ! [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)) ). % 154.47/154.44 % 154.47/154.44 fof(fact_not__add__less1,axiom, % 154.47/154.44 ! [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)) ). % 154.47/154.44 % 154.47/154.44 fof(fact_diff__mult__distrib2,axiom, % 154.47/154.44 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ). % 154.47/154.44 % 154.47/154.44 fof(fact_diff__mult__distrib,axiom, % 154.47/154.44 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__imp__diff__less,axiom, % 154.47/154.44 ! [V_n,V_k,V_j] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_n)),V_k)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_diff__less__mono2,axiom, % 154.47/154.44 ! [V_l,V_n,V_m] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l)) % 154.47/154.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_nat__mult__eq__1__iff,axiom, % 154.47/154.44 ! [V_n_2,V_m_2] : % 154.47/154.44 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 154.47/154.44 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 154.47/154.44 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_nat__mult__1__right,axiom, % 154.47/154.44 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 154.47/154.44 % 154.47/154.44 fof(fact_nat__1__eq__mult__iff,axiom, % 154.47/154.44 ! [V_n_2,V_m_2] : % 154.47/154.44 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) % 154.47/154.44 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 154.47/154.44 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_nat__mult__1,axiom, % 154.47/154.44 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__Sup__iff,axiom, % 154.47/154.44 ! [V_S_2,V_a_2,T_a] : % 154.47/154.44 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.44 & class_Orderings_Olinorder(T_a) ) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_S_2))) % 154.47/154.44 <=> ? [B_x] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 154.47/154.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),B_x)) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Inf__less__iff,axiom, % 154.47/154.44 ! [V_a_2,V_S_2,T_a] : % 154.47/154.44 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.44 & class_Orderings_Olinorder(T_a) ) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_S_2)),V_a_2)) % 154.47/154.44 <=> ? [B_x] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 154.47/154.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_a_2)) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_fun__left__comm,axiom, % 154.47/154.44 ! [T_a] : % 154.47/154.44 ( class_Groups_Oab__semigroup__mult(T_a) % 154.47/154.44 => c_Finite__Set_Ofun__left__comm(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_fun__left__comm__idem,axiom, % 154.47/154.44 ! [T_a] : % 154.47/154.44 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 154.47/154.44 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_Suc__diff__1,axiom, % 154.47/154.44 ! [V_n] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 154.47/154.44 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_setsum__product,axiom, % 154.47/154.44 ! [V_B_2,V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 154.47/154.44 ( class_Rings_Osemiring__0(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_a),tc_fun(T_c,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,T_a),tc_fun(tc_fun(T_c,T_a),tc_fun(T_c,T_a)),T_b),c_COMBB(T_a,T_a,T_c)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2))),V_g_2))),V_B_2)),V_A_2) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_setsum__left__distrib,axiom, % 154.47/154.44 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] : % 154.47/154.44 ( class_Rings_Osemiring__0(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_r_2)),V_A_2) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_setsum__right__distrib,axiom, % 154.47/154.44 ! [V_A_2,V_f_2,T_b,V_r_2,T_a] : % 154.47/154.44 ( class_Rings_Osemiring__0(T_a) % 154.47/154.44 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r_2)),V_f_2)),V_A_2) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_less__SUP__iff,axiom, % 154.47/154.44 ! [V_f_2,V_A_2,T_b,V_a_2,T_a] : % 154.47/154.44 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.44 & class_Orderings_Olinorder(T_a) ) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),V_f_2))) % 154.47/154.44 <=> ? [B_x] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 154.47/154.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_INF__less__iff,axiom, % 154.47/154.44 ! [V_a_2,V_f_2,V_A_2,T_b,T_a] : % 154.47/154.44 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.44 & class_Orderings_Olinorder(T_a) ) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),V_f_2)),V_a_2)) % 154.47/154.44 <=> ? [B_x] : % 154.47/154.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 154.47/154.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_add__scale__eq__noteq,axiom, % 154.47/154.44 ! [V_d,V_c,V_b,V_a,V_r,T_a] : % 154.47/154.44 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 154.47/154.44 => ( V_r != c_Groups_Ozero__class_Ozero(T_a) % 154.47/154.44 => ( ( V_a = V_b % 154.47/154.44 & V_c != V_d ) % 154.47/154.44 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)) ) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 154.47/154.44 ! [V_a_2,T_a] : % 154.47/154.44 ( class_Groups_Olinordered__ab__group__add(T_a) % 154.47/154.44 => ( 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_2),V_a_2))) % 154.47/154.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 154.47/154.44 ! [V_a_2,T_a] : % 154.47/154.44 ( class_Groups_Olinordered__ab__group__add(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 154.47/154.44 % 154.47/154.44 fof(fact_add__pos__pos,axiom, % 154.47/154.44 ! [V_b,V_a,T_a] : % 154.47/154.44 ( class_Groups_Oordered__comm__monoid__add(T_a) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.47/154.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 154.47/154.45 => 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))) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_add__neg__neg,axiom, % 154.47/154.45 ! [V_b,V_a,T_a] : % 154.47/154.45 ( class_Groups_Oordered__comm__monoid__add(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.45 => 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))) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_even__less__0__iff,axiom, % 154.47/154.45 ! [V_a_2,T_a] : % 154.47/154.45 ( class_Rings_Olinordered__idom(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_pos__add__strict,axiom, % 154.47/154.45 ! [V_c,V_b,V_a,T_a] : % 154.47/154.45 ( class_Rings_Olinordered__semidom(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 154.47/154.45 => 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))) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_less__iff__diff__less__0,axiom, % 154.47/154.45 ! [V_b_2,V_a_2,T_a] : % 154.47/154.45 ( class_Groups_Oordered__ab__group__add(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 154.47/154.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_eq__add__iff2,axiom, % 154.47/154.45 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] : % 154.47/154.45 ( class_Rings_Oring(T_a) % 154.47/154.45 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2) % 154.47/154.45 <=> V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_eq__add__iff1,axiom, % 154.47/154.45 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] : % 154.47/154.45 ( class_Rings_Oring(T_a) % 154.47/154.45 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2) % 154.47/154.45 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_c_2) = V_d_2 ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_zero__less__one,axiom, % 154.47/154.45 ! [T_a] : % 154.47/154.45 ( class_Rings_Olinordered__semidom(T_a) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_not__one__less__zero,axiom, % 154.47/154.45 ! [T_a] : % 154.47/154.45 ( class_Rings_Olinordered__semidom(T_a) % 154.47/154.45 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom, % 154.47/154.45 ! [V_m,T_a] : % 154.47/154.45 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_m) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom, % 154.47/154.45 ! [V_a,V_m,T_a] : % 154.47/154.45 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom, % 154.47/154.45 ! [V_m,V_a,T_a] : % 154.47/154.45 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_less__add__one,axiom, % 154.47/154.45 ! [V_a,T_a] : % 154.47/154.45 ( class_Rings_Olinordered__semidom(T_a) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_add__is__1,axiom, % 154.47/154.45 ! [V_n_2,V_m_2] : % 154.47/154.45 ( 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)) % 154.47/154.45 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 154.47/154.45 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 154.47/154.45 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.47/154.45 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_one__is__add,axiom, % 154.47/154.45 ! [V_n_2,V_m_2] : % 154.47/154.45 ( 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) % 154.47/154.45 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 154.47/154.45 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 154.47/154.45 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.47/154.45 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_One__nat__def,axiom, % 154.47/154.45 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 154.47/154.45 % 154.47/154.45 fof(fact_add__gr__0,axiom, % 154.47/154.45 ! [V_n_2,V_m_2] : % 154.47/154.45 ( 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))) % 154.47/154.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 154.47/154.45 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_zero__less__diff,axiom, % 154.47/154.45 ! [V_m_2,V_n_2] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2))) % 154.47/154.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_diff__less,axiom, % 154.47/154.45 ! [V_m,V_n] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_mult__eq__self__implies__10,axiom, % 154.47/154.45 ! [V_n,V_m] : % 154.47/154.45 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) % 154.47/154.45 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 154.47/154.45 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_diff__Suc__1,axiom, % 154.47/154.45 ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 154.47/154.45 % 154.47/154.45 fof(fact_less__diff__conv,axiom, % 154.47/154.45 ! [V_k_2,V_j_2,V_i_2] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))) % 154.47/154.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_add__diff__inverse,axiom, % 154.47/154.45 ! [V_n,V_m] : % 154.47/154.45 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 154.47/154.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Ints__odd__less__0,axiom, % 154.47/154.45 ! [V_a_2,T_a] : % 154.47/154.45 ( class_Rings_Olinordered__idom(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Ints__0,axiom, % 154.47/154.45 ! [T_a] : % 154.47/154.45 ( class_Rings_Oring__1(T_a) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Ints__add,axiom, % 154.47/154.45 ! [V_b_2,V_a_2,T_a] : % 154.47/154.45 ( class_Rings_Oring__1(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Body__triple__valid__Suc,axiom, % 154.47/154.45 ! [V_Q_2,V_pn_2,V_P_2,V_n_2,T_a] : % 154.47/154.45 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)) % 154.47/154.45 <=> c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Ints__diff,axiom, % 154.47/154.45 ! [V_b_2,V_a_2,T_a] : % 154.47/154.45 ( class_Rings_Oring__1(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Ints__1,axiom, % 154.47/154.45 ! [T_a] : % 154.47/154.45 ( class_Rings_Oring__1(T_a) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_zero__less__two,axiom, % 154.47/154.45 ! [T_a] : % 154.47/154.45 ( class_Rings_Olinordered__semidom(T_a) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_card__ge__0__finite,axiom, % 154.47/154.45 ! [V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) % 154.47/154.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_nat__diff__split,axiom, % 154.47/154.45 ! [V_b_2,V_a_2,V_P_2] : % 154.47/154.45 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 154.47/154.45 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 154.47/154.45 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 154.47/154.45 & ! [B_d] : % 154.47/154.45 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 154.47/154.45 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_nat__diff__split__asm,axiom, % 154.47/154.45 ! [V_b_2,V_a_2,V_P_2] : % 154.47/154.45 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 154.47/154.45 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 154.47/154.45 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 154.47/154.45 | ? [B_d] : % 154.47/154.45 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 154.47/154.45 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_fold__graph__insert__swap,axiom, % 154.47/154.45 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_a] : % 154.47/154.45 ( class_Groups_Oab__semigroup__mult(T_a) % 154.47/154.45 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_b_2,V_A_2),V_y_2)) % 154.47/154.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 154.47/154.45 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z_2),V_y_2))) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_setsum__eq__Suc0__iff,axiom, % 154.47/154.45 ! [V_f_2,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.45 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 154.47/154.45 <=> ? [B_x] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.47/154.45 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 154.47/154.45 & ! [B_xa] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 154.47/154.45 => ( B_x != B_xa % 154.47/154.45 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_fold__image__distrib,axiom, % 154.47/154.45 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 154.47/154.45 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.47/154.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.45 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Groups_Otimes__class_Otimes(T_b)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_b)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_h_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_card__insert__disjoint,axiom, % 154.47/154.45 ! [V_x_2,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.45 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_card__insert__if,axiom, % 154.47/154.45 ! [V_x_2,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.45 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.45 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) % 154.47/154.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.45 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_fold__image__insert,axiom, % 154.47/154.45 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_a,T_b] : % 154.47/154.45 ( class_Groups_Oab__semigroup__mult(T_b) % 154.47/154.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.45 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_a_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),V_A_2)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_card__gt__0__iff,axiom, % 154.47/154.45 ! [V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) % 154.47/154.45 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.45 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_finite__UNIV__card__ge__0,axiom, % 154.47/154.45 ! [T_a] : % 154.47/154.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Ints__double__eq__0__iff,axiom, % 154.47/154.45 ! [V_a_2,T_a] : % 154.47/154.45 ( class_Int_Oring__char__0(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 154.47/154.45 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 154.47/154.45 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_finite__Plus__iff,axiom, % 154.47/154.45 ! [V_B_2,V_A_2,T_b,T_a] : % 154.47/154.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))) % 154.47/154.45 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.45 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_finite__Plus,axiom, % 154.47/154.45 ! [V_B_2,T_b,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 154.47/154.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_finite__PlusD_I1_J,axiom, % 154.47/154.45 ! [V_B_2,V_A_2,T_b,T_a] : % 154.47/154.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))) % 154.47/154.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_finite__PlusD_I2_J,axiom, % 154.47/154.45 ! [V_B_2,V_A_2,T_b,T_a] : % 154.47/154.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))) % 154.47/154.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_card__insert,axiom, % 154.47/154.45 ! [V_x_2,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.45 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_card__Plus,axiom, % 154.47/154.45 ! [V_B_2,T_b,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 154.47/154.45 => hAPP(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),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_fold__graph__permute__diff,axiom, % 154.47/154.45 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_a] : % 154.47/154.45 ( class_Groups_Oab__semigroup__mult(T_a) % 154.47/154.45 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_b_2,V_A_2),V_x_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 154.47/154.45 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2)) ) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_fold__image__Un__Int,axiom, % 154.47/154.45 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 154.47/154.45 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.47/154.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_finite__fun__UNIVD1,axiom, % 154.47/154.45 ! [T_b,T_a] : % 154.47/154.45 ( hBOOL(hAPP(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)))) % 154.47/154.45 => ( hAPP(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)) % 154.47/154.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_add__eq__if,axiom, % 154.47/154.45 ! [V_n,V_m] : % 154.47/154.45 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.47/154.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) % 154.47/154.45 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.47/154.45 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Suc__pred_H,axiom, % 154.47/154.45 ! [V_n] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 154.47/154.45 => V_n = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_UNIV__Plus__UNIV,axiom, % 154.47/154.45 ! [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)) ). % 154.47/154.45 % 154.47/154.45 fof(fact_mult__eq__if,axiom, % 154.47/154.45 ! [V_n,V_m] : % 154.47/154.45 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.47/154.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 154.47/154.45 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.47/154.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_not__sum__squares__lt__zero,axiom, % 154.47/154.45 ! [V_y,V_x,T_a] : % 154.47/154.45 ( class_Rings_Olinordered__ring(T_a) % 154.47/154.45 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_sum__squares__gt__zero__iff,axiom, % 154.47/154.45 ! [V_y_2,V_x_2,T_a] : % 154.47/154.45 ( class_Rings_Olinordered__ring__strict(T_a) % 154.47/154.45 => ( 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))) % 154.47/154.45 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) % 154.47/154.45 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_diff__Suc__eq__diff__pred,axiom, % 154.47/154.45 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Suc__eq__plus1__left,axiom, % 154.47/154.45 ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ). % 154.47/154.45 % 154.47/154.45 fof(fact_nat__mult__assoc,axiom, % 154.47/154.45 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ). % 154.47/154.45 % 154.47/154.45 fof(fact_nat__mult__commute,axiom, % 154.47/154.45 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m) ). % 154.47/154.45 % 154.47/154.45 fof(fact_psubsetD,axiom, % 154.47/154.45 ! [V_c_2,V_B_2,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_not__psubset__empty,axiom, % 154.47/154.45 ! [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)))) ). % 154.47/154.45 % 154.47/154.45 fof(fact_psubset__card__mono,axiom, % 154.47/154.45 ! [V_A_2,V_B_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Plus__eq__empty__conv,axiom, % 154.47/154.45 ! [V_B_2,V_A_2,T_b,T_a] : % 154.47/154.45 ( 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)) % 154.47/154.45 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.45 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_sum__squares__eq__zero__iff,axiom, % 154.47/154.45 ! [V_y_2,V_x_2,T_a] : % 154.47/154.45 ( class_Rings_Olinordered__ring__strict(T_a) % 154.47/154.45 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a) % 154.47/154.45 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 154.47/154.45 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Suc__eq__plus1,axiom, % 154.47/154.45 ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 154.47/154.45 % 154.47/154.45 fof(fact_nat__mult__less__cancel1,axiom, % 154.47/154.45 ! [V_n_2,V_m_2,V_k_2] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 154.47/154.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_nat__mult__eq__cancel1,axiom, % 154.47/154.45 ! [V_n_2,V_m_2,V_k_2] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 154.47/154.45 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) % 154.47/154.45 <=> V_m_2 = V_n_2 ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_fold__image__Un__one,axiom, % 154.47/154.45 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 154.47/154.45 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.47/154.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 154.47/154.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 154.47/154.45 => ( ! [B_x] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))) % 154.47/154.45 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 154.47/154.45 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),V_T_2)) ) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_card__Suc__eq,axiom, % 154.47/154.45 ! [V_k_2,V_A_2,T_a] : % 154.47/154.45 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Nat_OSuc,V_k_2) % 154.47/154.45 <=> ? [B_b,B_B] : % 154.47/154.45 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),B_b),B_B) % 154.47/154.45 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_b),B_B)) % 154.47/154.45 & hAPP(c_Finite__Set_Ocard(T_a),B_B) = V_k_2 % 154.47/154.45 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.47/154.45 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_left__add__mult__distrib,axiom, % 154.47/154.45 ! [V_k,V_j,V_u,V_i] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k) ). % 154.47/154.45 % 154.47/154.45 fof(fact_nat__mult__eq__cancel__disj,axiom, % 154.47/154.45 ! [V_n_2,V_m_2,V_k_2] : % 154.47/154.45 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) % 154.47/154.45 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.47/154.45 | V_m_2 = V_n_2 ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_termination__basic__simps_I2_J,axiom, % 154.47/154.45 ! [V_y,V_z,V_x] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) % 154.47/154.45 => 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))) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_termination__basic__simps_I1_J,axiom, % 154.47/154.45 ! [V_z,V_y,V_x] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 154.47/154.45 => 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))) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_psubset__trans,axiom, % 154.47/154.45 ! [V_C_2,V_B_2,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_comp__cong,axiom, % 154.47/154.45 ! [T_e,T_d,T_c,T_a,T_b,V_x_H_2,V_g_H_2,V_f_H_2,V_x_2,V_g_2,V_f_2] : % 154.47/154.45 ( hAPP(V_f_2,hAPP(V_g_2,V_x_2)) = hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2)) % 154.47/154.45 => hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_d,T_a,T_e,V_f_H_2),V_g_H_2),V_x_H_2) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_com_Osize_I4_J,axiom, % 154.47/154.45 ! [V_com2,V_com1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1)),c_Com_Ocom_Ocom__size(V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 154.47/154.45 % 154.47/154.45 fof(fact_com_Osize_I5_J,axiom, % 154.47/154.45 ! [V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1_2)),c_Com_Ocom_Ocom__size(V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 154.47/154.45 % 154.47/154.45 fof(fact_com_Osize_I6_J,axiom, % 154.47/154.45 ! [V_com_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 154.47/154.45 % 154.47/154.45 fof(fact_com_Osize_I12_J,axiom, % 154.47/154.45 ! [V_com2,V_com1] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 154.47/154.45 % 154.47/154.45 fof(fact_com_Osize_I13_J,axiom, % 154.47/154.45 ! [V_com2_2,V_com1_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1_2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 154.47/154.45 % 154.47/154.45 fof(fact_com_Osize_I14_J,axiom, % 154.47/154.45 ! [V_com_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 154.47/154.45 % 154.47/154.45 fof(fact_setsum__strict__mono,axiom, % 154.47/154.45 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] : % 154.47/154.45 ( ( class_Groups_Ocomm__monoid__add(T_b) % 154.47/154.45 & class_Groups_Oordered__cancel__ab__semigroup__add(T_b) ) % 154.47/154.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.45 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.45 => ( ! [B_x] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2))) ) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_diff__Suc,axiom, % 154.47/154.45 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2)) ). % 154.47/154.45 % 154.47/154.45 fof(fact_nat__case__0,axiom, % 154.47/154.45 ! [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 ). % 154.47/154.45 % 154.47/154.45 fof(fact_nat__case__Suc,axiom, % 154.47/154.45 ! [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) ). % 154.47/154.45 % 154.47/154.45 fof(fact_com_Osize_I15_J,axiom, % 154.47/154.45 ! [V_pname] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.47/154.45 % 154.47/154.45 fof(fact_com_Osize_I7_J,axiom, % 154.47/154.45 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.47/154.45 % 154.47/154.45 fof(fact_com_Osize_I9_J,axiom, % 154.47/154.45 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.47/154.45 % 154.47/154.45 fof(fact_com_Osize_I1_J,axiom, % 154.47/154.45 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.47/154.45 % 154.47/154.45 fof(fact_fold1__eq__fold,axiom, % 154.47/154.45 ! [V_a_2,V_A_2,T_a] : % 154.47/154.45 ( class_Groups_Oab__semigroup__mult(T_a) % 154.47/154.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.45 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)),V_a_2),V_A_2) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_fold1__Un,axiom, % 154.47/154.45 ! [V_B_2,V_A_2,T_a] : % 154.47/154.45 ( class_Groups_Oab__semigroup__mult(T_a) % 154.47/154.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.45 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.45 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.45 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.45 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_B_2)) ) ) ) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_evaln_OBody,axiom, % 154.47/154.45 ! [V_s1,V_n,V_s0,V_pn] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_n),V_s1)) % 154.47/154.45 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),hAPP(c_Nat_OSuc,V_n)),V_s1)) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_fold1__insert,axiom, % 154.47/154.45 ! [V_x_2,V_A_2,T_a] : % 154.47/154.45 ( class_Groups_Oab__semigroup__mult(T_a) % 154.47/154.45 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.45 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)) ) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom, % 154.47/154.45 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_b,T_a] : % 154.47/154.45 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 154.47/154.45 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_v_2)) % 154.47/154.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.45 => ~ ! [B_y] : % 154.47/154.45 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y) % 154.47/154.45 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_arith__series__nat,axiom, % 154.47/154.45 ! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_d_2)))) ). % 154.47/154.45 % 154.47/154.45 fof(fact_psubset__insert__iff,axiom, % 154.47/154.45 ! [V_B_2,V_x_2,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) % 154.47/154.45 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 154.47/154.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 154.47/154.45 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2)) ) % 154.47/154.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_setsum__SucD,axiom, % 154.47/154.45 ! [V_n_2,V_A_2,V_f_2,T_a] : % 154.47/154.45 ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,V_n_2) % 154.47/154.45 => ? [B_x] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.47/154.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_order__refl,axiom, % 154.47/154.45 ! [V_x,T_a] : % 154.47/154.45 ( class_Orderings_Opreorder(T_a) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_equalityI,axiom, % 154.47/154.45 ! [V_B_2,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 154.47/154.45 => V_A_2 = V_B_2 ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_finite__lessThan,axiom, % 154.47/154.45 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ). % 154.47/154.45 % 154.47/154.45 fof(fact_subsetD,axiom, % 154.47/154.45 ! [V_c_2,V_B_2,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_empty__subsetI,axiom, % 154.47/154.45 ! [V_A_2,T_a] : hBOOL(hAPP(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)) ). % 154.47/154.45 % 154.47/154.45 fof(fact_evaln_OWhileTrue,axiom, % 154.47/154.45 ! [V_s2_2,V_s1_2,V_n_2,V_c_2,V_s0_2,V_b_2] : % 154.47/154.45 ( hBOOL(hAPP(V_b_2,V_s0_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c_2),V_s0_2),V_n_2),V_s1_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s1_2),V_n_2),V_s2_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s0_2),V_n_2),V_s2_2)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_evaln_OWhileFalse,axiom, % 154.47/154.45 ! [V_n_2,V_c_2,V_s_2,V_b_2] : % 154.47/154.45 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_n_2),V_s_2)) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_evaln__elim__cases_I5_J,axiom, % 154.47/154.45 ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)),V_s_2),V_n_2),V_t_2)) % 154.47/154.45 => ( ( hBOOL(hAPP(V_b_2,V_s_2)) % 154.47/154.45 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_t_2)) ) % 154.47/154.45 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 154.47/154.45 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2_2),V_s_2),V_n_2),V_t_2)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_evaln_OIfTrue,axiom, % 154.47/154.45 ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_b_2] : % 154.47/154.45 ( hBOOL(hAPP(V_b_2,V_s_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0_2),V_s_2),V_n_2),V_s1_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_n_2),V_s1_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_evaln_OIfFalse,axiom, % 154.47/154.45 ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_b_2] : % 154.47/154.45 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_s1_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_n_2),V_s1_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_evaln_OSemi,axiom, % 154.47/154.45 ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0),V_s0),V_n),V_s1)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s1),V_n),V_s2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_n),V_s2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_evaln__elim__cases_I1_J,axiom, % 154.47/154.45 ! [V_t,V_n,V_s] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_t)) % 154.47/154.45 => V_t = V_s ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_evaln_OSkip,axiom, % 154.47/154.45 ! [V_n,V_s] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_s)) ). % 154.47/154.45 % 154.47/154.45 fof(fact_lessThan__Suc,axiom, % 154.47/154.45 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2)) ). % 154.47/154.45 % 154.47/154.45 fof(fact_UN__lessThan__UNIV,axiom, % 154.47/154.45 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 154.47/154.45 % 154.47/154.45 fof(fact_INF__subset,axiom, % 154.47/154.45 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 154.47/154.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2))) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_lessThan__eq__iff,axiom, % 154.47/154.45 ! [V_y_2,V_x_2,T_a] : % 154.47/154.45 ( class_Orderings_Olinorder(T_a) % 154.47/154.45 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2) % 154.47/154.45 <=> V_x_2 = V_y_2 ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_lessThan__subset__iff,axiom, % 154.47/154.45 ! [V_y_2,V_x_2,T_a] : % 154.47/154.45 ( class_Orderings_Olinorder(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2))) % 154.47/154.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_linorder__le__cases,axiom, % 154.47/154.45 ! [V_y,V_x,T_a] : % 154.47/154.45 ( class_Orderings_Olinorder(T_a) % 154.47/154.45 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_le__funE,axiom, % 154.47/154.45 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 154.47/154.45 ( class_Orderings_Oord(T_b) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_equalityE,axiom, % 154.47/154.45 ! [T_a,V_B_2,V_A_2] : % 154.47/154.45 ( V_A_2 = V_B_2 % 154.47/154.45 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.45 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_xt1_I6_J,axiom, % 154.47/154.45 ! [V_z,V_x,V_y,T_a] : % 154.47/154.45 ( class_Orderings_Oorder(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_xt1_I5_J,axiom, % 154.47/154.45 ! [V_x,V_y,T_a] : % 154.47/154.45 ( class_Orderings_Oorder(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 154.47/154.45 => V_x = V_y ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_order__trans,axiom, % 154.47/154.45 ! [V_z,V_y,V_x,T_a] : % 154.47/154.45 ( class_Orderings_Opreorder(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_order__antisym,axiom, % 154.47/154.45 ! [V_y,V_x,T_a] : % 154.47/154.45 ( class_Orderings_Oorder(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 154.47/154.45 => V_x = V_y ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_xt1_I4_J,axiom, % 154.47/154.45 ! [V_c,V_a,V_b,T_a] : % 154.47/154.45 ( class_Orderings_Oorder(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 154.47/154.45 => ( V_b = V_c % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_ord__le__eq__trans,axiom, % 154.47/154.45 ! [V_c,V_b,V_a,T_a] : % 154.47/154.45 ( class_Orderings_Oord(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 154.47/154.45 => ( V_b = V_c % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_subset__trans,axiom, % 154.47/154.45 ! [V_C_2,V_B_2,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_xt1_I3_J,axiom, % 154.47/154.45 ! [V_c,V_b,V_a,T_a] : % 154.47/154.45 ( class_Orderings_Oorder(T_a) % 154.47/154.45 => ( V_a = V_b % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_ord__eq__le__trans,axiom, % 154.47/154.45 ! [V_c,V_b,V_a,T_a] : % 154.47/154.45 ( class_Orderings_Oord(T_a) % 154.47/154.45 => ( V_a = V_b % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_predicate1D,axiom, % 154.47/154.45 ! [V_x_2,V_Q_2,V_P_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2)) % 154.47/154.45 => ( hBOOL(hAPP(V_P_2,V_x_2)) % 154.47/154.45 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_order__antisym__conv,axiom, % 154.47/154.45 ! [V_x_2,V_y_2,T_a] : % 154.47/154.45 ( class_Orderings_Oorder(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 154.47/154.45 <=> V_x_2 = V_y_2 ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_le__funD,axiom, % 154.47/154.45 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 154.47/154.45 ( class_Orderings_Oord(T_b) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_order__eq__refl,axiom, % 154.47/154.45 ! [V_y,V_x,T_a] : % 154.47/154.45 ( class_Orderings_Opreorder(T_a) % 154.47/154.45 => ( V_x = V_y % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_equalityD2,axiom, % 154.47/154.45 ! [T_a,V_B_2,V_A_2] : % 154.47/154.45 ( V_A_2 = V_B_2 % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_equalityD1,axiom, % 154.47/154.45 ! [T_a,V_B_2,V_A_2] : % 154.47/154.45 ( V_A_2 = V_B_2 % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_rev__predicate1D,axiom, % 154.47/154.45 ! [V_Q_2,T_a,V_x_2,V_P_2] : % 154.47/154.45 ( hBOOL(hAPP(V_P_2,V_x_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2)) % 154.47/154.45 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_order__eq__iff,axiom, % 154.47/154.45 ! [V_y_2,V_x_2,T_a] : % 154.47/154.45 ( class_Orderings_Oorder(T_a) % 154.47/154.45 => ( V_x_2 = V_y_2 % 154.47/154.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 154.47/154.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_set__eq__subset,axiom, % 154.47/154.45 ! [T_a,V_B_2,V_A_2] : % 154.47/154.45 ( V_A_2 = V_B_2 % 154.47/154.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_linorder__linear,axiom, % 154.47/154.45 ! [V_y,V_x,T_a] : % 154.47/154.45 ( class_Orderings_Olinorder(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 154.47/154.45 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_le__fun__def,axiom, % 154.47/154.45 ! [V_g_2,V_f_2,T_a,T_b] : % 154.47/154.45 ( class_Orderings_Oord(T_b) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 154.47/154.45 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_subset__refl,axiom, % 154.47/154.45 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2)) ). % 154.47/154.45 % 154.47/154.45 fof(fact_SUP__subset,axiom, % 154.47/154.45 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 154.47/154.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_B_2),V_f_2))) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Union__mono,axiom, % 154.47/154.45 ! [V_B_2,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2))) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Inter__anti__mono,axiom, % 154.47/154.45 ! [V_A_2,V_B_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2))) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_card__lessThan,axiom, % 154.47/154.45 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_u_2)) = V_u_2 ). % 154.47/154.45 % 154.47/154.45 fof(fact_lessThan__0,axiom, % 154.47/154.45 hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 154.47/154.45 % 154.47/154.45 fof(fact_evaln__Suc,axiom, % 154.47/154.45 ! [V_s_H,V_n,V_s,V_c] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_s_H)) % 154.47/154.45 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),hAPP(c_Nat_OSuc,V_n)),V_s_H)) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_xt1_I8_J,axiom, % 154.47/154.45 ! [V_z,V_x,V_y,T_a] : % 154.47/154.45 ( class_Orderings_Oorder(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_order__le__less__trans,axiom, % 154.47/154.45 ! [V_z,V_y,V_x,T_a] : % 154.47/154.45 ( class_Orderings_Opreorder(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_xt1_I7_J,axiom, % 154.47/154.45 ! [V_z,V_x,V_y,T_a] : % 154.47/154.45 ( class_Orderings_Oorder(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_order__less__le__trans,axiom, % 154.47/154.45 ! [V_z,V_y,V_x,T_a] : % 154.47/154.45 ( class_Orderings_Opreorder(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_xt1_I11_J,axiom, % 154.47/154.45 ! [V_a,V_b,T_a] : % 154.47/154.45 ( class_Orderings_Oorder(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 154.47/154.45 => ( V_a != V_b % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_order__le__neq__trans,axiom, % 154.47/154.45 ! [V_b,V_a,T_a] : % 154.47/154.45 ( class_Orderings_Oorder(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 154.47/154.45 => ( V_a != V_b % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_order__le__imp__less__or__eq,axiom, % 154.47/154.45 ! [V_y,V_x,T_a] : % 154.47/154.45 ( class_Orderings_Oorder(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 154.47/154.45 | V_x = V_y ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_linorder__antisym__conv2,axiom, % 154.47/154.45 ! [V_y_2,V_x_2,T_a] : % 154.47/154.45 ( class_Orderings_Olinorder(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 154.47/154.45 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 154.47/154.45 <=> V_x_2 = V_y_2 ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_order__less__imp__le,axiom, % 154.47/154.45 ! [V_y,V_x,T_a] : % 154.47/154.45 ( class_Orderings_Opreorder(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_leD,axiom, % 154.47/154.45 ! [V_x,V_y,T_a] : % 154.47/154.45 ( class_Orderings_Olinorder(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 154.47/154.45 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_xt1_I12_J,axiom, % 154.47/154.45 ! [V_b,V_a,T_a] : % 154.47/154.45 ( class_Orderings_Oorder(T_a) % 154.47/154.45 => ( V_a != V_b % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_order__neq__le__trans,axiom, % 154.47/154.45 ! [V_b,V_a,T_a] : % 154.47/154.45 ( class_Orderings_Oorder(T_a) % 154.47/154.45 => ( V_a != V_b % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_linorder__antisym__conv1,axiom, % 154.47/154.45 ! [V_y_2,V_x_2,T_a] : % 154.47/154.45 ( class_Orderings_Olinorder(T_a) % 154.47/154.45 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 154.47/154.45 <=> V_x_2 = V_y_2 ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_not__leE,axiom, % 154.47/154.45 ! [V_x,V_y,T_a] : % 154.47/154.45 ( class_Orderings_Olinorder(T_a) % 154.47/154.45 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_leI,axiom, % 154.47/154.45 ! [V_y,V_x,T_a] : % 154.47/154.45 ( class_Orderings_Olinorder(T_a) % 154.47/154.45 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_order__le__less,axiom, % 154.47/154.45 ! [V_y_2,V_x_2,T_a] : % 154.47/154.45 ( class_Orderings_Oorder(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 154.47/154.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 154.47/154.45 | V_x_2 = V_y_2 ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_less__le__not__le,axiom, % 154.47/154.45 ! [V_y_2,V_x_2,T_a] : % 154.47/154.45 ( class_Orderings_Opreorder(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 154.47/154.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 154.47/154.45 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_order__less__le,axiom, % 154.47/154.45 ! [V_y_2,V_x_2,T_a] : % 154.47/154.45 ( class_Orderings_Oorder(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 154.47/154.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 154.47/154.45 & V_x_2 != V_y_2 ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_linorder__le__less__linear,axiom, % 154.47/154.45 ! [V_y,V_x,T_a] : % 154.47/154.45 ( class_Orderings_Olinorder(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 154.47/154.45 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_linorder__not__le,axiom, % 154.47/154.45 ! [V_y_2,V_x_2,T_a] : % 154.47/154.45 ( class_Orderings_Olinorder(T_a) % 154.47/154.45 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 154.47/154.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_linorder__not__less,axiom, % 154.47/154.45 ! [V_y_2,V_x_2,T_a] : % 154.47/154.45 ( class_Orderings_Olinorder(T_a) % 154.47/154.45 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 154.47/154.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_in__mono,axiom, % 154.47/154.45 ! [V_x_2,V_B_2,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_set__rev__mp,axiom, % 154.47/154.45 ! [V_B_2,V_A_2,V_x_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_set__mp,axiom, % 154.47/154.45 ! [V_x_2,V_B_2,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_add__le__cancel__right,axiom, % 154.47/154.45 ! [V_b_2,V_c_2,V_a_2,T_a] : % 154.47/154.45 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2))) % 154.47/154.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_add__le__cancel__left,axiom, % 154.47/154.45 ! [V_b_2,V_a_2,V_c_2,T_a] : % 154.47/154.45 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2))) % 154.47/154.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_add__right__mono,axiom, % 154.47/154.45 ! [V_c,V_b,V_a,T_a] : % 154.47/154.45 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 154.47/154.45 => hBOOL(hAPP(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))) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_add__left__mono,axiom, % 154.47/154.45 ! [V_c,V_b,V_a,T_a] : % 154.47/154.45 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 154.47/154.45 => hBOOL(hAPP(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))) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_add__mono,axiom, % 154.47/154.45 ! [V_d,V_c,V_b,V_a,T_a] : % 154.47/154.45 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 154.47/154.45 => hBOOL(hAPP(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))) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_add__le__imp__le__right,axiom, % 154.47/154.45 ! [V_b,V_c,V_a,T_a] : % 154.47/154.45 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 154.47/154.45 => ( hBOOL(hAPP(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))) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_add__le__imp__le__left,axiom, % 154.47/154.45 ! [V_b,V_a,V_c,T_a] : % 154.47/154.45 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 154.47/154.45 => ( hBOOL(hAPP(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))) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_bot__least,axiom, % 154.47/154.45 ! [V_x,T_a] : % 154.47/154.45 ( class_Orderings_Obot(T_a) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_diff__eq__diff__less__eq,axiom, % 154.47/154.45 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 154.47/154.45 ( class_Groups_Oordered__ab__group__add(T_a) % 154.47/154.45 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 154.47/154.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_d_2)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_subset__empty,axiom, % 154.47/154.45 ! [V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(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)))) % 154.47/154.45 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_le__supE,axiom, % 154.47/154.45 ! [V_x,V_b,V_a,T_a] : % 154.47/154.45 ( class_Lattices_Osemilattice__sup(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x)) % 154.47/154.45 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 154.47/154.45 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_sup__mono,axiom, % 154.47/154.45 ! [V_d,V_b,V_c,V_a,T_a] : % 154.47/154.45 ( class_Lattices_Osemilattice__sup(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_c),V_d))) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_sup__least,axiom, % 154.47/154.45 ! [V_z,V_x,V_y,T_a] : % 154.47/154.45 ( class_Lattices_Osemilattice__sup(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_le__supI,axiom, % 154.47/154.45 ! [V_b,V_x,V_a,T_a] : % 154.47/154.45 ( class_Lattices_Osemilattice__sup(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_sup__absorb1,axiom, % 154.47/154.45 ! [V_x,V_y,T_a] : % 154.47/154.45 ( class_Lattices_Osemilattice__sup(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 154.47/154.45 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_sup__absorb2,axiom, % 154.47/154.45 ! [V_y,V_x,T_a] : % 154.47/154.45 ( class_Lattices_Osemilattice__sup(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 154.47/154.45 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_le__supI2,axiom, % 154.47/154.45 ! [V_a,V_b,V_x,T_a] : % 154.47/154.45 ( class_Lattices_Osemilattice__sup(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_le__supI1,axiom, % 154.47/154.45 ! [V_b,V_a,V_x,T_a] : % 154.47/154.45 ( class_Lattices_Osemilattice__sup(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_le__sup__iff,axiom, % 154.47/154.45 ! [V_z_2,V_y_2,V_x_2,T_a] : % 154.47/154.45 ( class_Lattices_Osemilattice__sup(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2)),V_z_2)) % 154.47/154.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 154.47/154.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_le__iff__sup,axiom, % 154.47/154.45 ! [V_y_2,V_x_2,T_a] : % 154.47/154.45 ( class_Lattices_Osemilattice__sup(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 154.47/154.45 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = V_y_2 ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_sup__ge2,axiom, % 154.47/154.45 ! [V_x,V_y,T_a] : % 154.47/154.45 ( class_Lattices_Osemilattice__sup(T_a) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_inf__sup__ord_I4_J,axiom, % 154.47/154.45 ! [V_x,V_y,T_a] : % 154.47/154.45 ( class_Lattices_Olattice(T_a) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_sup__ge1,axiom, % 154.47/154.45 ! [V_y,V_x,T_a] : % 154.47/154.45 ( class_Lattices_Osemilattice__sup(T_a) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_inf__sup__ord_I3_J,axiom, % 154.47/154.45 ! [V_y,V_x,T_a] : % 154.47/154.45 ( class_Lattices_Olattice(T_a) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_rev__finite__subset,axiom, % 154.47/154.45 ! [V_A_2,V_B_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_finite__subset,axiom, % 154.47/154.45 ! [V_B_2,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_le__infE,axiom, % 154.47/154.45 ! [V_b,V_a,V_x,T_a] : % 154.47/154.45 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))) % 154.47/154.45 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 154.47/154.45 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_inf__mono,axiom, % 154.47/154.45 ! [V_d,V_b,V_c,V_a,T_a] : % 154.47/154.45 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_c),V_d))) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_inf__greatest,axiom, % 154.47/154.45 ! [V_z,V_y,V_x,T_a] : % 154.47/154.45 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_le__infI,axiom, % 154.47/154.45 ! [V_b,V_a,V_x,T_a] : % 154.47/154.45 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_inf__absorb2,axiom, % 154.47/154.45 ! [V_x,V_y,T_a] : % 154.47/154.45 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 154.47/154.45 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_inf__absorb1,axiom, % 154.47/154.45 ! [V_y,V_x,T_a] : % 154.47/154.45 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 154.47/154.45 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_le__infI2,axiom, % 154.47/154.45 ! [V_a,V_x,V_b,T_a] : % 154.47/154.45 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_le__infI1,axiom, % 154.47/154.45 ! [V_b,V_x,V_a,T_a] : % 154.47/154.45 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_le__inf__iff,axiom, % 154.47/154.45 ! [V_z_2,V_y_2,V_x_2,T_a] : % 154.47/154.45 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y_2),V_z_2))) % 154.47/154.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 154.47/154.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_le__iff__inf,axiom, % 154.47/154.45 ! [V_y_2,V_x_2,T_a] : % 154.47/154.45 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 154.47/154.45 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = V_x_2 ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_inf__le2,axiom, % 154.47/154.45 ! [V_y,V_x,T_a] : % 154.47/154.45 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_inf__sup__ord_I2_J,axiom, % 154.47/154.45 ! [V_y,V_x,T_a] : % 154.47/154.45 ( class_Lattices_Olattice(T_a) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_inf__le1,axiom, % 154.47/154.45 ! [V_y,V_x,T_a] : % 154.47/154.45 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_inf__sup__ord_I1_J,axiom, % 154.47/154.45 ! [V_y,V_x,T_a] : % 154.47/154.45 ( class_Lattices_Olattice(T_a) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_top__greatest,axiom, % 154.47/154.45 ! [V_x,T_a] : % 154.47/154.45 ( class_Orderings_Otop(T_a) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_insert__mono,axiom, % 154.47/154.45 ! [V_a_2,V_D_2,V_C_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_D_2))) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_subset__insertI2,axiom, % 154.47/154.45 ! [V_b_2,V_B_2,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_subset__insertI,axiom, % 154.47/154.45 ! [V_a_2,V_B_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))) ). % 154.47/154.45 % 154.47/154.45 fof(fact_subset__UNIV,axiom, % 154.47/154.45 ! [V_A_2,T_a] : hBOOL(hAPP(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)))) ). % 154.47/154.45 % 154.47/154.45 fof(fact_image__mono,axiom, % 154.47/154.45 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_subset__image__iff,axiom, % 154.47/154.45 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 154.47/154.45 <=> ? [B_AA] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_AA),V_A_2)) % 154.47/154.45 & V_B_2 = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),B_AA) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Un__mono,axiom, % 154.47/154.45 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Un__least,axiom, % 154.47/154.45 ! [V_B_2,V_C_2,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Un__absorb2,axiom, % 154.47/154.45 ! [V_A_2,V_B_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 154.47/154.45 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Un__absorb1,axiom, % 154.47/154.45 ! [V_B_2,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.45 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_subset__Un__eq,axiom, % 154.47/154.45 ! [V_B_2,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.45 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Un__upper2,axiom, % 154.47/154.45 ! [V_A_2,V_B_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Un__upper1,axiom, % 154.47/154.45 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Int__mono,axiom, % 154.47/154.45 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Int__greatest,axiom, % 154.47/154.45 ! [V_B_2,V_A_2,V_C_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Int__absorb1,axiom, % 154.47/154.45 ! [V_A_2,V_B_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 154.47/154.45 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Int__absorb2,axiom, % 154.47/154.45 ! [V_B_2,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.45 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Int__lower2,axiom, % 154.47/154.45 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Int__lower1,axiom, % 154.47/154.45 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ). % 154.47/154.45 % 154.47/154.45 fof(fact_double__diff,axiom, % 154.47/154.45 ! [V_C_2,V_B_2,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 154.47/154.45 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2 ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Diff__mono,axiom, % 154.47/154.45 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_D_2),V_B_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Diff__subset,axiom, % 154.47/154.45 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ). % 154.47/154.45 % 154.47/154.45 fof(fact_evaln__evalc,axiom, % 154.47/154.45 ! [V_t,V_n,V_s,V_c] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t)) % 154.47/154.45 => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c),V_s),V_t)) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_eval__eq,axiom, % 154.47/154.45 ! [V_t_2,V_s_2,V_c_2] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c_2),V_s_2),V_t_2)) % 154.47/154.45 <=> ? [B_n] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c_2),V_s_2),B_n),V_t_2)) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_Sup__le__iff,axiom, % 154.47/154.45 ! [V_b_2,V_A_2,T_a] : % 154.47/154.45 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)),V_b_2)) % 154.47/154.45 <=> ! [B_x] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.47/154.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_evaln_Oequations_I8_J,axiom, % 154.47/154.45 ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a4_2),V_a6_2)) % 154.47/154.45 <=> ( ( V_a6_2 = V_a2_2 % 154.47/154.45 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) % 154.47/154.45 | ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 154.47/154.45 & ? [B_s1] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1)) % 154.47/154.45 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a4_2),V_a6_2)) ) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_evaln_Oequations_I7_J,axiom, % 154.47/154.45 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a4_2),V_a2_2)) % 154.47/154.45 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 154.47/154.45 => ? [B_s1] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1)) % 154.47/154.45 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a4_2),V_a2_2)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_less__fun__def,axiom, % 154.47/154.45 ! [V_g_2,V_f_2,T_a,T_b] : % 154.47/154.45 ( class_Orderings_Oord(T_b) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 154.47/154.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 154.47/154.45 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_g_2),V_f_2)) ) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_thin,axiom, % 154.47/154.45 ! [V_Ga_2,V_ts_2,V_G_H_2,T_a] : % 154.47/154.45 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_G_H_2),V_Ga_2)) % 154.47/154.45 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_weaken,axiom, % 154.47/154.45 ! [V_ts_2,V_ts_H_2,V_Ga_2,T_a] : % 154.47/154.45 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_H_2) % 154.47/154.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_ts_2),V_ts_H_2)) % 154.47/154.45 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_asm,axiom, % 154.47/154.45 ! [V_Ga_2,V_ts_2,T_a] : % 154.47/154.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_ts_2),V_Ga_2)) % 154.47/154.45 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ). % 154.47/154.45 % 154.47/154.45 fof(fact_evaln_Oequations_I6_J,axiom, % 154.47/154.45 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_a1_2,V_a6_2,V_a3_2)),V_a2_2),V_a4_2),V_a5_2)) % 154.47/154.46 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 154.47/154.46 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) ) % 154.47/154.46 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 154.47/154.46 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_evaln_Oequations_I5_J,axiom, % 154.47/154.46 ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a6_2)),V_a2_2),V_a4_2),V_a5_2)) % 154.47/154.46 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 154.47/154.46 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) ) % 154.47/154.46 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 154.47/154.46 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__Inf__iff,axiom, % 154.47/154.46 ! [V_A_2,V_b_2,T_a] : % 154.47/154.46 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2))) % 154.47/154.46 <=> ! [B_x] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_vimage__mono,axiom, % 154.47/154.46 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_evaln_Oequations_I4_J,axiom, % 154.47/154.46 ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_a1_2,V_a5_2)),V_a2_2),V_a3_2),V_a6_2)) % 154.47/154.46 <=> ? [B_s1] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a1_2),V_a2_2),V_a3_2),B_s1)) % 154.47/154.46 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a5_2),B_s1),V_a3_2),V_a6_2)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_evaln_Oequations_I1_J,axiom, % 154.47/154.46 ! [V_a2,V_a1] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_a1),V_a2),V_a1)) ). % 154.47/154.46 % 154.47/154.46 fof(fact_subset__psubset__trans,axiom, % 154.47/154.46 ! [V_C_2,V_B_2,V_A_2,T_a] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_psubset__subset__trans,axiom, % 154.47/154.46 ! [V_C_2,V_B_2,V_A_2,T_a] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_psubset__imp__subset,axiom, % 154.47/154.46 ! [V_B_2,V_A_2,T_a] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_subset__iff__psubset__eq,axiom, % 154.47/154.46 ! [V_B_2,V_A_2,T_a] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.46 | V_A_2 = V_B_2 ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_psubset__eq,axiom, % 154.47/154.46 ! [V_B_2,V_A_2,T_a] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.46 & V_A_2 != V_B_2 ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_lessThan__Suc__eq__insert__0,axiom, % 154.47/154.46 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) ). % 154.47/154.46 % 154.47/154.46 fof(fact_pred__subset__eq,axiom, % 154.47/154.46 ! [V_S_2,V_R_2,T_a] : % 154.47/154.46 ( hBOOL(hAPP(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))) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_fold1__belowI,axiom, % 154.47/154.46 ! [V_a_2,V_A_2,T_a] : % 154.47/154.46 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2)),V_a_2)) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_below__fold1__iff,axiom, % 154.47/154.46 ! [V_x_2,V_A_2,T_a] : % 154.47/154.46 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2))) % 154.47/154.46 <=> ! [B_x] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_SUP__le__iff,axiom, % 154.47/154.46 ! [V_u_2,V_M_2,V_A_2,T_b,T_a] : % 154.47/154.46 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),V_M_2)),V_u_2)) % 154.47/154.46 <=> ! [B_x] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_UN__subset__iff,axiom, % 154.47/154.46 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2)) % 154.47/154.46 <=> ! [B_x] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__INF__iff,axiom, % 154.47/154.46 ! [V_M_2,V_A_2,T_b,V_u_2,T_a] : % 154.47/154.46 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),V_M_2))) % 154.47/154.46 <=> ! [B_x] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_INT__subset__iff,axiom, % 154.47/154.46 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2))) % 154.47/154.46 <=> ! [B_x] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x))) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_lessThan__iff,axiom, % 154.47/154.46 ! [V_k_2,V_i_2,T_a] : % 154.47/154.46 ( class_Orderings_Oord(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2))) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_i_2),V_k_2)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_setsum__lessThan__Suc,axiom, % 154.47/154.46 ! [V_n_2,V_f_2,T_a] : % 154.47/154.46 ( class_Groups_Ocomm__monoid__add(T_a) % 154.47/154.46 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,V_n_2)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_lessThan__strict__subset__iff,axiom, % 154.47/154.46 ! [V_n_2,V_m_2,T_a] : % 154.47/154.46 ( class_Orderings_Olinorder(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_n_2))) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_n_2)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 154.47/154.46 ! [V_a_2,T_a] : % 154.47/154.46 ( class_Groups_Olinordered__ab__group__add(T_a) % 154.47/154.46 => ( hBOOL(hAPP(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_2),V_a_2))) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 154.47/154.46 ! [V_a_2,T_a] : % 154.47/154.46 ( class_Groups_Olinordered__ab__group__add(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_add__nonneg__nonneg,axiom, % 154.47/154.46 ! [V_b,V_a,T_a] : % 154.47/154.46 ( class_Groups_Oordered__comm__monoid__add(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 154.47/154.46 => hBOOL(hAPP(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))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_add__nonneg__eq__0__iff,axiom, % 154.47/154.46 ! [V_y_2,V_x_2,T_a] : % 154.47/154.46 ( class_Groups_Oordered__comm__monoid__add(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y_2)) % 154.47/154.46 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a) % 154.47/154.46 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 154.47/154.46 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_add__increasing,axiom, % 154.47/154.46 ! [V_c,V_b,V_a,T_a] : % 154.47/154.46 ( class_Groups_Oordered__comm__monoid__add(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_add__increasing2,axiom, % 154.47/154.46 ! [V_a,V_b,V_c,T_a] : % 154.47/154.46 ( class_Groups_Oordered__comm__monoid__add(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_add__nonpos__nonpos,axiom, % 154.47/154.46 ! [V_b,V_a,T_a] : % 154.47/154.46 ( class_Groups_Oordered__comm__monoid__add(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.46 => hBOOL(hAPP(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))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_split__mult__neg__le,axiom, % 154.47/154.46 ! [V_b,V_a,T_a] : % 154.47/154.46 ( class_Rings_Oordered__cancel__semiring(T_a) % 154.47/154.46 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.47/154.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) % 154.47/154.46 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_split__mult__pos__le,axiom, % 154.47/154.46 ! [V_b,V_a,T_a] : % 154.47/154.46 ( class_Rings_Oordered__ring(T_a) % 154.47/154.46 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.47/154.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) % 154.47/154.46 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__mono,axiom, % 154.47/154.46 ! [V_d,V_c,V_b,V_a,T_a] : % 154.47/154.46 ( class_Rings_Oordered__semiring(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__mono_H,axiom, % 154.47/154.46 ! [V_d,V_c,V_b,V_a,T_a] : % 154.47/154.46 ( class_Rings_Oordered__semiring(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__left__mono__neg,axiom, % 154.47/154.46 ! [V_c,V_a,V_b,T_a] : % 154.47/154.46 ( class_Rings_Oordered__ring(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__right__mono__neg,axiom, % 154.47/154.46 ! [V_c,V_a,V_b,T_a] : % 154.47/154.46 ( class_Rings_Oordered__ring(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_comm__mult__left__mono,axiom, % 154.47/154.46 ! [V_c,V_b,V_a,T_a] : % 154.47/154.46 ( class_Rings_Oordered__comm__semiring(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__left__mono,axiom, % 154.47/154.46 ! [V_c,V_b,V_a,T_a] : % 154.47/154.46 ( class_Rings_Oordered__semiring(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__right__mono,axiom, % 154.47/154.46 ! [V_c,V_b,V_a,T_a] : % 154.47/154.46 ( class_Rings_Oordered__semiring(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__nonpos__nonpos,axiom, % 154.47/154.46 ! [V_b,V_a,T_a] : % 154.47/154.46 ( class_Rings_Oordered__ring(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__nonpos__nonneg,axiom, % 154.47/154.46 ! [V_b,V_a,T_a] : % 154.47/154.46 ( class_Rings_Oordered__cancel__semiring(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__nonneg__nonpos2,axiom, % 154.47/154.46 ! [V_b,V_a,T_a] : % 154.47/154.46 ( class_Rings_Oordered__cancel__semiring(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__nonneg__nonpos,axiom, % 154.47/154.46 ! [V_b,V_a,T_a] : % 154.47/154.46 ( class_Rings_Oordered__cancel__semiring(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__nonneg__nonneg,axiom, % 154.47/154.46 ! [V_b,V_a,T_a] : % 154.47/154.46 ( class_Rings_Oordered__cancel__semiring(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__le__0__iff,axiom, % 154.47/154.46 ! [V_b_2,V_a_2,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__ring__strict(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.46 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 154.47/154.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 154.47/154.46 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_zero__le__mult__iff,axiom, % 154.47/154.46 ! [V_b_2,V_a_2,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__ring__strict(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))) % 154.47/154.46 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 154.47/154.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 154.47/154.46 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_zero__le__square,axiom, % 154.47/154.46 ! [V_a,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__ring(T_a) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_add__less__le__mono,axiom, % 154.47/154.46 ! [V_d,V_c,V_b,V_a,T_a] : % 154.47/154.46 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 154.47/154.46 => 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))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_add__le__less__mono,axiom, % 154.47/154.46 ! [V_d,V_c,V_b,V_a,T_a] : % 154.47/154.46 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 154.47/154.46 => 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))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__iff__diff__le__0,axiom, % 154.47/154.46 ! [V_b_2,V_a_2,T_a] : % 154.47/154.46 ( class_Groups_Oordered__ab__group__add(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_zero__le__one,axiom, % 154.47/154.46 ! [T_a] : % 154.47/154.46 ( class_Rings_Olinordered__semidom(T_a) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_not__one__le__zero,axiom, % 154.47/154.46 ! [T_a] : % 154.47/154.46 ( class_Rings_Olinordered__semidom(T_a) % 154.47/154.46 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_insert__subset,axiom, % 154.47/154.46 ! [V_B_2,V_A_2,V_x_2,T_a] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2)) % 154.47/154.46 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 154.47/154.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_subset__insert,axiom, % 154.47/154.46 ! [V_B_2,V_A_2,V_x_2,T_a] : % 154.47/154.46 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_distrib__sup__le,axiom, % 154.47/154.46 ! [V_z,V_y,V_x,T_a] : % 154.47/154.46 ( class_Lattices_Olattice(T_a) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_distrib__inf__le,axiom, % 154.47/154.46 ! [V_z,V_y,V_x,T_a] : % 154.47/154.46 ( class_Lattices_Olattice(T_a) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_subset__singletonD,axiom, % 154.47/154.46 ! [V_x_2,V_A_2,T_a] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 154.47/154.46 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.46 | V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_finite__surj,axiom, % 154.47/154.46 ! [V_f_2,V_B_2,T_b,V_A_2,T_a] : % 154.47/154.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 154.47/154.46 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_image__Int__subset,axiom, % 154.47/154.46 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)))) ). % 154.47/154.46 % 154.47/154.46 fof(fact_Sup__upper,axiom, % 154.47/154.46 ! [V_A_2,V_x_2,T_a] : % 154.47/154.46 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2))) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_Un__Int__assoc__eq,axiom, % 154.47/154.46 ! [V_C_2,V_B_2,V_A_2,T_a] : % 154.47/154.46 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_image__diff__subset,axiom, % 154.47/154.46 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 154.47/154.46 % 154.47/154.46 fof(fact_Diff__subset__conv,axiom, % 154.47/154.46 ! [V_C_2,V_B_2,V_A_2,T_a] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_Diff__partition,axiom, % 154.47/154.46 ! [V_B_2,V_A_2,T_a] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.46 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2 ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_Inf__lower,axiom, % 154.47/154.46 ! [V_A_2,V_x_2,T_a] : % 154.47/154.46 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)),V_x_2)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_image__vimage__subset,axiom, % 154.47/154.46 ! [V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))),V_A_2)) ). % 154.47/154.46 % 154.47/154.46 fof(fact_Union__Int__subset,axiom, % 154.47/154.46 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)))) ). % 154.47/154.46 % 154.47/154.46 fof(fact_Union__upper,axiom, % 154.47/154.46 ! [V_A_2,V_B_2,T_a] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_fold1__singleton__def,axiom, % 154.47/154.46 ! [V_a_2,V_f_2,T_a,V_g_2] : % 154.47/154.46 ( V_g_2 = c_Finite__Set_Ofold1(T_a,V_f_2) % 154.47/154.46 => hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_fold1__singleton,axiom, % 154.47/154.46 ! [V_a_2,V_f_2,T_a] : hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ). % 154.47/154.46 % 154.47/154.46 fof(fact_Inter__Un__subset,axiom, % 154.47/154.46 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 154.47/154.46 % 154.47/154.46 fof(fact_Inter__lower,axiom, % 154.47/154.46 ! [V_A_2,V_B_2,T_a] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),V_B_2)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__SUPI,axiom, % 154.47/154.46 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] : % 154.47/154.46 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_M_2))) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_INF__leI,axiom, % 154.47/154.46 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] : % 154.47/154.46 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2))) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_UN__upper,axiom, % 154.47/154.46 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_triple__valid__def2,axiom, % 154.47/154.46 ! [V_Q_2,V_c_2,V_P_2,V_n_2,T_a] : % 154.47/154.46 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)) % 154.47/154.46 <=> ! [B_Z,B_s] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 154.47/154.46 => ! [B_s_H] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c_2),B_s),V_n_2),B_s_H)) % 154.47/154.46 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_INT__lower,axiom, % 154.47/154.46 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_folding__image__simple__idem_Osubset__idem,axiom, % 154.47/154.46 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 154.47/154.46 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 154.47/154.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 154.47/154.46 => hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_single__Diff__lessThan,axiom, % 154.47/154.46 ! [V_k_2,T_a] : % 154.47/154.46 ( class_Orderings_Oorder(T_a) % 154.47/154.46 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_folding__one_Oeq__fold,axiom, % 154.47/154.46 ! [V_A_2,V_F_2,V_f_2,T_a] : % 154.47/154.46 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 154.47/154.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.46 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_add__pos__nonneg,axiom, % 154.47/154.46 ! [V_b,V_a,T_a] : % 154.47/154.46 ( class_Groups_Oordered__comm__monoid__add(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 154.47/154.46 => 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))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_add__nonneg__pos,axiom, % 154.47/154.46 ! [V_b,V_a,T_a] : % 154.47/154.46 ( class_Groups_Oordered__comm__monoid__add(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 154.47/154.46 => 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))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_add__strict__increasing,axiom, % 154.47/154.46 ! [V_c,V_b,V_a,T_a] : % 154.47/154.46 ( class_Groups_Oordered__comm__monoid__add(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 154.47/154.46 => 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))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_add__strict__increasing2,axiom, % 154.47/154.46 ! [V_c,V_b,V_a,T_a] : % 154.47/154.46 ( class_Groups_Oordered__comm__monoid__add(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 154.47/154.46 => 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))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_add__neg__nonpos,axiom, % 154.47/154.46 ! [V_b,V_a,T_a] : % 154.47/154.46 ( class_Groups_Oordered__comm__monoid__add(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.46 => 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))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_add__nonpos__neg,axiom, % 154.47/154.46 ! [V_b,V_a,T_a] : % 154.47/154.46 ( class_Groups_Oordered__comm__monoid__add(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.46 => 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))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__left__le__imp__le,axiom, % 154.47/154.46 ! [V_b,V_a,V_c,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__semiring__strict(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__right__le__imp__le,axiom, % 154.47/154.46 ! [V_b,V_c,V_a,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__semiring__strict(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__less__imp__less__left,axiom, % 154.47/154.46 ! [V_b,V_a,V_c,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__semiring__strict(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__left__less__imp__less,axiom, % 154.47/154.46 ! [V_b,V_a,V_c,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__semiring(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__less__imp__less__right,axiom, % 154.47/154.46 ! [V_b,V_c,V_a,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__semiring__strict(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__right__less__imp__less,axiom, % 154.47/154.46 ! [V_b,V_c,V_a,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__semiring(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__le__less__imp__less,axiom, % 154.47/154.46 ! [V_d,V_c,V_b,V_a,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__semiring__strict(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__less__le__imp__less,axiom, % 154.47/154.46 ! [V_d,V_c,V_b,V_a,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__semiring__strict(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__strict__mono_H,axiom, % 154.47/154.46 ! [V_d,V_c,V_b,V_a,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__semiring__strict(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__strict__mono,axiom, % 154.47/154.46 ! [V_d,V_c,V_b,V_a,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__semiring__strict(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__le__cancel__left__neg,axiom, % 154.47/154.46 ! [V_b_2,V_a_2,V_c_2,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__ring__strict(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__le__cancel__left__pos,axiom, % 154.47/154.46 ! [V_b_2,V_a_2,V_c_2,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__ring__strict(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_sum__squares__ge__zero,axiom, % 154.47/154.46 ! [V_y,V_x,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__ring(T_a) % 154.47/154.46 => hBOOL(hAPP(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_sum__squares__le__zero__iff,axiom, % 154.47/154.46 ! [V_y_2,V_x_2,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__ring__strict(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_a))) % 154.47/154.46 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 154.47/154.46 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__left__le__one__le,axiom, % 154.47/154.46 ! [V_y,V_x,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__idom(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x)) ) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__right__le__one__le,axiom, % 154.47/154.46 ! [V_y,V_x,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__idom(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x)) ) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__add__iff2,axiom, % 154.47/154.46 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] : % 154.47/154.46 ( class_Rings_Oordered__ring(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__add__iff1,axiom, % 154.47/154.46 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] : % 154.47/154.46 ( class_Rings_Oordered__ring(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_vimage__subsetD,axiom, % 154.47/154.46 ! [V_A_2,V_B_2,V_f_2,T_a,T_b] : % 154.47/154.46 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2)),V_A_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_finite__nat__set__iff__bounded,axiom, % 154.47/154.46 ! [V_N_2] : % 154.47/154.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 154.47/154.46 <=> ? [B_m] : % 154.47/154.46 ! [B_x] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_fold1__def,axiom, % 154.47/154.46 ! [V_A_2,V_f_2,T_a] : hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) = c_HOL_OThe(T_a,c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2)) ). % 154.47/154.46 % 154.47/154.46 fof(fact_folding__one__idem_Osubset__idem,axiom, % 154.47/154.46 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 154.47/154.46 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 154.47/154.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 154.47/154.46 => hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_Sup__fin_OF__eq,axiom, % 154.47/154.46 ! [V_A_2,T_a] : % 154.47/154.46 ( class_Lattices_Olattice(T_a) % 154.47/154.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.46 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_A_2) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_Inf__fin_OF__eq,axiom, % 154.47/154.46 ! [V_A_2,T_a] : % 154.47/154.46 ( class_Lattices_Olattice(T_a) % 154.47/154.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.46 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_folding__idem_Osubset__comp__idem,axiom, % 154.47/154.46 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 154.47/154.46 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 154.47/154.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 154.47/154.46 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_convex__bound__le,axiom, % 154.47/154.46 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__semiring__1(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 154.47/154.46 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_diff__single__insert,axiom, % 154.47/154.46 ! [V_B_2,V_x_2,V_A_2,T_a] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_subset__insert__iff,axiom, % 154.47/154.46 ! [V_B_2,V_x_2,V_A_2,T_a] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) % 154.47/154.46 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2)) ) % 154.47/154.46 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_sup__le__fold__sup,axiom, % 154.47/154.46 ! [V_b_2,V_a_2,V_A_2,T_a] : % 154.47/154.46 ( class_Lattices_Osemilattice__sup(T_a) % 154.47/154.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_b_2),V_A_2))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_fold__inf__le__inf,axiom, % 154.47/154.46 ! [V_b_2,V_a_2,V_A_2,T_a] : % 154.47/154.46 ( class_Lattices_Osemilattice__inf(T_a) % 154.47/154.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),V_b_2))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_setsum__diff,axiom, % 154.47/154.46 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 154.47/154.46 ( class_Groups_Oab__group__add(T_b) % 154.47/154.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 154.47/154.46 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2)) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_card__Diff__subset,axiom, % 154.47/154.46 ! [V_A_2,V_B_2,T_a] : % 154.47/154.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 154.47/154.46 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_Sup__fin_Osubset__idem,axiom, % 154.47/154.46 ! [V_B_2,V_A_2,T_a] : % 154.47/154.46 ( class_Lattices_Olattice(T_a) % 154.47/154.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 154.47/154.46 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) ) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_Inf__fin_Osubset__idem,axiom, % 154.47/154.46 ! [V_B_2,V_A_2,T_a] : % 154.47/154.46 ( class_Lattices_Olattice(T_a) % 154.47/154.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 154.47/154.46 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) ) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_card__psubset,axiom, % 154.47/154.46 ! [V_A_2,V_B_2,T_a] : % 154.47/154.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_triple__valid__def,axiom, % 154.47/154.46 ! [V_t_2,V_n_2,T_a] : % 154.47/154.46 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,V_t_2) % 154.47/154.46 <=> hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(T_a,tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_HOL_OAll(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBS(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_Com_Ocom),c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))),hAPP(hAPP(c_COMBC(tc_Com_Ocom,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_Natural_Oevaln)),V_n_2))))))))),V_t_2)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_setsum__diff__nat,axiom, % 154.47/154.46 ! [V_f_2,V_A_2,V_B_2,T_a] : % 154.47/154.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 154.47/154.46 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_B_2)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_Inf__le__Sup,axiom, % 154.47/154.46 ! [V_A_2,T_a] : % 154.47/154.46 ( class_Lattices_Olattice(T_a) % 154.47/154.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2))) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_fold1__insert__idem,axiom, % 154.47/154.46 ! [V_x_2,V_A_2,T_a] : % 154.47/154.46 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 154.47/154.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.46 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_fold1__Un2,axiom, % 154.47/154.46 ! [V_B_2,V_A_2,T_a] : % 154.47/154.46 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 154.47/154.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.46 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_B_2)) ) ) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_evaln_Oequations_I9_J,axiom, % 154.47/154.46 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),hAPP(c_Nat_OSuc,V_a3_2)),V_a4_2)) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_a1_2))),V_a2_2),V_a3_2),V_a4_2)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_fold1__eq__fold__idem,axiom, % 154.47/154.46 ! [V_a_2,V_A_2,T_a] : % 154.47/154.46 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 154.47/154.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.46 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)),V_a_2),V_A_2) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_convex__bound__lt,axiom, % 154.47/154.46 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__semiring__1__strict(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 154.47/154.46 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_semilattice__big_OF__eq,axiom, % 154.47/154.46 ! [V_A_2,V_F_2,V_f_2,T_a] : % 154.47/154.46 ( c_Big__Operators_Osemilattice__big(T_a,V_f_2,V_F_2) % 154.47/154.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.46 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_evaln__elim__cases_I6_J,axiom, % 154.47/154.46 ! [V_s1,V_n,V_s,V_P] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_n),V_s1)) % 154.47/154.46 => ~ ! [B_n] : % 154.47/154.46 ( V_n = hAPP(c_Nat_OSuc,B_n) % 154.47/154.46 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),B_n),V_s1)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_setsum__mono2,axiom, % 154.47/154.46 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] : % 154.47/154.46 ( class_Groups_Oordered__comm__monoid__add(T_b) % 154.47/154.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.46 => ( ! [B_b] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_b))) ) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2))) ) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_flat__lub__def,axiom, % 154.47/154.46 ! [V_b_2,V_A_2,T_a] : % 154.47/154.46 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 154.47/154.46 => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = V_b_2 ) % 154.47/154.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 154.47/154.46 => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_arith__series__general,axiom, % 154.47/154.46 ! [V_n_2,V_d_2,V_a_2,T_a] : % 154.47/154.46 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.46 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_a)),c_Nat_Osemiring__1__class_Oof__nat(T_a))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_fold1__in,axiom, % 154.47/154.46 ! [V_A_2,T_a] : % 154.47/154.46 ( class_Groups_Oab__semigroup__mult(T_a) % 154.47/154.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.46 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),V_A_2)) ) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_setsum__mono3,axiom, % 154.47/154.46 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] : % 154.47/154.46 ( ( class_Groups_Ocomm__monoid__add(T_b) % 154.47/154.46 & class_Groups_Oordered__ab__semigroup__add(T_b) ) % 154.47/154.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.46 => ( ! [B_x] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2))) ) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le0,axiom, % 154.47/154.46 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 154.47/154.46 % 154.47/154.46 fof(fact_int__le__0__conv,axiom, % 154.47/154.46 ! [V_n_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.47/154.46 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_zdiff__int,axiom, % 154.47/154.46 ! [V_m,V_n] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 154.47/154.46 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_finite__nat__set__iff__bounded__le,axiom, % 154.47/154.46 ! [V_N_2] : % 154.47/154.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 154.47/154.46 <=> ? [B_m] : % 154.47/154.46 ! [B_x] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_of__nat__eq__iff,axiom, % 154.47/154.46 ! [V_n_2,V_m_2,T_a] : % 154.47/154.46 ( class_Nat_Osemiring__char__0(T_a) % 154.47/154.46 => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2) % 154.47/154.46 <=> V_m_2 = V_n_2 ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_infinite__UNIV__nat,axiom, % 154.47/154.46 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 154.47/154.46 % 154.47/154.46 fof(fact_of__nat__diff,axiom, % 154.47/154.46 ! [V_m,V_n,T_a] : % 154.47/154.46 ( class_Rings_Oring__1(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 154.47/154.46 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_int__eq__0__conv,axiom, % 154.47/154.46 ! [V_n_2] : % 154.47/154.46 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.47/154.46 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_int__0,axiom, % 154.47/154.46 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 154.47/154.46 % 154.47/154.46 fof(fact_zless__iff__Suc__zadd,axiom, % 154.47/154.46 ! [V_z_2,V_w_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 154.47/154.46 <=> ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_int__Suc,axiom, % 154.47/154.46 ! [V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) ). % 154.47/154.46 % 154.47/154.46 fof(fact_zless__int,axiom, % 154.47/154.46 ! [V_n_2,V_m_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_zadd__int__left,axiom, % 154.47/154.46 ! [V_z,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),V_z) ). % 154.47/154.46 % 154.47/154.46 fof(fact_zadd__int,axiom, % 154.47/154.46 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ). % 154.47/154.46 % 154.47/154.46 fof(fact_of__nat__le__iff,axiom, % 154.47/154.46 ! [V_n_2,V_m_2,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__semidom(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_zmult__int,axiom, % 154.47/154.46 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ). % 154.47/154.46 % 154.47/154.46 fof(fact_int__mult,axiom, % 154.47/154.46 ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) ). % 154.47/154.46 % 154.47/154.46 fof(fact_int__1,axiom, % 154.47/154.46 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__0__eq,axiom, % 154.47/154.46 ! [V_n_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 154.47/154.46 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 154.47/154.46 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 154.47/154.46 % 154.47/154.46 fof(fact_Suc__n__not__le__n,axiom, % 154.47/154.46 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ). % 154.47/154.46 % 154.47/154.46 fof(fact_not__less__eq__eq,axiom, % 154.47/154.46 ! [V_n_2,V_m_2] : % 154.47/154.46 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__Suc__eq,axiom, % 154.47/154.46 ! [V_n_2,V_m_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 154.47/154.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 154.47/154.46 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_Suc__le__mono,axiom, % 154.47/154.46 ! [V_m_2,V_n_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Nat_OSuc,V_m_2))) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__SucI,axiom, % 154.47/154.46 ! [V_n,V_m] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__SucE,axiom, % 154.47/154.46 ! [V_n,V_m] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 154.47/154.46 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 154.47/154.46 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_Suc__leD,axiom, % 154.47/154.46 ! [V_n,V_m] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_nat__less__le,axiom, % 154.47/154.46 ! [V_n_2,V_m_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 154.47/154.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 154.47/154.46 & V_m_2 != V_n_2 ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__eq__less__or__eq,axiom, % 154.47/154.46 ! [V_n_2,V_m_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 154.47/154.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 154.47/154.46 | V_m_2 = V_n_2 ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_less__imp__le__nat,axiom, % 154.47/154.46 ! [V_n,V_m] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__neq__implies__less,axiom, % 154.47/154.46 ! [V_n,V_m] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 154.47/154.46 => ( V_m != V_n % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_less__or__eq__imp__le,axiom, % 154.47/154.46 ! [V_n,V_m] : % 154.47/154.46 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 154.47/154.46 | V_m = V_n ) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_termination__basic__simps_I5_J,axiom, % 154.47/154.46 ! [V_y,V_x] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__add2,axiom, % 154.47/154.46 ! [V_m,V_n] : hBOOL(hAPP(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))) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__add1,axiom, % 154.47/154.46 ! [V_m,V_n] : hBOOL(hAPP(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))) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__iff__add,axiom, % 154.47/154.46 ! [V_n_2,V_m_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 154.47/154.46 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_nat__add__left__cancel__le,axiom, % 154.47/154.46 ! [V_n_2,V_m_2,V_k_2] : % 154.47/154.46 ( hBOOL(hAPP(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))) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_trans__le__add1,axiom, % 154.47/154.46 ! [V_m,V_j,V_i] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 154.47/154.46 => hBOOL(hAPP(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))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_trans__le__add2,axiom, % 154.47/154.46 ! [V_m,V_j,V_i] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 154.47/154.46 => hBOOL(hAPP(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))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_add__le__mono1,axiom, % 154.47/154.46 ! [V_k,V_j,V_i] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 154.47/154.46 => hBOOL(hAPP(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))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_add__le__mono,axiom, % 154.47/154.46 ! [V_l,V_k,V_j,V_i] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 154.47/154.46 => hBOOL(hAPP(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))) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_add__leD2,axiom, % 154.47/154.46 ! [V_n,V_k,V_m] : % 154.47/154.46 ( hBOOL(hAPP(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)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_add__leD1,axiom, % 154.47/154.46 ! [V_n,V_k,V_m] : % 154.47/154.46 ( hBOOL(hAPP(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)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_add__leE,axiom, % 154.47/154.46 ! [V_n,V_k,V_m] : % 154.47/154.46 ( hBOOL(hAPP(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)) % 154.47/154.46 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 154.47/154.46 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_termination__basic__simps_I4_J,axiom, % 154.47/154.46 ! [V_y,V_z,V_x] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z)) % 154.47/154.46 => hBOOL(hAPP(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))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_termination__basic__simps_I3_J,axiom, % 154.47/154.46 ! [V_z,V_y,V_x] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) % 154.47/154.46 => hBOOL(hAPP(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))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__diff__iff,axiom, % 154.47/154.46 ! [V_n_2,V_m_2,V_k_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2))) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_Nat_Odiff__diff__eq,axiom, % 154.47/154.46 ! [V_n,V_m,V_k] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 154.47/154.46 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_eq__diff__iff,axiom, % 154.47/154.46 ! [V_n_2,V_m_2,V_k_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 154.47/154.46 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2) % 154.47/154.46 <=> V_m_2 = V_n_2 ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_diff__diff__cancel,axiom, % 154.47/154.46 ! [V_n,V_i] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n)) % 154.47/154.46 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = V_i ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_diff__le__mono,axiom, % 154.47/154.46 ! [V_l,V_n,V_m] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_l)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_l))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_diff__le__mono2,axiom, % 154.47/154.46 ! [V_l,V_n,V_m] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_diff__le__self,axiom, % 154.47/154.46 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__le__mono,axiom, % 154.47/154.46 ! [V_l,V_k,V_j,V_i] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l))) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__le__mono2,axiom, % 154.47/154.46 ! [V_k,V_j,V_i] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__le__mono1,axiom, % 154.47/154.46 ! [V_k,V_j,V_i] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__cube,axiom, % 154.47/154.46 ! [V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__square,axiom, % 154.47/154.46 ! [V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))) ). % 154.47/154.46 % 154.47/154.46 fof(fact_evaln__nonstrict,axiom, % 154.47/154.46 ! [V_m,V_t,V_n,V_s,V_c] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 154.47/154.46 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_m),V_t)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_less__eq__nat_Osimps_I2_J,axiom, % 154.47/154.46 ! [V_n_2,V_m_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 154.47/154.46 <=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_int__setsum,axiom, % 154.47/154.46 ! [V_A_2,V_f_2,T_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ). % 154.47/154.46 % 154.47/154.46 fof(fact_int__Suc0__eq__1,axiom, % 154.47/154.46 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 154.47/154.46 % 154.47/154.46 fof(fact_zero__less__int__conv,axiom, % 154.47/154.46 ! [V_n_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_zmult__zless__mono2__lemma,axiom, % 154.47/154.46 ! [V_k,V_j,V_i] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_j))) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_zero__le__imp__of__nat,axiom, % 154.47/154.46 ! [V_m,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__semidom(T_a) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_of__nat__0__le__iff,axiom, % 154.47/154.46 ! [V_n,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__semidom(T_a) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_of__nat__less__0__iff,axiom, % 154.47/154.46 ! [V_m,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__semidom(T_a) % 154.47/154.46 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_of__nat__0,axiom, % 154.47/154.46 ! [T_a] : % 154.47/154.46 ( class_Rings_Osemiring__1(T_a) % 154.47/154.46 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_of__nat__less__iff,axiom, % 154.47/154.46 ! [V_n_2,V_m_2,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__semidom(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_less__imp__of__nat__less,axiom, % 154.47/154.46 ! [V_n,V_m,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__semidom(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_of__nat__less__imp__less,axiom, % 154.47/154.46 ! [V_n,V_m,T_a] : % 154.47/154.46 ( class_Rings_Olinordered__semidom(T_a) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_of__nat__add,axiom, % 154.47/154.46 ! [V_n,V_m,T_a] : % 154.47/154.46 ( class_Rings_Osemiring__1(T_a) % 154.47/154.46 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_less__eq__Suc__le,axiom, % 154.47/154.46 ! [V_m_2,V_n_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_less__Suc__eq__le,axiom, % 154.47/154.46 ! [V_n_2,V_m_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_Suc__le__eq,axiom, % 154.47/154.46 ! [V_n_2,V_m_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__imp__less__Suc,axiom, % 154.47/154.46 ! [V_n,V_m] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_Suc__leI,axiom, % 154.47/154.46 ! [V_n,V_m] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__less__Suc__eq,axiom, % 154.47/154.46 ! [V_n_2,V_m_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 154.47/154.46 <=> V_n_2 = V_m_2 ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_Suc__le__lessD,axiom, % 154.47/154.46 ! [V_n,V_m] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_of__nat__mult,axiom, % 154.47/154.46 ! [V_n,V_m,T_a] : % 154.47/154.46 ( class_Rings_Osemiring__1(T_a) % 154.47/154.46 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_diff__is__0__eq_H,axiom, % 154.47/154.46 ! [V_n,V_m] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 154.47/154.46 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_diff__is__0__eq,axiom, % 154.47/154.46 ! [V_n_2,V_m_2] : % 154.47/154.46 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_Suc__diff__le,axiom, % 154.47/154.46 ! [V_m,V_n] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 154.47/154.46 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_Suc__mult__le__cancel1,axiom, % 154.47/154.46 ! [V_n_2,V_m_2,V_k_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2))) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_less__diff__iff,axiom, % 154.47/154.46 ! [V_n_2,V_m_2,V_k_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2))) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_diff__less__mono,axiom, % 154.47/154.46 ! [V_c,V_b,V_a] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_b),V_c))) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_diff__add__assoc2,axiom, % 154.47/154.46 ! [V_i,V_j,V_k] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 154.47/154.46 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_add__diff__assoc2,axiom, % 154.47/154.46 ! [V_i,V_j,V_k] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 154.47/154.46 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_diff__add__assoc,axiom, % 154.47/154.46 ! [V_i,V_j,V_k] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 154.47/154.46 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__imp__diff__is__add,axiom, % 154.47/154.46 ! [V_k_2,V_j_2,V_i_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 154.47/154.46 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2 % 154.47/154.46 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__add__diff__inverse2,axiom, % 154.47/154.46 ! [V_m,V_n] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 154.47/154.46 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__diff__conv2,axiom, % 154.47/154.46 ! [V_i_2,V_j_2,V_k_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2)) % 154.47/154.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_add__diff__assoc,axiom, % 154.47/154.46 ! [V_i,V_j,V_k] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 154.47/154.46 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__add__diff__inverse,axiom, % 154.47/154.46 ! [V_m,V_n] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 154.47/154.46 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__add__diff,axiom, % 154.47/154.46 ! [V_m,V_n,V_k] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_k))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_le__diff__conv,axiom, % 154.47/154.46 ! [V_i_2,V_k_2,V_j_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)),V_i_2)) % 154.47/154.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_diff__diff__right,axiom, % 154.47/154.46 ! [V_i,V_j,V_k] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 154.47/154.46 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_of__nat__1,axiom, % 154.47/154.46 ! [T_a] : % 154.47/154.46 ( class_Rings_Osemiring__1(T_a) % 154.47/154.46 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_Ints__of__nat,axiom, % 154.47/154.46 ! [V_n_2,T_a] : % 154.47/154.46 ( class_Rings_Oring__1(T_a) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_less__eq__Suc__le__raw,axiom, % 154.47/154.46 ! [V_n_2] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) ). % 154.47/154.46 % 154.47/154.46 fof(fact_of__nat__setsum,axiom, % 154.47/154.46 ! [V_A_2,V_f_2,T_b,T_a] : % 154.47/154.46 ( class_Rings_Osemiring__1(T_a) % 154.47/154.46 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_a)),V_f_2)),V_A_2) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_of__nat__Suc,axiom, % 154.47/154.46 ! [V_m,T_a] : % 154.47/154.46 ( class_Rings_Osemiring__1(T_a) % 154.47/154.46 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_card__insert__le,axiom, % 154.47/154.46 ! [V_x_2,V_A_2,T_a] : % 154.47/154.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)))) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_one__le__mult__iff,axiom, % 154.47/154.46 ! [V_n_2,V_m_2] : % 154.47/154.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))) % 154.47/154.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2)) % 154.47/154.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2)) ) ) ). % 154.47/154.46 % 154.47/154.46 fof(fact_mult__le__cancel1,axiom, % 154.47/154.46 ! [V_n_2,V_m_2,V_k_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 154.47/154.47 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_mult__le__cancel2,axiom, % 154.47/154.47 ! [V_n_2,V_k_2,V_m_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) % 154.47/154.47 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_nat__mult__le__cancel1,axiom, % 154.47/154.47 ! [V_n_2,V_m_2,V_k_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_card__mono,axiom, % 154.47/154.47 ! [V_A_2,V_B_2,T_a] : % 154.47/154.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_card__seteq,axiom, % 154.47/154.47 ! [V_A_2,V_B_2,T_a] : % 154.47/154.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) % 154.47/154.47 => V_A_2 = V_B_2 ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_card__image__le,axiom, % 154.47/154.47 ! [V_f_2,T_b,V_A_2,T_a] : % 154.47/154.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_diff__Suc__diff__eq1,axiom, % 154.47/154.47 ! [V_m,V_j,V_k] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 154.47/154.47 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(c_Nat_OSuc,V_j)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_diff__Suc__diff__eq2,axiom, % 154.47/154.47 ! [V_m,V_j,V_k] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 154.47/154.47 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))),V_m) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_j)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_nat__eq__add__iff2,axiom, % 154.47/154.47 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 154.47/154.47 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2) % 154.47/154.47 <=> V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_nat__diff__add__eq2,axiom, % 154.47/154.47 ! [V_n,V_m,V_u,V_j,V_i] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 154.47/154.47 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i)),V_u)),V_n)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_nat__le__add__iff2,axiom, % 154.47/154.47 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_nat__eq__add__iff1,axiom, % 154.47/154.47 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 154.47/154.47 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2) % 154.47/154.47 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2) = V_n_2 ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_nat__diff__add__eq1,axiom, % 154.47/154.47 ! [V_n,V_m,V_u,V_i,V_j] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 154.47/154.47 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_u)),V_m)),V_n) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_nat__le__add__iff1,axiom, % 154.47/154.47 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_setsum__constant,axiom, % 154.47/154.47 ! [V_A_2,V_y_2,T_b,T_a] : % 154.47/154.47 ( class_Rings_Osemiring__1(T_a) % 154.47/154.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(c_COMBK(T_a,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_y_2) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_of__nat__0__less__iff,axiom, % 154.47/154.47 ! [V_n_2,T_a] : % 154.47/154.47 ( class_Rings_Olinordered__semidom(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_nat__less__add__iff1,axiom, % 154.47/154.47 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_nat__less__add__iff2,axiom, % 154.47/154.47 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_diff__card__le__card__Diff,axiom, % 154.47/154.47 ! [V_A_2,V_B_2,T_a] : % 154.47/154.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_card__Diff1__le,axiom, % 154.47/154.47 ! [V_x_2,V_A_2,T_a] : % 154.47/154.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_semiring__1__class_Oof__nat__code,axiom, % 154.47/154.47 ! [V_n_2,T_a] : % 154.47/154.47 ( class_Rings_Osemiring__1(T_a) % 154.47/154.47 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_Groups_Oone__class_Oone(T_a)),V_n_2,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_setsum__bounded,axiom, % 154.47/154.47 ! [V_K_2,V_f_2,V_A_2,T_a,T_b] : % 154.47/154.47 ( ( class_Groups_Oordered__ab__semigroup__add(T_b) % 154.47/154.47 & class_Rings_Osemiring__1(T_b) ) % 154.47/154.47 => ( ! [B_i] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_A_2)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_i)),V_K_2)) ) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))),V_K_2))) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ord_OgreaterThanAtMost__iff,axiom, % 154.47/154.47 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] : % 154.47/154.47 ( 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))) % 154.47/154.47 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 154.47/154.47 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ord_OatLeastLessThan__iff,axiom, % 154.47/154.47 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] : % 154.47/154.47 ( 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))) % 154.47/154.47 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 154.47/154.47 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ord_OgreaterThanLessThan__iff,axiom, % 154.47/154.47 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_a] : % 154.47/154.47 ( 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))) % 154.47/154.47 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 154.47/154.47 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ord_OatLeastAtMost__iff,axiom, % 154.47/154.47 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_a] : % 154.47/154.47 ( 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))) % 154.47/154.47 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 154.47/154.47 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ord_OgreaterThan__iff,axiom, % 154.47/154.47 ! [V_k_2,V_less_2,V_i_2,T_a] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zero__zle__int,axiom, % 154.47/154.47 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zadd__left__mono,axiom, % 154.47/154.47 ! [V_k,V_j,V_i] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j))) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zle__iff__zadd,axiom, % 154.47/154.47 ! [V_z_2,V_w_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) % 154.47/154.47 <=> ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zle__antisym,axiom, % 154.47/154.47 ! [V_w,V_z] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) % 154.47/154.47 => V_z = V_w ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zle__trans,axiom, % 154.47/154.47 ! [V_k,V_j,V_i] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zle__int,axiom, % 154.47/154.47 ! [V_n_2,V_m_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zle__linear,axiom, % 154.47/154.47 ! [V_w,V_z] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 154.47/154.47 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zle__refl,axiom, % 154.47/154.47 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_le__antisym,axiom, % 154.47/154.47 ! [V_n,V_m] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 154.47/154.47 => V_m = V_n ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_le__trans,axiom, % 154.47/154.47 ! [V_k,V_j,V_i] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_eq__imp__le,axiom, % 154.47/154.47 ! [V_n,V_m] : % 154.47/154.47 ( V_m = V_n % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_nat__le__linear,axiom, % 154.47/154.47 ! [V_n,V_m] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 154.47/154.47 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_le__refl,axiom, % 154.47/154.47 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zless__le,axiom, % 154.47/154.47 ! [V_w_2,V_z_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) % 154.47/154.47 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) % 154.47/154.47 & V_z_2 != V_w_2 ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zadd__zless__mono,axiom, % 154.47/154.47 ! [V_z,V_z_H,V_w,V_w_H] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z))) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zless__imp__add1__zle,axiom, % 154.47/154.47 ! [V_z,V_w] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_add1__zle__eq,axiom, % 154.47/154.47 ! [V_z_2,V_w_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2)) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zle__add1__eq__le,axiom, % 154.47/154.47 ! [V_z_2,V_w_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zle__diff1__eq,axiom, % 154.47/154.47 ! [V_z_2,V_w_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_int__one__le__iff__zero__less,axiom, % 154.47/154.47 ! [V_z_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_le__imp__0__less,axiom, % 154.47/154.47 ! [V_z] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z))) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_odd__less__0,axiom, % 154.47/154.47 ! [V_z_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zmult__zless__mono2,axiom, % 154.47/154.47 ! [V_k,V_j,V_i] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j))) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_pos__zmult__eq__1__iff,axiom, % 154.47/154.47 ! [V_n_2,V_m_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) % 154.47/154.47 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 154.47/154.47 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 154.47/154.47 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_int__0__less__1,axiom, % 154.47/154.47 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_int__less__0__conv,axiom, % 154.47/154.47 ! [V_k] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_less__bin__lemma,axiom, % 154.47/154.47 ! [V_l_2,V_k_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zless__add1__eq,axiom, % 154.47/154.47 ! [V_z_2,V_w_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) % 154.47/154.47 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 154.47/154.47 | V_w_2 = V_z_2 ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zadd__strict__right__mono,axiom, % 154.47/154.47 ! [V_k,V_j,V_i] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k))) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zless__linear,axiom, % 154.47/154.47 ! [V_y,V_x] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) % 154.47/154.47 | V_x = V_y % 154.47/154.47 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_int__int__eq,axiom, % 154.47/154.47 ! [V_n_2,V_m_2] : % 154.47/154.47 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) % 154.47/154.47 <=> V_m_2 = V_n_2 ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zmult__1,axiom, % 154.47/154.47 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ). % 154.47/154.47 % 154.47/154.47 fof(fact_zmult__1__right,axiom, % 154.47/154.47 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ). % 154.47/154.47 % 154.47/154.47 fof(fact_zadd__zmult__distrib,axiom, % 154.47/154.47 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zadd__zmult__distrib2,axiom, % 154.47/154.47 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zmult__assoc,axiom, % 154.47/154.47 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zmult__commute,axiom, % 154.47/154.47 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zdiff__zmult__distrib2,axiom, % 154.47/154.47 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zdiff__zmult__distrib,axiom, % 154.47/154.47 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zadd__0__right,axiom, % 154.47/154.47 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ). % 154.47/154.47 % 154.47/154.47 fof(fact_zadd__0,axiom, % 154.47/154.47 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ). % 154.47/154.47 % 154.47/154.47 fof(fact_odd__nonzero,axiom, % 154.47/154.47 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 154.47/154.47 % 154.47/154.47 fof(fact_int__0__neq__1,axiom, % 154.47/154.47 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zadd__assoc,axiom, % 154.47/154.47 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zadd__left__commute,axiom, % 154.47/154.47 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zadd__commute,axiom, % 154.47/154.47 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z) ). % 154.47/154.47 % 154.47/154.47 fof(fact_of__nat__aux_Osimps_I1_J,axiom, % 154.47/154.47 ! [V_i_2,V_inc_2,T_a] : % 154.47/154.47 ( class_Rings_Osemiring__1(T_a) % 154.47/154.47 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2 ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_of__nat__aux_Osimps_I2_J,axiom, % 154.47/154.47 ! [V_i_2,V_n_2,V_inc_2,T_a] : % 154.47/154.47 ( class_Rings_Osemiring__1(T_a) % 154.47/154.47 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zdiff__int__split,axiom, % 154.47/154.47 ! [V_y_2,V_x_2,V_P_2] : % 154.47/154.47 ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2)))) % 154.47/154.47 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) % 154.47/154.47 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))) ) % 154.47/154.47 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 154.47/154.47 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_self__quotient__aux2,axiom, % 154.47/154.47 ! [V_q,V_r,V_a] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 154.47/154.47 => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_self__quotient__aux1,axiom, % 154.47/154.47 ! [V_q,V_r,V_a] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 154.47/154.47 => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zdiv__mono2__neg__lemma,axiom, % 154.47/154.47 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 154.47/154.47 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_unique__quotient__lemma__neg,axiom, % 154.47/154.47 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zdiv__mono2__lemma,axiom, % 154.47/154.47 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 154.47/154.47 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_q__pos__lemma,axiom, % 154.47/154.47 ! [V_r_H,V_q_H,V_b_H] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_q__neg__lemma,axiom, % 154.47/154.47 ! [V_r_H,V_q_H,V_b_H] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_unique__quotient__lemma,axiom, % 154.47/154.47 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_transfer__int__nat__numerals_I2_J,axiom, % 154.47/154.47 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom, % 154.47/154.47 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom, % 154.47/154.47 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_y)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_transfer__int__nat__relations_I3_J,axiom, % 154.47/154.47 ! [V_y_2,V_x_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_transfer__int__nat__relations_I2_J,axiom, % 154.47/154.47 ! [V_y_2,V_x_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom, % 154.47/154.47 ! [V_y,V_x] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_transfer__nat__int__set__relations_I5_J,axiom, % 154.47/154.47 ! [V_B_2,V_A_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_transfer__nat__int__set__relations_I4_J,axiom, % 154.47/154.47 ! [V_B_2,V_A_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_transfer__nat__int__set__relations_I2_J,axiom, % 154.47/154.47 ! [V_A_2,V_x_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2)) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_transfer__nat__int__set__relations_I3_J,axiom, % 154.47/154.47 ! [V_B_2,V_A_2] : % 154.47/154.47 ( V_A_2 = V_B_2 % 154.47/154.47 <=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_transfer__int__nat__relations_I1_J,axiom, % 154.47/154.47 ! [V_y_2,V_x_2] : % 154.47/154.47 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2) % 154.47/154.47 <=> V_x_2 = V_y_2 ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom, % 154.47/154.47 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom, % 154.47/154.47 c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom, % 154.47/154.47 ! [V_A_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_transfer__nat__int__set__relations_I1_J,axiom, % 154.47/154.47 ! [V_A_2] : % 154.47/154.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2)) % 154.47/154.47 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_transfer__int__nat__numerals_I1_J,axiom, % 154.47/154.47 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom, % 154.47/154.47 ! [V_y,V_x] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom, % 154.47/154.47 ! [V_z] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom, % 154.47/154.47 ! [V_P_2] : % 154.47/154.47 ( ? [B_x] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 154.47/154.47 & hBOOL(hAPP(V_P_2,B_x)) ) % 154.47/154.47 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom, % 154.47/154.47 ! [V_P_2] : % 154.47/154.47 ( ! [B_x] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 154.47/154.47 => hBOOL(hAPP(V_P_2,B_x)) ) % 154.47/154.47 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom, % 154.47/154.47 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ord_OatMost__iff,axiom, % 154.47/154.47 ! [V_k_2,V_less__eq_2,V_i_2,T_a] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ord_OatLeast__iff,axiom, % 154.47/154.47 ! [V_k_2,V_less__eq_2,V_i_2,T_a] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ord_OlessThan__iff,axiom, % 154.47/154.47 ! [V_k_2,V_less_2,V_i_2,T_a] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_tsub__def,axiom, % 154.47/154.47 ! [V_x,V_y] : % 154.47/154.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 154.47/154.47 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) % 154.47/154.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 154.47/154.47 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_image__minus__const__atLeastLessThan__nat,axiom, % 154.47/154.47 ! [V_x_2,V_y_2,V_c_2] : % 154.47/154.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2)) % 154.47/154.47 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_c_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_c_2)) ) % 154.47/154.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2)) % 154.47/154.47 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 154.47/154.47 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) % 154.47/154.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 154.47/154.47 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_Powp__mono,axiom, % 154.47/154.47 ! [V_B_2,V_A_2,T_a] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_a,V_A_2)),c_Predicate_OPowp(T_a,V_B_2))) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_finite__atLeastLessThan,axiom, % 154.47/154.47 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_infinite__UNIV__int,axiom, % 154.47/154.47 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastLessThan__inj_I2_J,axiom, % 154.47/154.47 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 154.47/154.47 ( class_Orderings_Olinorder(T_a) % 154.47/154.47 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2)) % 154.47/154.47 => V_b_2 = V_d_2 ) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastLessThan__inj_I1_J,axiom, % 154.47/154.47 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 154.47/154.47 ( class_Orderings_Olinorder(T_a) % 154.47/154.47 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2)) % 154.47/154.47 => V_a_2 = V_c_2 ) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastLessThan__eq__iff,axiom, % 154.47/154.47 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 154.47/154.47 ( class_Orderings_Olinorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2)) % 154.47/154.47 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2) % 154.47/154.47 <=> ( V_a_2 = V_c_2 % 154.47/154.47 & V_b_2 = V_d_2 ) ) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastLessThan__add__Un,axiom, % 154.47/154.47 ! [V_k_2,V_j_2,V_i_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 154.47/154.47 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2))) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastLessThan0,axiom, % 154.47/154.47 ! [V_m_2] : hAPP(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)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeast0LessThan,axiom, % 154.47/154.47 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) ). % 154.47/154.47 % 154.47/154.47 fof(fact_subset__card__intvl__is__intvl,axiom, % 154.47/154.47 ! [V_k_2,V_A_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2))))) % 154.47/154.47 => V_A_2 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2))) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_card__atLeastLessThan,axiom, % 154.47/154.47 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2) ). % 154.47/154.47 % 154.47/154.47 fof(fact_image__Suc__atLeastLessThan,axiom, % 154.47/154.47 ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2)),hAPP(c_Nat_OSuc,V_j_2)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastLessThan__empty,axiom, % 154.47/154.47 ! [V_a_2,V_b_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) % 154.47/154.47 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastLessThan__empty__iff2,axiom, % 154.47/154.47 ! [V_b_2,V_a_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) % 154.47/154.47 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastLessThan__empty__iff,axiom, % 154.47/154.47 ! [V_b_2,V_a_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.47 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastLessThan__subset__iff,axiom, % 154.47/154.47 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 154.47/154.47 ( class_Orderings_Olinorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2))) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) % 154.47/154.47 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_a_2)) % 154.47/154.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_setsum__shift__bounds__Suc__ivl,axiom, % 154.47/154.47 ! [V_n_2,V_m_2,V_f_2,T_a] : % 154.47/154.47 ( class_Groups_Ocomm__monoid__add(T_a) % 154.47/154.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__un_I17_J,axiom, % 154.47/154.47 ! [V_u_2,V_m_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Olinorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_setsum__shift__bounds__nat__ivl,axiom, % 154.47/154.47 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] : % 154.47/154.47 ( class_Groups_Ocomm__monoid__add(T_a) % 154.47/154.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(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))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(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))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__diff,axiom, % 154.47/154.47 ! [V_m_2,V_n_2,V_i_2,T_a] : % 154.47/154.47 ( class_Orderings_Olinorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_n_2)) % 154.47/154.47 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_n_2),V_m_2) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__int_I11_J,axiom, % 154.47/154.47 ! [V_u_2,V_m_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_image__add__atLeastLessThan,axiom, % 154.47/154.47 ! [V_j_2,V_i_2,V_k_2] : hAPP(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)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(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)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_setsum__add__nat__ivl,axiom, % 154.47/154.47 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] : % 154.47/154.47 ( class_Groups_Ocomm__monoid__add(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 154.47/154.47 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2)) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_setsum__diff__nat__ivl,axiom, % 154.47/154.47 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] : % 154.47/154.47 ( class_Groups_Oab__group__add(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 154.47/154.47 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2)) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastLessThan__singleton,axiom, % 154.47/154.47 ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_m_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_m_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_UN__UN__finite__eq,axiom, % 154.47/154.47 ! [V_A_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__un_I8_J,axiom, % 154.47/154.47 ! [V_u_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Olinorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__int_I2_J,axiom, % 154.47/154.47 ! [V_u_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom, % 154.47/154.47 ! [V_k_2,V_f_2,T_a] : % 154.47/154.47 ( class_Groups_Ocomm__monoid__add(T_a) % 154.47/154.47 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) % 154.47/154.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_setsum__head__upt__Suc,axiom, % 154.47/154.47 ! [V_f_2,V_n_2,V_m_2,T_a] : % 154.47/154.47 ( class_Groups_Ocomm__monoid__add(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 154.47/154.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(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)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2))) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastLessThanSuc,axiom, % 154.47/154.47 ! [V_n_2,V_m_2] : % 154.47/154.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 154.47/154.47 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_n_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) % 154.47/154.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 154.47/154.47 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_setsum__op__ivl__Suc,axiom, % 154.47/154.47 ! [V_f_2,V_m_2,V_n_2,T_a] : % 154.47/154.47 ( class_Groups_Ocomm__monoid__add(T_a) % 154.47/154.47 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 154.47/154.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(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) ) % 154.47/154.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 154.47/154.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(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),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(V_f_2,V_n_2)) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom, % 154.47/154.47 ! [V_y,V_x] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(V_x,V_y))) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_tsub__eq,axiom, % 154.47/154.47 ! [V_x,V_y] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 154.47/154.47 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom, % 154.47/154.47 ! [V_y,V_x] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x),V_y)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_all__nat__less__eq,axiom, % 154.47/154.47 ! [V_P_2,V_n_2] : % 154.47/154.47 ( ! [B_m] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 154.47/154.47 => hBOOL(hAPP(V_P_2,B_m)) ) % 154.47/154.47 <=> ! [B_x] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) % 154.47/154.47 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ex__nat__less__eq,axiom, % 154.47/154.47 ! [V_P_2,V_n_2] : % 154.47/154.47 ( ? [B_m] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 154.47/154.47 & hBOOL(hAPP(V_P_2,B_m)) ) % 154.47/154.47 <=> ? [B_x] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) % 154.47/154.47 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_UN__finite2__subset,axiom, % 154.47/154.47 ! [V_B_2,V_k_2,V_A_2,T_a] : % 154.47/154.47 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2))) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2))) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_UN__finite2__eq,axiom, % 154.47/154.47 ! [V_B_2,V_k_2,V_A_2,T_a] : % 154.47/154.47 ( ! [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2) % 154.47/154.47 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_UN__finite__subset,axiom, % 154.47/154.47 ! [V_C_2,V_A_2,T_a] : % 154.47/154.47 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),V_C_2)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),V_C_2)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__un_I3_J,axiom, % 154.47/154.47 ! [V_u_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Olinorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_finite__greaterThanLessThan,axiom, % 154.47/154.47 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_finite__atLeastLessThan__int,axiom, % 154.47/154.47 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_finite__greaterThanLessThan__int,axiom, % 154.47/154.47 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom, % 154.47/154.47 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2) ). % 154.47/154.47 % 154.47/154.47 fof(fact_finite__atLeastZeroLessThan__int,axiom, % 154.47/154.47 ! [V_u_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_greaterThanLessThan__empty,axiom, % 154.47/154.47 ! [V_k_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2)) % 154.47/154.47 => c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom, % 154.47/154.47 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2) ). % 154.47/154.47 % 154.47/154.47 fof(fact_image__add__int__atLeastLessThan,axiom, % 154.47/154.47 ! [V_u_2,V_l_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__int_I9_J,axiom, % 154.47/154.47 ! [V_u_2,V_m_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_card__greaterThanLessThan,axiom, % 154.47/154.47 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),hAPP(c_Nat_OSuc,V_l_2)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__un_I15_J,axiom, % 154.47/154.47 ! [V_u_2,V_m_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Olinorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__un_I4_J,axiom, % 154.47/154.47 ! [V_u_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Olinorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_setsum__nonneg__0,axiom, % 154.47/154.47 ! [V_i_2,V_f_2,V_s_2,T_a,T_b] : % 154.47/154.47 ( class_Groups_Oordered__ab__group__add(T_b) % 154.47/154.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 154.47/154.47 => ( ! [B_i] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) ) % 154.47/154.47 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = c_Groups_Ozero__class_Ozero(T_b) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2)) % 154.47/154.47 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_setsum__nonneg__leq__bound,axiom, % 154.47/154.47 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_a,T_b] : % 154.47/154.47 ( class_Groups_Oordered__ab__group__add(T_b) % 154.47/154.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 154.47/154.47 => ( ! [B_i] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) ) % 154.47/154.47 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = V_B_2 % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2)) % 154.47/154.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_greaterThan__0,axiom, % 154.47/154.47 hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(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))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_sum__diff__distrib,axiom, % 154.47/154.47 ! [V_n_2,V_P_2,V_Q_2] : % 154.47/154.47 ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Q_2,B_x)),hAPP(V_P_2,B_x))) % 154.47/154.47 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_P_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Q_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_P_2)),V_Q_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_setsum__natinterval__difff,axiom, % 154.47/154.47 ! [V_f_2,V_n_2,V_m_2,T_a] : % 154.47/154.47 ( class_Groups_Oab__group__add(T_a) % 154.47/154.47 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 154.47/154.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),hAPP(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)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) % 154.47/154.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 154.47/154.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),hAPP(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)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_finite__greaterThanAtMost,axiom, % 154.47/154.47 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_finite__greaterThanAtMost__int,axiom, % 154.47/154.47 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_finite__atLeastAtMost,axiom, % 154.47/154.47 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_greaterThan__eq__iff,axiom, % 154.47/154.47 ! [V_y_2,V_x_2,T_a] : % 154.47/154.47 ( class_Orderings_Olinorder(T_a) % 154.47/154.47 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2) % 154.47/154.47 <=> V_x_2 = V_y_2 ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom, % 154.47/154.47 ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__un_I22_J,axiom, % 154.47/154.47 ! [V_u_2,V_m_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Olinorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__int_I16_J,axiom, % 154.47/154.47 ! [V_u_2,V_m_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__int_I7_J,axiom, % 154.47/154.47 ! [V_u_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__un_I11_J,axiom, % 154.47/154.47 ! [V_u_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Olinorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__int_I5_J,axiom, % 154.47/154.47 ! [V_u_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_setsum__head,axiom, % 154.47/154.47 ! [V_P_2,V_n_2,V_m_2,T_a] : % 154.47/154.47 ( class_Groups_Ocomm__monoid__add(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 154.47/154.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_P_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(V_P_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_P_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_all__nat__less,axiom, % 154.47/154.47 ! [V_P_2,V_n_2] : % 154.47/154.47 ( ! [B_m] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 154.47/154.47 => hBOOL(hAPP(V_P_2,B_m)) ) % 154.47/154.47 <=> ! [B_x] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) % 154.47/154.47 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ex__nat__less,axiom, % 154.47/154.47 ! [V_P_2,V_n_2] : % 154.47/154.47 ( ? [B_m] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 154.47/154.47 & hBOOL(hAPP(V_P_2,B_m)) ) % 154.47/154.47 <=> ? [B_x] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) % 154.47/154.47 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom, % 154.47/154.47 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),hAPP(c_Nat_OSuc,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__un_I5_J,axiom, % 154.47/154.47 ! [V_u_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Olinorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastatMost__empty__iff,axiom, % 154.47/154.47 ! [V_b_2,V_a_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.47 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastatMost__empty__iff2,axiom, % 154.47/154.47 ! [V_b_2,V_a_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) % 154.47/154.47 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastatMost__empty,axiom, % 154.47/154.47 ! [V_a_2,V_b_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) % 154.47/154.47 => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastatMost__subset__iff,axiom, % 154.47/154.47 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2))) % 154.47/154.47 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 154.47/154.47 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_a_2)) % 154.47/154.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastAtMost__singleton,axiom, % 154.47/154.47 ! [V_a_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastAtMost__singleton__iff,axiom, % 154.47/154.47 ! [V_c_2,V_b_2,V_a_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) % 154.47/154.47 <=> ( V_a_2 = V_b_2 % 154.47/154.47 & V_b_2 = V_c_2 ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastAtMost__singleton_H,axiom, % 154.47/154.47 ! [V_b_2,V_a_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => ( V_a_2 = V_b_2 % 154.47/154.47 => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__un_I19_J,axiom, % 154.47/154.47 ! [V_u_2,V_m_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Olinorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_image__Suc__atLeastAtMost,axiom, % 154.47/154.47 ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2),hAPP(c_Nat_OSuc,V_j_2)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom, % 154.47/154.47 ! [V_n_2,V_m_2,V_f_2,T_a] : % 154.47/154.47 ( class_Groups_Ocomm__monoid__add(T_a) % 154.47/154.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom, % 154.47/154.47 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] : % 154.47/154.47 ( class_Groups_Ocomm__monoid__add(T_a) % 154.47/154.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(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))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(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_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_greaterThanAtMost__empty,axiom, % 154.47/154.47 ! [V_k_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2)) % 154.47/154.47 => c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_greaterThanAtMost__empty__iff2,axiom, % 154.47/154.47 ! [V_l_2,V_k_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) % 154.47/154.47 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_greaterThanAtMost__empty__iff,axiom, % 154.47/154.47 ! [V_l_2,V_k_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.47 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__un_I20_J,axiom, % 154.47/154.47 ! [V_u_2,V_m_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Olinorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__int_I14_J,axiom, % 154.47/154.47 ! [V_u_2,V_m_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_image__add__atLeastAtMost,axiom, % 154.47/154.47 ! [V_j_2,V_i_2,V_k_2] : hAPP(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_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(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)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_card__greaterThanAtMost,axiom, % 154.47/154.47 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2) ). % 154.47/154.47 % 154.47/154.47 fof(fact_greaterThan__iff,axiom, % 154.47/154.47 ! [V_k_2,V_i_2,T_a] : % 154.47/154.47 ( class_Orderings_Oord(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_i_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_greaterThan__subset__iff,axiom, % 154.47/154.47 ! [V_y_2,V_x_2,T_a] : % 154.47/154.47 ( class_Orderings_Olinorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_card__atLeastAtMost,axiom, % 154.47/154.47 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_u_2)),V_l_2) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastAtMostSuc__conv,axiom, % 154.47/154.47 ! [V_n_2,V_m_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 154.47/154.47 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_setsum__shift__lb__Suc0__0,axiom, % 154.47/154.47 ! [V_k_2,V_f_2] : % 154.47/154.47 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.47/154.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__un_I21_J,axiom, % 154.47/154.47 ! [V_u_2,V_m_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Olinorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__int_I15_J,axiom, % 154.47/154.47 ! [V_u_2,V_m_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastatMost__psubset__iff,axiom, % 154.47/154.47 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2))) % 154.47/154.47 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 154.47/154.47 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_a_2)) % 154.47/154.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) % 154.47/154.47 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_a_2)) % 154.47/154.47 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_d_2)) ) ) ) % 154.47/154.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_d_2)) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__int_I4_J,axiom, % 154.47/154.47 ! [V_u_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__int_I12_J,axiom, % 154.47/154.47 ! [V_u_2,V_m_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__int_I13_J,axiom, % 154.47/154.47 ! [V_u_2,V_m_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_INT__greaterThan__UNIV,axiom, % 154.47/154.47 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_setsum__head__Suc,axiom, % 154.47/154.47 ! [V_f_2,V_n_2,V_m_2,T_a] : % 154.47/154.47 ( class_Groups_Ocomm__monoid__add(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 154.47/154.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(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)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__int_I10_J,axiom, % 154.47/154.47 ! [V_u_2,V_m_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_greaterThan__Suc,axiom, % 154.47/154.47 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_setsum__cl__ivl__Suc,axiom, % 154.47/154.47 ! [V_f_2,V_m_2,V_n_2,T_a] : % 154.47/154.47 ( class_Groups_Ocomm__monoid__add(T_a) % 154.47/154.47 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 154.47/154.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_a) ) % 154.47/154.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 154.47/154.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_setsum__ub__add__nat,axiom, % 154.47/154.47 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_a] : % 154.47/154.47 ( class_Groups_Ocomm__monoid__add(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) % 154.47/154.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2)))) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__un_I16_J,axiom, % 154.47/154.47 ! [V_u_2,V_m_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Olinorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2)) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__un_I6_J,axiom, % 154.47/154.47 ! [V_u_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Olinorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__un_I18_J,axiom, % 154.47/154.47 ! [V_u_2,V_m_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Olinorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2)) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_gauss__sum,axiom, % 154.47/154.47 ! [V_n_2,T_a] : % 154.47/154.47 ( class_Rings_Ocomm__semiring__1(T_a) % 154.47/154.47 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),c_Nat_Osemiring__1__class_Oof__nat(T_a)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Groups_Oone__class_Oone(T_a))) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_UN__le__eq__Un0,axiom, % 154.47/154.47 ! [V_M_2,V_n_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2)),V_M_2)),hAPP(V_M_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_image__atLeastZeroLessThan__int,axiom, % 154.47/154.47 ! [V_u_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) % 154.47/154.47 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,V_u_2))) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__un_I12_J,axiom, % 154.47/154.47 ! [V_u_2,V_l_2,T_a] : % 154.47/154.47 ( class_Orderings_Olinorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_decr__mult__lemma,axiom, % 154.47/154.47 ! [V_k_2,V_P_2,V_d_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 154.47/154.47 => ( ! [B_x] : % 154.47/154.47 ( hBOOL(hAPP(V_P_2,B_x)) % 154.47/154.47 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) ) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 154.47/154.47 => ! [B_x] : % 154.47/154.47 ( hBOOL(hAPP(V_P_2,B_x)) % 154.47/154.47 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_hom__fold1__commute,axiom, % 154.47/154.47 ! [V_N_2,V_h_2,T_a] : % 154.47/154.47 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 154.47/154.47 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),B_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 154.47/154.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 154.47/154.47 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.47/154.47 => hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_incr__mult__lemma,axiom, % 154.47/154.47 ! [V_k_2,V_P_2,V_d_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 154.47/154.47 => ( ! [B_x] : % 154.47/154.47 ( hBOOL(hAPP(V_P_2,B_x)) % 154.47/154.47 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) ) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 154.47/154.47 => ! [B_x] : % 154.47/154.47 ( hBOOL(hAPP(V_P_2,B_x)) % 154.47/154.47 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_finite__atLeastAtMost__int,axiom, % 154.47/154.47 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_finite__atMost,axiom, % 154.47/154.47 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom, % 154.47/154.47 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeast__eq__iff,axiom, % 154.47/154.47 ! [V_y_2,V_x_2,T_a] : % 154.47/154.47 ( class_Orderings_Olinorder(T_a) % 154.47/154.47 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2) % 154.47/154.47 <=> V_x_2 = V_y_2 ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atMost__eq__iff,axiom, % 154.47/154.47 ! [V_y_2,V_x_2,T_a] : % 154.47/154.47 ( class_Orderings_Olinorder(T_a) % 154.47/154.47 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2) % 154.47/154.47 <=> V_x_2 = V_y_2 ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom, % 154.47/154.47 ! [V_n_2,V_m_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_nat__int,axiom, % 154.47/154.47 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ). % 154.47/154.47 % 154.47/154.47 fof(fact_transfer__nat__int__numerals_I1_J,axiom, % 154.47/154.47 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_nat__0,axiom, % 154.47/154.47 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ex__nat,axiom, % 154.47/154.47 ! [V_P_2] : % 154.47/154.47 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 154.47/154.47 <=> ? [B_x] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 154.47/154.47 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_all__nat,axiom, % 154.47/154.47 ! [V_P_2] : % 154.47/154.47 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 154.47/154.47 <=> ! [B_x] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 154.47/154.47 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_transfer__nat__int__relations_I1_J,axiom, % 154.47/154.47 ! [V_y_2,V_x_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 154.47/154.47 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2) % 154.47/154.47 <=> V_x_2 = V_y_2 ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_eq__nat__nat__iff,axiom, % 154.47/154.47 ! [V_z_H_2,V_z_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2)) % 154.47/154.47 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2) % 154.47/154.47 <=> V_z_2 = V_z_H_2 ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom, % 154.47/154.47 ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2) ). % 154.47/154.47 % 154.47/154.47 fof(fact_card__atLeastAtMost__int,axiom, % 154.47/154.47 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_transfer__nat__int__numerals_I2_J,axiom, % 154.47/154.47 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atMost__Int__atLeast,axiom, % 154.47/154.47 ! [V_n_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_transfer__int__nat__set__return__embed,axiom, % 154.47/154.47 ! [V_A_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) = V_A_2 ). % 154.47/154.47 % 154.47/154.47 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom, % 154.47/154.47 ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_card__greaterThanAtMost__int,axiom, % 154.47/154.47 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeast0AtMost,axiom, % 154.47/154.47 ! [V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) ). % 154.47/154.47 % 154.47/154.47 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom, % 154.47/154.47 c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_lessThan__Suc__atMost,axiom, % 154.47/154.47 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2) ). % 154.47/154.47 % 154.47/154.47 fof(fact_card__atMost,axiom, % 154.47/154.47 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_u_2)) = hAPP(c_Nat_OSuc,V_u_2) ). % 154.47/154.47 % 154.47/154.47 fof(fact_nat__0__iff,axiom, % 154.47/154.47 ! [V_i_2] : % 154.47/154.47 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_nat__le__0,axiom, % 154.47/154.47 ! [V_z] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.47/154.47 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zless__nat__conj,axiom, % 154.47/154.47 ! [V_z_2,V_w_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) % 154.47/154.47 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 154.47/154.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_nat__mono__iff,axiom, % 154.47/154.47 ! [V_w_2,V_z_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atMost__Suc,axiom, % 154.47/154.47 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeast__iff,axiom, % 154.47/154.47 ! [V_k_2,V_i_2,T_a] : % 154.47/154.47 ( class_Orderings_Oord(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_k_2),V_i_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atMost__iff,axiom, % 154.47/154.47 ! [V_k_2,V_i_2,T_a] : % 154.47/154.47 ( class_Orderings_Oord(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_k_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_transfer__nat__int__relations_I3_J,axiom, % 154.47/154.47 ! [V_y_2,V_x_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_nat__1,axiom, % 154.47/154.47 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_nat__0__le,axiom, % 154.47/154.47 ! [V_z] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 154.47/154.47 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_int__eq__iff,axiom, % 154.47/154.47 ! [V_z_2,V_m_2] : % 154.47/154.47 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2 % 154.47/154.47 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2) % 154.47/154.47 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_int__nat__eq,axiom, % 154.47/154.47 ! [V_z] : % 154.47/154.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 154.47/154.47 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) % 154.47/154.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 154.47/154.47 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zless__nat__eq__int__zless,axiom, % 154.47/154.47 ! [V_z_2,V_m_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atMost__subset__iff,axiom, % 154.47/154.47 ! [V_y_2,V_x_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeast__subset__iff,axiom, % 154.47/154.47 ! [V_y_2,V_x_2,T_a] : % 154.47/154.47 ( class_Orderings_Oorder(T_a) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeast__0,axiom, % 154.47/154.47 hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom, % 154.47/154.47 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_u_2),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atLeast__Suc__greaterThan,axiom, % 154.47/154.47 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2) ). % 154.47/154.47 % 154.47/154.47 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom, % 154.47/154.47 ! [V_A_2,V_f_2,T_a] : % 154.47/154.47 ( ( class_Groups_Ocomm__monoid__add(T_a) % 154.47/154.47 & class_Groups_Ocomm__monoid__mult(T_a) ) % 154.47/154.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_card__atLeastZeroLessThan__int,axiom, % 154.47/154.47 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) = hAPP(c_Int_Onat,V_u_2) ). % 154.47/154.47 % 154.47/154.47 fof(fact_card__atLeastLessThan__int,axiom, % 154.47/154.47 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_zero__less__nat__eq,axiom, % 154.47/154.47 ! [V_z_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,V_z_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_transfer__nat__int__relations_I2_J,axiom, % 154.47/154.47 ! [V_y_2,V_x_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_nat__less__eq__zless,axiom, % 154.47/154.47 ! [V_z_2,V_w_2] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_nat__eq__iff2,axiom, % 154.47/154.47 ! [V_w_2,V_m_2] : % 154.47/154.47 ( V_m_2 = hAPP(c_Int_Onat,V_w_2) % 154.47/154.47 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 154.47/154.47 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 154.47/154.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 154.47/154.47 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_nat__eq__iff,axiom, % 154.47/154.47 ! [V_m_2,V_w_2] : % 154.47/154.47 ( hAPP(c_Int_Onat,V_w_2) = V_m_2 % 154.47/154.47 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 154.47/154.47 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 154.47/154.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 154.47/154.47 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_nat__le__eq__zle,axiom, % 154.47/154.47 ! [V_z_2,V_w_2] : % 154.47/154.47 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 154.47/154.47 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) % 154.47/154.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_split__nat,axiom, % 154.47/154.47 ! [V_i_2,V_P_2] : % 154.47/154.47 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2))) % 154.47/154.47 <=> ( ! [B_n] : % 154.47/154.47 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) % 154.47/154.47 => hBOOL(hAPP(V_P_2,B_n)) ) % 154.47/154.47 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.47/154.47 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom, % 154.47/154.47 ! [V_y,V_x] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 154.47/154.47 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_nat__add__distrib,axiom, % 154.47/154.47 ! [V_z_H,V_z] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 154.47/154.47 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom, % 154.47/154.47 ! [V_y,V_x] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 154.47/154.47 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_nat__mult__distrib,axiom, % 154.47/154.47 ! [V_z_H,V_z] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 154.47/154.47 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom, % 154.47/154.47 ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_nat__diff__distrib,axiom, % 154.47/154.47 ! [V_z,V_z_H] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 154.47/154.47 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom, % 154.47/154.47 ! [V_A_2,V_f_2,T_a] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_UN__atMost__UNIV,axiom, % 154.47/154.47 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 154.47/154.47 % 154.47/154.47 fof(fact_setsum__atMost__Suc,axiom, % 154.47/154.47 ! [V_n_2,V_f_2,T_a] : % 154.47/154.47 ( class_Groups_Ocomm__monoid__add(T_a) % 154.47/154.47 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_atMost__0,axiom, % 154.47/154.47 hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 154.47/154.47 % 154.47/154.47 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom, % 154.47/154.47 ! [V_y,V_x] : % 154.47/154.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 154.47/154.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 154.47/154.47 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 154.47/154.47 % 154.47/154.47 fof(fact_ivl__disj__un_I14_J,axiom, % 154.47/154.47 ! [V_u_2,V_l_2,T_a] : % 154.47/154.48 ( class_Orderings_Olinorder(T_a) % 154.47/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 154.47/154.48 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2) ) ) ). % 154.47/154.48 % 154.47/154.48 fof(fact_simp__from__to,axiom, % 154.47/154.48 ! [V_i_2,V_j_2] : % 154.47/154.48 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 154.47/154.48 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) ) % 154.47/154.48 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 154.47/154.48 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),V_i_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ) ) ). % 154.47/154.48 % 154.47/154.48 fof(fact_ivl__disj__int_I8_J,axiom, % 154.47/154.48 ! [V_u_2,V_l_2,T_a] : % 154.47/154.48 ( class_Orderings_Oorder(T_a) % 154.47/154.48 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.47/154.48 % 154.47/154.48 fof(fact_UN__atLeast__UNIV,axiom, % 154.47/154.48 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 154.47/154.48 % 154.47/154.48 fof(fact_ivl__disj__un_I9_J,axiom, % 154.47/154.48 ! [V_u_2,V_l_2,T_a] : % 154.47/154.48 ( class_Orderings_Olinorder(T_a) % 154.47/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 154.47/154.48 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2) ) ) ). % 154.47/154.48 % 154.47/154.48 fof(fact_UN__le__add__shift,axiom, % 154.47/154.48 ! [V_k_2,V_M_2,V_n_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool),tc_Nat_Onat),V_M_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))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_k_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))),V_M_2) ). % 154.47/154.48 % 154.47/154.48 fof(fact_ivl__disj__int_I3_J,axiom, % 154.47/154.48 ! [V_u_2,V_l_2,T_a] : % 154.47/154.48 ( class_Orderings_Oorder(T_a) % 154.47/154.48 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.47/154.48 % 154.47/154.48 fof(fact_ivl__disj__int_I6_J,axiom, % 154.47/154.48 ! [V_u_2,V_l_2,T_a] : % 154.47/154.48 ( class_Orderings_Oorder(T_a) % 154.47/154.48 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_ivl__disj__int_I1_J,axiom, % 154.70/154.48 ! [V_u_2,V_l_2,T_a] : % 154.70/154.48 ( class_Orderings_Oorder(T_a) % 154.70/154.48 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_atLeast__Suc,axiom, % 154.70/154.48 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_one__less__nat__eq,axiom, % 154.70/154.48 ! [V_z_2] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,V_z_2))) % 154.70/154.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_nat__less__iff,axiom, % 154.70/154.48 ! [V_m_2,V_w_2] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2)) % 154.70/154.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Suc__nat__eq__nat__zadd1,axiom, % 154.70/154.48 ! [V_z] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 154.70/154.48 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_card__greaterThanLessThan__int,axiom, % 154.70/154.48 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_ivl__disj__un_I2_J,axiom, % 154.70/154.48 ! [V_u_2,T_a] : % 154.70/154.48 ( class_Orderings_Olinorder(T_a) % 154.70/154.48 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_ivl__disj__un_I10_J,axiom, % 154.70/154.48 ! [V_u_2,V_l_2,T_a] : % 154.70/154.48 ( class_Orderings_Olinorder(T_a) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 154.70/154.48 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_ivl__disj__un_I1_J,axiom, % 154.70/154.48 ! [V_l_2,T_a] : % 154.70/154.48 ( class_Orderings_Olinorder(T_a) % 154.70/154.48 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_ivl__disj__un_I13_J,axiom, % 154.70/154.48 ! [V_u_2,V_l_2,T_a] : % 154.70/154.48 ( class_Orderings_Olinorder(T_a) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 154.70/154.48 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_ivl__disj__un_I7_J,axiom, % 154.70/154.48 ! [V_u_2,V_l_2,T_a] : % 154.70/154.48 ( class_Orderings_Olinorder(T_a) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 154.70/154.48 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_nat__aux__def,axiom, % 154.70/154.48 ! [V_n,V_i] : c_Int_Onat__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_i)),V_n) ). % 154.70/154.48 % 154.70/154.48 fof(fact_transfer__morphism__nat__int,axiom, % 154.70/154.48 c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_aset_I6_J,axiom, % 154.70/154.48 ! [V_A_2,V_t_2,V_D_2] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2)) % 154.70/154.48 => ! [B_x] : % 154.70/154.48 ( ! [B_xa] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 154.70/154.48 => ! [B_xb] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 154.70/154.48 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_bset_I8_J,axiom, % 154.70/154.48 ! [V_B_2,V_t_2,V_D_2] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2)) % 154.70/154.48 => ! [B_x] : % 154.70/154.48 ( ! [B_xa] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 154.70/154.48 => ! [B_xb] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 154.70/154.48 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_aset_I4_J,axiom, % 154.70/154.48 ! [V_A_2,V_t_2,V_D_2] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 154.70/154.48 => ! [B_x] : % 154.70/154.48 ( ! [B_xa] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 154.70/154.48 => ! [B_xb] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 154.70/154.48 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 154.70/154.48 => ( B_x != V_t_2 % 154.70/154.48 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_bset_I4_J,axiom, % 154.70/154.48 ! [V_B_2,V_t_2,V_D_2] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 154.70/154.48 => ! [B_x] : % 154.70/154.48 ( ! [B_xa] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 154.70/154.48 => ! [B_xb] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 154.70/154.48 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 154.70/154.48 => ( B_x != V_t_2 % 154.70/154.48 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom, % 154.70/154.48 ! [V_B_2,V_A_2] : % 154.70/154.48 ( c_Nat__Transfer_Onat__set(V_A_2) % 154.70/154.48 => ( c_Nat__Transfer_Onat__set(V_B_2) % 154.70/154.48 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom, % 154.70/154.48 ! [V_B_2,V_A_2] : % 154.70/154.48 ( c_Nat__Transfer_Onat__set(V_A_2) % 154.70/154.48 => ( c_Nat__Transfer_Onat__set(V_B_2) % 154.70/154.48 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_bset_I3_J,axiom, % 154.70/154.48 ! [V_B_2,V_t_2,V_D_2] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2)) % 154.70/154.48 => ( ! [B_x] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 154.70/154.48 => ! [B_xa] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2)) % 154.70/154.48 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) ) % 154.70/154.48 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_aset_I3_J,axiom, % 154.70/154.48 ! [V_A_2,V_t_2,V_D_2] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2)) % 154.70/154.48 => ( ! [B_x] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 154.70/154.48 => ! [B_xa] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2)) % 154.70/154.48 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) ) % 154.70/154.48 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_aset_I5_J,axiom, % 154.70/154.48 ! [V_A_2,V_t_2,V_D_2] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 154.70/154.48 => ! [B_x] : % 154.70/154.48 ( ! [B_xa] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 154.70/154.48 => ! [B_xb] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 154.70/154.48 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom, % 154.70/154.48 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom, % 154.70/154.48 ! [V_B_2,V_A_2] : % 154.70/154.48 ( c_Nat__Transfer_Onat__set(V_A_2) % 154.70/154.48 => ( c_Nat__Transfer_Onat__set(V_B_2) % 154.70/154.48 => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom, % 154.70/154.48 ! [V_B_2,V_A_2] : % 154.70/154.48 ( c_Nat__Transfer_Onat__set(V_A_2) % 154.70/154.48 => ( c_Nat__Transfer_Onat__set(V_B_2) % 154.70/154.48 => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_nat__set__def,axiom, % 154.70/154.48 ! [V_S_2] : % 154.70/154.48 ( c_Nat__Transfer_Onat__set(V_S_2) % 154.70/154.48 <=> ! [B_x] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom, % 154.70/154.48 ! [V_C_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_C_2)) ). % 154.70/154.48 % 154.70/154.48 fof(fact_transfer__int__nat__set__relations_I3_J,axiom, % 154.70/154.48 ! [V_B_2,V_A_2] : % 154.70/154.48 ( c_Nat__Transfer_Onat__set(V_A_2) % 154.70/154.48 => ( c_Nat__Transfer_Onat__set(V_B_2) % 154.70/154.48 => ( V_A_2 = V_B_2 % 154.70/154.48 <=> hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom, % 154.70/154.48 ! [V_y_2,V_x_2] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 154.70/154.48 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom, % 154.70/154.48 ! [V_x_2,V_A_2] : % 154.70/154.48 ( c_Nat__Transfer_Onat__set(V_A_2) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_transfer__nat__int__set__return__embed,axiom, % 154.70/154.48 ! [V_A_2] : % 154.70/154.48 ( c_Nat__Transfer_Onat__set(V_A_2) % 154.70/154.48 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) = V_A_2 ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_transfer__int__nat__set__relations_I1_J,axiom, % 154.70/154.48 ! [V_A_2] : % 154.70/154.48 ( c_Nat__Transfer_Onat__set(V_A_2) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2)) % 154.70/154.48 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom, % 154.70/154.48 ! [V_A_2] : % 154.70/154.48 ( c_Nat__Transfer_Onat__set(V_A_2) % 154.70/154.48 => hAPP(c_Finite__Set_Ocard(tc_Int_Oint),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_transfer__int__nat__set__relations_I5_J,axiom, % 154.70/154.48 ! [V_B_2,V_A_2] : % 154.70/154.48 ( c_Nat__Transfer_Onat__set(V_A_2) % 154.70/154.48 => ( c_Nat__Transfer_Onat__set(V_B_2) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.70/154.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_transfer__int__nat__set__relations_I4_J,axiom, % 154.70/154.48 ! [V_B_2,V_A_2] : % 154.70/154.48 ( c_Nat__Transfer_Onat__set(V_A_2) % 154.70/154.48 => ( c_Nat__Transfer_Onat__set(V_B_2) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.70/154.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom, % 154.70/154.48 ! [V_f_2,V_A_2,T_a] : % 154.70/154.48 ( ( class_Groups_Ocomm__monoid__add(T_a) % 154.70/154.48 & class_Groups_Ocomm__monoid__mult(T_a) ) % 154.70/154.48 => ( c_Nat__Transfer_Onat__set(V_A_2) % 154.70/154.48 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_bset_I7_J,axiom, % 154.70/154.48 ! [V_B_2,V_t_2,V_D_2] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 154.70/154.48 => ! [B_x] : % 154.70/154.48 ( ! [B_xa] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 154.70/154.48 => ! [B_xb] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 154.70/154.48 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_aset_I8_J,axiom, % 154.70/154.48 ! [V_t_2,V_A_2,V_D_2] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 154.70/154.48 => ! [B_x] : % 154.70/154.48 ( ! [B_xa] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 154.70/154.48 => ! [B_xb] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 154.70/154.48 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_bset_I6_J,axiom, % 154.70/154.48 ! [V_t_2,V_B_2,V_D_2] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 154.70/154.48 => ! [B_x] : % 154.70/154.48 ( ! [B_xa] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 154.70/154.48 => ! [B_xb] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 154.70/154.48 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_transfer__int__nat__set__relations_I2_J,axiom, % 154.70/154.48 ! [V_A_2,V_x_2] : % 154.70/154.48 ( c_Nat__Transfer_Ois__nat(V_x_2) % 154.70/154.48 => ( c_Nat__Transfer_Onat__set(V_A_2) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 154.70/154.48 <=> hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_periodic__finite__ex,axiom, % 154.70/154.48 ! [V_P_2,V_d_2] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 154.70/154.48 => ( ! [B_x,B_k] : % 154.70/154.48 ( hBOOL(hAPP(V_P_2,B_x)) % 154.70/154.48 <=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2)))) ) % 154.70/154.48 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 154.70/154.48 <=> ? [B_x] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_d_2))) % 154.70/154.48 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom, % 154.70/154.48 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom, % 154.70/154.48 ! [V_y,V_x] : % 154.70/154.48 ( c_Nat__Transfer_Ois__nat(V_x) % 154.70/154.48 => ( c_Nat__Transfer_Ois__nat(V_y) % 154.70/154.48 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom, % 154.70/154.48 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom, % 154.70/154.48 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom, % 154.70/154.48 ! [V_y,V_x] : % 154.70/154.48 ( c_Nat__Transfer_Ois__nat(V_x) % 154.70/154.48 => ( c_Nat__Transfer_Ois__nat(V_y) % 154.70/154.48 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom, % 154.70/154.48 ! [V_y,V_x] : % 154.70/154.48 ( c_Nat__Transfer_Ois__nat(V_x) % 154.70/154.48 => ( c_Nat__Transfer_Ois__nat(V_y) % 154.70/154.48 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_is__nat__def,axiom, % 154.70/154.48 ! [V_x_2] : % 154.70/154.48 ( c_Nat__Transfer_Ois__nat(V_x_2) % 154.70/154.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom, % 154.70/154.48 ! [V_y_2,V_x_2] : % 154.70/154.48 ( c_Nat__Transfer_Ois__nat(V_x_2) % 154.70/154.48 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom, % 154.70/154.48 ! [V_x_2,V_A_2] : % 154.70/154.48 ( c_Nat__Transfer_Onat__set(V_A_2) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 154.70/154.48 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom, % 154.70/154.48 ! [V_n_2,V_m_2] : % 154.70/154.48 ( c_Nat__Transfer_Ois__nat(V_m_2) % 154.70/154.48 => ( c_Nat__Transfer_Ois__nat(V_n_2) % 154.70/154.48 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,V_m_2),hAPP(c_Int_Onat,V_n_2))) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom, % 154.70/154.48 ! [V_f_2,V_A_2,T_a] : % 154.70/154.48 ( ! [B_x] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.48 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 154.70/154.48 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_a),c_Int_Onat),V_f_2)),V_A_2)) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_aset_I7_J,axiom, % 154.70/154.48 ! [V_t_2,V_A_2,V_D_2] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 154.70/154.48 => ! [B_x] : % 154.70/154.48 ( ! [B_xa] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 154.70/154.48 => ! [B_xb] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 154.70/154.48 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_bset_I5_J,axiom, % 154.70/154.48 ! [V_t_2,V_B_2,V_D_2] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 154.70/154.48 => ! [B_x] : % 154.70/154.48 ( ! [B_xa] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 154.70/154.48 => ! [B_xb] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 154.70/154.48 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_ex__least__nat__less,axiom, % 154.70/154.48 ! [V_n_2,V_P_2] : % 154.70/154.48 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 154.70/154.48 => ( hBOOL(hAPP(V_P_2,V_n_2)) % 154.70/154.48 => ? [B_k] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) % 154.70/154.48 & ! [B_i] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) % 154.70/154.48 => ~ hBOOL(hAPP(V_P_2,B_i)) ) % 154.70/154.48 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_zero__less__imp__eq__int,axiom, % 154.70/154.48 ! [V_k] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 154.70/154.48 => ? [B_n] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 154.70/154.48 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_setsum__mono__zero__right,axiom, % 154.70/154.48 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 154.70/154.48 ( class_Groups_Ocomm__monoid__add(T_b) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 154.70/154.48 => ( ! [B_x] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2))) % 154.70/154.48 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 154.70/154.48 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_S_2) ) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_setsum__mono__zero__left,axiom, % 154.70/154.48 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 154.70/154.48 ( class_Groups_Ocomm__monoid__add(T_b) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 154.70/154.48 => ( ! [B_x] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2))) % 154.70/154.48 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 154.70/154.48 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_T_2) ) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_finite__subset__induct,axiom, % 154.70/154.48 ! [V_P_2,V_A_2,V_F_2,T_a] : % 154.70/154.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_A_2)) % 154.70/154.48 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 154.70/154.48 => ( ! [B_a,B_F] : % 154.70/154.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F)) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 154.70/154.48 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_F)) % 154.70/154.48 => ( hBOOL(hAPP(V_P_2,B_F)) % 154.70/154.48 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_F))) ) ) ) ) % 154.70/154.48 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__vimage__singleton,axiom, % 154.70/154.48 ! [V_a_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_a),c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_decr__lemma,axiom, % 154.70/154.48 ! [V_z,V_x,V_d] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))),V_z)) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__on__empty,axiom, % 154.70/154.48 ! [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))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_setsum__abs,axiom, % 154.70/154.48 ! [V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2))) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_setsum__abs__ge__zero,axiom, % 154.70/154.48 ! [V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2))) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__of__nat,axiom, % 154.70/154.48 ! [V_n,T_a] : % 154.70/154.48 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.48 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__le__D1,axiom, % 154.70/154.48 ! [V_b,V_a,T_a] : % 154.70/154.48 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__ge__self,axiom, % 154.70/154.48 ! [V_a,T_a] : % 154.70/154.48 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__eq__0,axiom, % 154.70/154.48 ! [V_a_2,T_a] : % 154.70/154.48 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.48 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.48 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__zero,axiom, % 154.70/154.48 ! [T_a] : % 154.70/154.48 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.48 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__fun,axiom, % 154.70/154.48 ! [T_c,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 154.70/154.48 => c_Fun_Oinj__on(T_a,tc_fun(T_c,T_b),hAPP(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))) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__on__contraD,axiom, % 154.70/154.48 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.48 => ( V_x_2 != V_y_2 % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 154.70/154.48 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__on__iff,axiom, % 154.70/154.48 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 154.70/154.48 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 154.70/154.48 <=> V_x_2 = V_y_2 ) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__onD,axiom, % 154.70/154.48 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.48 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 154.70/154.48 => V_x_2 = V_y_2 ) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__idempotent,axiom, % 154.70/154.48 ! [V_a,T_a] : % 154.70/154.48 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.48 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__on__def,axiom, % 154.70/154.48 ! [V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.48 <=> ! [B_x] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.48 => ! [B_xa] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 154.70/154.48 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) % 154.70/154.48 => B_x = B_xa ) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__on__id2,axiom, % 154.70/154.48 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__on__diff,axiom, % 154.70/154.48 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.48 => c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__one,axiom, % 154.70/154.48 ! [T_a] : % 154.70/154.48 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.48 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__minus__commute,axiom, % 154.70/154.48 ! [V_b,V_a,T_a] : % 154.70/154.48 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.48 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__on__imageI2,axiom, % 154.70/154.48 ! [V_A_2,V_f_2,V_f_H_2,T_c,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_H_2),V_f_2),V_A_2) % 154.70/154.48 => c_Fun_Oinj__on(T_a,T_c,V_f_2,V_A_2) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__on__Int,axiom, % 154.70/154.48 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.48 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 154.70/154.48 => c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__mult__self,axiom, % 154.70/154.48 ! [V_a,T_a] : % 154.70/154.48 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.48 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__mult,axiom, % 154.70/154.48 ! [V_b,V_a,T_a] : % 154.70/154.48 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.48 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__add__abs,axiom, % 154.70/154.48 ! [V_b,V_a,T_a] : % 154.70/154.48 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.48 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__eq,axiom, % 154.70/154.48 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 154.70/154.48 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 154.70/154.48 <=> V_x_2 = V_y_2 ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_injD,axiom, % 154.70/154.48 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 154.70/154.48 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 154.70/154.48 => V_x_2 = V_y_2 ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_subset__inj__on,axiom, % 154.70/154.48 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.70/154.48 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__Suc,axiom, % 154.70/154.48 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__int__eq,axiom, % 154.70/154.48 ! [V_m] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__on__add__nat,axiom, % 154.70/154.48 ! [V_N_2,V_k_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2),V_N_2) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__setsum__abs,axiom, % 154.70/154.48 ! [V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.48 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__ge__zero,axiom, % 154.70/154.48 ! [V_a,T_a] : % 154.70/154.48 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__le__zero__iff,axiom, % 154.70/154.48 ! [V_a_2,T_a] : % 154.70/154.48 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.48 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__of__nonneg,axiom, % 154.70/154.48 ! [V_a,T_a] : % 154.70/154.48 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.70/154.48 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__not__less__zero,axiom, % 154.70/154.48 ! [V_a,T_a] : % 154.70/154.48 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.48 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_zero__less__abs__iff,axiom, % 154.70/154.48 ! [V_a_2,T_a] : % 154.70/154.48 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2))) % 154.70/154.48 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__of__pos,axiom, % 154.70/154.48 ! [V_a,T_a] : % 154.70/154.48 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.70/154.48 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__triangle__ineq,axiom, % 154.70/154.48 ! [V_b,V_a,T_a] : % 154.70/154.48 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_finite__imageD,axiom, % 154.70/154.48 ! [V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 154.70/154.48 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) % 154.70/154.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__mult__less,axiom, % 154.70/154.48 ! [V_d,V_b,V_c,V_a,T_a] : % 154.70/154.48 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c)) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d)) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__triangle__ineq2__sym,axiom, % 154.70/154.48 ! [V_b,V_a,T_a] : % 154.70/154.48 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)))) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__triangle__ineq2,axiom, % 154.70/154.48 ! [V_b,V_a,T_a] : % 154.70/154.48 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__triangle__ineq3,axiom, % 154.70/154.48 ! [V_b,V_a,T_a] : % 154.70/154.48 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__image__eq__iff,axiom, % 154.70/154.48 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 154.70/154.48 => ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2) % 154.70/154.48 <=> V_A_2 = V_B_2 ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__on__Un__image__eq__iff,axiom, % 154.70/154.48 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.70/154.48 => ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2) % 154.70/154.48 <=> V_A_2 = V_B_2 ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_comp__inj__on__iff,axiom, % 154.70/154.48 ! [V_f_H_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.48 => ( c_Fun_Oinj__on(T_b,T_c,V_f_H_2,hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) % 154.70/154.48 <=> c_Fun_Oinj__on(T_a,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_f_H_2),V_f_2),V_A_2) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_comp__inj__on,axiom, % 154.70/154.48 ! [V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.48 => ( c_Fun_Oinj__on(T_b,T_c,V_g_2,hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) % 154.70/154.48 => c_Fun_Oinj__on(T_a,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_g_2),V_f_2),V_A_2) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__on__imageI,axiom, % 154.70/154.48 ! [V_A_2,V_f_2,V_g_2,T_c,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_g_2),V_f_2),V_A_2) % 154.70/154.48 => c_Fun_Oinj__on(T_c,T_b,V_g_2,hAPP(c_Set_Oimage(T_a,T_c,V_f_2),V_A_2)) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__comp,axiom, % 154.70/154.48 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 154.70/154.48 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 154.70/154.48 => c_Fun_Oinj__on(T_c,T_b,hAPP(c_Fun_Ocomp(T_a,T_b,T_c,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_card__image,axiom, % 154.70/154.48 ! [V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.48 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__on__strict__subset,axiom, % 154.70/154.48 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__zmult__eq__1,axiom, % 154.70/154.48 ! [V_n,V_m] : % 154.70/154.48 ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 154.70/154.48 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__of__nat,axiom, % 154.70/154.48 ! [T_a] : % 154.70/154.48 ( class_Nat_Osemiring__char__0(T_a) % 154.70/154.48 => c_Fun_Oinj__on(tc_Nat_Onat,T_a,c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__int,axiom, % 154.70/154.48 c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__image__mem__iff,axiom, % 154.70/154.48 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 154.70/154.48 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_range__ex1__eq,axiom, % 154.70/154.48 ! [V_b_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) % 154.70/154.48 <=> ? [B_x] : % 154.70/154.48 ( V_b_2 = hAPP(V_f_2,B_x) % 154.70/154.48 & ! [B_y] : % 154.70/154.48 ( V_b_2 = hAPP(V_f_2,B_y) % 154.70/154.48 => B_y = B_x ) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__mult__pos,axiom, % 154.70/154.48 ! [V_y,V_x,T_a] : % 154.70/154.48 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 154.70/154.48 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_y)),V_x) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__eq__mult,axiom, % 154.70/154.48 ! [V_b,V_a,T_a] : % 154.70/154.48 ( class_Rings_Oordered__ring__abs(T_a) % 154.70/154.48 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.70/154.48 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) % 154.70/154.48 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 154.70/154.48 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 154.70/154.48 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__on__iff__surj,axiom, % 154.70/154.48 ! [V_A_H_2,T_b,T_a,V_A_2] : % 154.70/154.48 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.48 => ( ? [B_f] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 154.70/154.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,B_f),V_A_2)),V_A_H_2)) ) % 154.70/154.48 <=> ? [B_g] : hAPP(c_Set_Oimage(T_b,T_a,B_g),V_A_H_2) = V_A_2 ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_finite__surj__inj,axiom, % 154.70/154.48 ! [V_f_2,V_A_2,T_a] : % 154.70/154.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2))) % 154.70/154.48 => c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_endo__inj__surj,axiom, % 154.70/154.48 ! [V_f_2,V_A_2,T_a] : % 154.70/154.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2)),V_A_2)) % 154.70/154.48 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) % 154.70/154.48 => hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2) = V_A_2 ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_finite__UNIV__inj__surj,axiom, % 154.70/154.48 ! [V_f_2,T_a] : % 154.70/154.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 154.70/154.48 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 154.70/154.48 => hAPP(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)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_finite__UNIV__surj__inj,axiom, % 154.70/154.48 ! [V_f_2,T_a] : % 154.70/154.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 154.70/154.48 => ( hAPP(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)) % 154.70/154.48 => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__diff__triangle__ineq,axiom, % 154.70/154.48 ! [V_d,V_c,V_b,V_a,T_a] : % 154.70/154.48 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_c))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_d))))) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_abs__triangle__ineq4,axiom, % 154.70/154.48 ! [V_b,V_a,T_a] : % 154.70/154.48 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__image__subset__iff,axiom, % 154.70/154.48 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))) % 154.70/154.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__on__image__Int,axiom, % 154.70/154.48 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 154.70/154.48 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_image__Int,axiom, % 154.70/154.48 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 154.70/154.48 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__on__iff__eq__card,axiom, % 154.70/154.48 ! [V_f_2,T_b,V_A_2,T_a] : % 154.70/154.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.48 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.48 <=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_eq__card__imp__inj__on,axiom, % 154.70/154.48 ! [V_f_2,T_b,V_A_2,T_a] : % 154.70/154.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.48 => ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) % 154.70/154.48 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__on__image__set__diff,axiom, % 154.70/154.48 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 154.70/154.48 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_image__set__diff,axiom, % 154.70/154.48 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 154.70/154.48 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_setsum__reindex,axiom, % 154.70/154.48 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] : % 154.70/154.48 ( class_Groups_Ocomm__monoid__add(T_c) % 154.70/154.48 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 154.70/154.48 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)),V_B_2) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_pigeonhole,axiom, % 154.70/154.48 ! [V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) % 154.70/154.48 => ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__on__fun__updI,axiom, % 154.70/154.48 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.48 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 154.70/154.48 => c_Fun_Oinj__on(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_A_2) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_finite__vimageI,axiom, % 154.70/154.48 ! [V_h_2,T_b,V_F_2,T_a] : % 154.70/154.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 154.70/154.48 => ( c_Fun_Oinj__on(T_b,T_a,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 154.70/154.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_a,V_h_2),V_F_2))) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__vimage__image__eq,axiom, % 154.70/154.48 ! [V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 154.70/154.48 => hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = V_A_2 ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_zabs__less__one__iff,axiom, % 154.70/154.48 ! [V_z_2] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))) % 154.70/154.48 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_nat__abs__mult__distrib,axiom, % 154.70/154.48 ! [V_z,V_w] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_w))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__singleton,axiom, % 154.70/154.48 ! [T_a] : c_Fun_Oinj__on(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_setsum_Oreindex,axiom, % 154.70/154.48 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] : % 154.70/154.48 ( class_Groups_Ocomm__monoid__add(T_b) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.48 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2) % 154.70/154.48 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,T_b,T_a,V_g_2),V_h_2)),V_A_2) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_card__bij__eq,axiom, % 154.70/154.48 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),V_B_2)) % 154.70/154.48 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),V_B_2)),V_A_2)) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 154.70/154.48 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),V_B_2) ) ) ) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_vimage__subsetI,axiom, % 154.70/154.48 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)),V_A_2)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__on__insert,axiom, % 154.70/154.48 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) % 154.70/154.48 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.48 & ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__on__Un,axiom, % 154.70/154.48 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.70/154.48 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.48 & c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 154.70/154.48 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_card__inj__on__le,axiom, % 154.70/154.48 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),V_B_2)) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__on__iff__card__le,axiom, % 154.70/154.48 ! [V_B_2,T_b,V_A_2,T_a] : % 154.70/154.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 154.70/154.48 => ( ? [B_f] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 154.70/154.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,B_f),V_A_2)),V_B_2)) ) % 154.70/154.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_fold__image__reindex,axiom, % 154.70/154.48 ! [V_z_2,V_g_2,V_h_2,T_b,V_A_2,T_a,T_c] : % 154.70/154.48 ( class_Groups_Oab__semigroup__mult(T_c) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.48 => ( c_Fun_Oinj__on(T_a,T_b,V_h_2,V_A_2) % 154.70/154.48 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),hAPP(c_Set_Oimage(T_a,T_b,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_a,c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_g_2),V_h_2)),V_z_2),V_A_2) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_incr__lemma,axiom, % 154.70/154.48 ! [V_x,V_z,V_d] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)))) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_folding__image_Oreindex,axiom, % 154.70/154.48 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 154.70/154.48 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 154.70/154.48 => hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_b,T_a,T_b,V_g_2),V_h_2)),V_A_2) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_image__INT,axiom, % 154.70/154.48 ! [V_j_2,V_B_2,V_A_2,T_c,V_C_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 154.70/154.48 => ( ! [B_x] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) ) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_j_2),V_A_2)) % 154.70/154.48 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Oimage(T_a,T_b,V_f_2)),V_B_2)) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Nitpick_Oint__lcm__def,axiom, % 154.70/154.48 ! [V_y,V_x] : c_Nitpick_Oint__lcm(V_x,V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_the__inv__into__comp,axiom, % 154.70/154.48 ! [V_x_2,V_A_2,V_g_2,T_c,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(c_Set_Oimage(T_c,T_a,V_g_2),V_A_2)) % 154.70/154.48 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,V_A_2) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_a,V_g_2),V_A_2)))) % 154.70/154.48 => hAPP(c_Fun_Othe__inv__into(T_c,T_b,V_A_2,hAPP(c_Fun_Ocomp(T_a,T_b,T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_a,T_c,T_b,c_Fun_Othe__inv__into(T_c,T_a,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_a,T_b,hAPP(c_Set_Oimage(T_c,T_a,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_the__inv__into__into,axiom, % 154.70/154.48 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.70/154.48 => 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)) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_folding__image_Odistrib,axiom, % 154.70/154.48 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 154.70/154.48 => hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),V_f_2),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(V_f_2,hAPP(hAPP(V_F_2,V_g_2),V_A_2)),hAPP(hAPP(V_F_2,V_h_2),V_A_2)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_the__inv__into__f__f,axiom, % 154.70/154.48 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.48 => 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 ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_the__inv__into__f__eq,axiom, % 154.70/154.48 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.48 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.48 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__on__the__inv__into,axiom, % 154.70/154.48 ! [V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.48 => c_Fun_Oinj__on(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_the__inv__into__onto,axiom, % 154.70/154.48 ! [V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.48 => hAPP(c_Set_Oimage(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = V_A_2 ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_the__inv__f__f,axiom, % 154.70/154.48 ! [V_x_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 154.70/154.48 => 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 ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_the__inv__into__def,axiom, % 154.70/154.48 ! [V_x_2,V_f_2,V_A_2,T_b,T_a] : hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_x_2))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_folding__image_Oeq__fold,axiom, % 154.70/154.48 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 154.70/154.48 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_f__the__inv__into__f,axiom, % 154.70/154.48 ! [V_y_2,V_A_2,V_f_2,T_b,T_a] : % 154.70/154.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 154.70/154.48 => 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 ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom, % 154.70/154.48 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] : % 154.70/154.48 ( ( class_Groups_Ocomm__monoid__add(T_a) % 154.70/154.48 & class_Groups_Ocomm__monoid__mult(T_a) ) % 154.70/154.48 => ( V_A_2 = V_B_2 % 154.70/154.48 => ( c_Nat__Transfer_Onat__set(V_B_2) % 154.70/154.48 => ( ! [B_x] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 154.70/154.48 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 154.70/154.48 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_g_2),V_B_2) ) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__on__Inter,axiom, % 154.70/154.48 ! [V_f_2,T_b,T_a,V_S_2] : % 154.70/154.48 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 154.70/154.48 => ( ! [B_A] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_A),V_S_2)) % 154.70/154.48 => c_Fun_Oinj__on(T_a,T_b,V_f_2,B_A) ) % 154.70/154.48 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_S_2)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Inter__subset,axiom, % 154.70/154.48 ! [V_B_2,V_A_2,T_a] : % 154.70/154.48 ( ! [B_X] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_A_2)) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_X),V_B_2)) ) % 154.70/154.48 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),V_B_2)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_nat0__intermed__int__val,axiom, % 154.70/154.48 ! [V_k_2,V_f_2,V_n_2] : % 154.70/154.48 ( ! [B_i] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 154.70/154.48 => ? [B_i] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 154.70/154.48 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_int__val__lemma,axiom, % 154.70/154.48 ! [V_k_2,V_f_2,V_n_2] : % 154.70/154.48 ( ! [B_i] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) % 154.70/154.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 154.70/154.48 => ? [B_i] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 154.70/154.48 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__on__INTER,axiom, % 154.70/154.48 ! [V_A_2,V_f_2,T_c,T_b,T_a,V_I_2] : % 154.70/154.48 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.48 => ( ! [B_i] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_I_2)) % 154.70/154.48 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(V_A_2,B_i)) ) % 154.70/154.48 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_card__less__Suc,axiom, % 154.70/154.48 ! [V_i_2,V_M_2] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 154.70/154.48 => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_card__less,axiom, % 154.70/154.48 ! [V_i_2,V_M_2] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 154.70/154.48 => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_card__less__Suc2,axiom, % 154.70/154.48 ! [V_i_2,V_M_2] : % 154.70/154.48 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 154.70/154.48 => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inj__on__diff__nat,axiom, % 154.70/154.48 ! [V_k_2,V_N_2] : % 154.70/154.48 ( ! [B_x] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) ) % 154.70/154.48 => 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_Ominus__class_Ominus(tc_Nat_Onat)),V_k_2),V_N_2) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_CollectI,axiom, % 154.70/154.48 ! [T_a,V_a_2,V_P_2] : % 154.70/154.48 ( hBOOL(hAPP(V_P_2,V_a_2)) % 154.70/154.48 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_finite__Collect__conjI,axiom, % 154.70/154.48 ! [V_Q_2,V_P_2,T_a] : % 154.70/154.48 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 154.70/154.48 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) % 154.70/154.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),V_Q_2)))) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_finite__Collect__less__nat,axiom, % 154.70/154.48 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_k_2)))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_finite__Collect__le__nat,axiom, % 154.70/154.48 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_k_2)))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_empty__Collect__eq,axiom, % 154.70/154.48 ! [V_P_2,T_a] : % 154.70/154.48 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),V_P_2) % 154.70/154.48 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Collect__empty__eq,axiom, % 154.70/154.48 ! [V_P_2,T_a] : % 154.70/154.48 ( hAPP(c_Set_OCollect(T_a),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.48 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Collect__def,axiom, % 154.70/154.48 ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),V_P_2) = V_P_2 ). % 154.70/154.48 % 154.70/154.48 fof(fact_Collect__mem__eq,axiom, % 154.70/154.48 ! [V_A_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)) = V_A_2 ). % 154.70/154.48 % 154.70/154.48 fof(fact_mem__Collect__eq,axiom, % 154.70/154.48 ! [V_P_2,V_a_2,T_a] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 154.70/154.48 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_CollectD,axiom, % 154.70/154.48 ! [V_P_2,V_a_2,T_a] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 154.70/154.48 => hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_CollectE,axiom, % 154.70/154.48 ! [V_P_2,V_a_2,T_a] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 154.70/154.48 => hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_empty__def,axiom, % 154.70/154.48 ! [T_a] : c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),hAPP(c_COMBK(tc_HOL_Obool,T_a),c_fFalse)) ). % 154.70/154.48 % 154.70/154.48 fof(fact_finite__Collect__disjI,axiom, % 154.70/154.48 ! [V_Q_2,V_P_2,T_a] : % 154.70/154.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),V_P_2)),V_Q_2)))) % 154.70/154.48 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 154.70/154.48 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_insert__Collect,axiom, % 154.70/154.48 ! [V_P_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)))),V_P_2)) ). % 154.70/154.48 % 154.70/154.48 fof(fact_UNIV__def,axiom, % 154.70/154.48 ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),hAPP(c_COMBK(tc_HOL_Obool,T_a),c_fTrue)) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Collect__disj__eq,axiom, % 154.70/154.48 ! [V_Q_2,V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(c_Set_OCollect(T_a),V_Q_2)) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Collect__conj__eq,axiom, % 154.70/154.48 ! [V_Q_2,V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(c_Set_OCollect(T_a),V_Q_2)) ). % 154.70/154.48 % 154.70/154.48 fof(fact_vimage__Collect__eq,axiom, % 154.70/154.48 ! [V_P_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_a),V_P_2),V_f_2)) ). % 154.70/154.48 % 154.70/154.48 fof(fact_insert__compr__raw,axiom, % 154.70/154.48 ! [V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_insert__compr,axiom, % 154.70/154.48 ! [V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Un__def,axiom, % 154.70/154.48 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Int__def,axiom, % 154.70/154.48 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Int__Collect,axiom, % 154.70/154.48 ! [V_P_2,V_A_2,V_x_2,T_a] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2)))) % 154.70/154.48 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.48 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Collect__conv__if,axiom, % 154.70/154.48 ! [T_a,V_a_2,V_P_2] : % 154.70/154.48 ( ( hBOOL(hAPP(V_P_2,V_a_2)) % 154.70/154.48 => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) % 154.70/154.48 & ( ~ hBOOL(hAPP(V_P_2,V_a_2)) % 154.70/154.48 => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Collect__conv__if2,axiom, % 154.70/154.48 ! [T_a,V_a_2,V_P_2] : % 154.70/154.48 ( ( hBOOL(hAPP(V_P_2,V_a_2)) % 154.70/154.48 => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) % 154.70/154.48 & ( ~ hBOOL(hAPP(V_P_2,V_a_2)) % 154.70/154.48 => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_singleton__conv,axiom, % 154.70/154.48 ! [V_a_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_singleton__conv2,axiom, % 154.70/154.48 ! [V_a_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_set__diff__eq,axiom, % 154.70/154.48 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2)))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_finite__Collect__not,axiom, % 154.70/154.48 ! [V_P_2,T_a] : % 154.70/154.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)))) % 154.70/154.48 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_insert__def,axiom, % 154.70/154.48 ! [V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2) ). % 154.70/154.48 % 154.70/154.48 fof(fact_vimage__def,axiom, % 154.70/154.48 ! [V_B_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(T_b)),V_f_2)),V_B_2)) ). % 154.70/154.48 % 154.70/154.48 fof(fact_finite__M__bounded__by__nat,axiom, % 154.70/154.48 ! [V_i_2,V_P_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),V_P_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_setsum__setsum__restrict,axiom, % 154.70/154.48 ! [V_R_2,V_f_2,V_T_2,T_b,V_S_2,T_a,T_c] : % 154.70/154.48 ( class_Groups_Ocomm__monoid__add(T_c) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 154.70/154.48 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_a,T_c),tc_fun(tc_fun(T_a,tc_HOL_Obool),T_c),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c)),hAPP(c_COMBC(T_a,T_b,T_c),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)))),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_R_2))))),V_T_2) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_if__image__distrib,axiom, % 154.70/154.48 ! [V_S_2,V_g_2,V_f_2,V_P_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),V_P_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_b),V_P_2)))),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Collect__all__eq,axiom, % 154.70/154.48 ! [V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),V_P_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_P_2))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_nat__seg__image__imp__finite,axiom, % 154.70/154.48 ! [V_n_2,V_f_2,T_a,V_A_2] : % 154.70/154.48 ( V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_a,V_f_2),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_n_2))) % 154.70/154.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_setsum__restrict__set_H,axiom, % 154.70/154.48 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] : % 154.70/154.48 ( class_Groups_Ocomm__monoid__add(T_b) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.48 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(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,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_setsum__image__gen,axiom, % 154.70/154.48 ! [V_f_2,T_c,V_g_2,V_S_2,T_a,T_b] : % 154.70/154.48 ( class_Groups_Ocomm__monoid__add(T_b) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 154.70/154.48 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),T_b,T_c),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_OCollect(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)))),hAPP(c_COMBC(T_a,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_a),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_a,T_c,V_f_2),V_S_2)) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_dom__if,axiom, % 154.70/154.48 ! [V_g_2,V_f_2,V_P_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBS(T_a,tc_Option_Ooption(T_b),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBS(T_a,tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),T_a),c_If(tc_Option_Ooption(T_b))),V_P_2)),V_f_2)),V_g_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_f_2)),hAPP(c_Set_OCollect(T_a),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_g_2)),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_dom__override__on,axiom, % 154.70/154.48 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Fun_Ooverride__on(T_a,tc_Option_Ooption(T_b),V_f_2,V_g_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_f_2)),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_a,T_b,V_g_2)))))),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_a,T_b,V_g_2))))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_setsum__multicount,axiom, % 154.70/154.48 ! [V_k_2,V_R_2,V_T_2,T_b,V_S_2,T_a] : % 154.70/154.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 154.70/154.48 => ( ! [B_x] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_T_2)) % 154.70/154.48 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_R_2),B_x)))) = V_k_2 ) % 154.70/154.48 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat,T_a),c_Finite__Set_Ocard(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),V_T_2)) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_setsum__multicount__gen,axiom, % 154.70/154.48 ! [V_k_2,V_R_2,V_t_2,T_b,V_s_2,T_a] : % 154.70/154.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_t_2)) % 154.70/154.48 => ( ! [B_x] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_t_2)) % 154.70/154.48 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_s_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_R_2),B_x)))) = hAPP(V_k_2,B_x) ) % 154.70/154.48 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat,T_a),c_Finite__Set_Ocard(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_k_2),V_t_2) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inf__Sup1__distrib,axiom, % 154.70/154.48 ! [V_x_2,V_A_2,T_a] : % 154.70/154.48 ( class_Lattices_Odistrib__lattice(T_a) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.48 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.48 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_finite__Collect__subsets,axiom, % 154.70/154.48 ! [V_A_2,T_a] : % 154.70/154.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),V_A_2)))) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_finite__Collect__bounded__ex,axiom, % 154.70/154.48 ! [V_Q_2,T_b,V_P_2,T_a] : % 154.70/154.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),V_Q_2))))) % 154.70/154.48 <=> ! [B_y] : % 154.70/154.48 ( hBOOL(hAPP(V_P_2,B_y)) % 154.70/154.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),V_Q_2),B_y)))) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_finite__image__set,axiom, % 154.70/154.48 ! [V_f_2,T_b,V_P_2,T_a] : % 154.70/154.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 154.70/154.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_a)),c_fequal)),V_f_2)))),V_P_2))))) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_override__on__apply__in,axiom, % 154.70/154.48 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 154.70/154.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.70/154.48 => hAPP(c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_override__on__apply__notin,axiom, % 154.70/154.48 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 154.70/154.48 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.70/154.48 => hAPP(c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_override__on__emptyset,axiom, % 154.70/154.48 ! [V_g_2,V_f_2,T_b,T_a] : c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_f_2 ). % 154.70/154.48 % 154.70/154.48 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom, % 154.70/154.48 ! [V_P_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_override__on__def,axiom, % 154.70/154.48 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 154.70/154.48 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.70/154.48 => hAPP(c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) % 154.70/154.48 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.70/154.48 => hAPP(c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom, % 154.70/154.48 ! [V_P_2] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom, % 154.70/154.48 ! [V_P_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_P_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),V_P_2),c_Int_Onat)))) ). % 154.70/154.48 % 154.70/154.48 fof(fact_sup__Inf2__distrib,axiom, % 154.70/154.48 ! [V_B_2,V_A_2,T_a] : % 154.70/154.48 ( class_Lattices_Odistrib__lattice(T_a) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.48 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.70/154.48 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.48 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_sup__Inf1__distrib,axiom, % 154.70/154.48 ! [V_x_2,V_A_2,T_a] : % 154.70/154.48 ( class_Lattices_Odistrib__lattice(T_a) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.48 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.48 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ) ). % 154.70/154.48 % 154.70/154.48 fof(fact_inf__Sup2__distrib,axiom, % 154.70/154.48 ! [V_B_2,V_A_2,T_a] : % 154.70/154.48 ( class_Lattices_Odistrib__lattice(T_a) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.48 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.70/154.48 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_add__Min__commute,axiom, % 154.70/154.49 ! [V_k_2,V_N_2,T_a] : % 154.70/154.49 ( class_Groups_Olinordered__ab__semigroup__add(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 154.70/154.49 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_N_2))))) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_add__Max__commute,axiom, % 154.70/154.49 ! [V_k_2,V_N_2,T_a] : % 154.70/154.49 ( class_Groups_Olinordered__ab__semigroup__add(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 154.70/154.49 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_N_2))))) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_finite__conv__nat__seg__image,axiom, % 154.70/154.49 ! [V_A_2,T_a] : % 154.70/154.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 <=> ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_a,B_f),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),B_n))) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_pigeonhole__infinite,axiom, % 154.70/154.49 ! [V_f_2,T_b,V_A_2,T_a] : % 154.70/154.49 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 154.70/154.49 => ? [B_x] : % 154.70/154.49 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.49 & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),hAPP(V_f_2,B_x)))))) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_diff__nat__eq__if,axiom, % 154.70/154.49 ! [V_z_2,V_z_H_2] : % 154.70/154.49 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 154.70/154.49 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(c_Int_Onat,V_z_2) ) % 154.70/154.49 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 154.70/154.49 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),V_z_H_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_not__neg__0,axiom, % 154.70/154.49 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 154.70/154.49 % 154.70/154.49 fof(fact_not__neg__int,axiom, % 154.70/154.49 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 154.70/154.49 % 154.70/154.49 fof(fact_not__neg__1,axiom, % 154.70/154.49 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Min_Osingleton,axiom, % 154.70/154.49 ! [V_x_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Max_Osingleton,axiom, % 154.70/154.49 ! [V_x_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_not__neg__eq__ge__0,axiom, % 154.70/154.49 ! [V_x_2] : % 154.70/154.49 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2)) % 154.70/154.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_neg__def,axiom, % 154.70/154.49 ! [V_Z_2] : % 154.70/154.49 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2)) % 154.70/154.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_neg__nat,axiom, % 154.70/154.49 ! [V_z] : % 154.70/154.49 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 154.70/154.49 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_not__neg__nat,axiom, % 154.70/154.49 ! [V_z] : % 154.70/154.49 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 154.70/154.49 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Max__ge,axiom, % 154.70/154.49 ! [V_x_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2))) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Min__le,axiom, % 154.70/154.49 ! [V_x_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_x_2)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Max__in,axiom, % 154.70/154.49 ! [V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Min__in,axiom, % 154.70/154.49 ! [V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Min__antimono,axiom, % 154.70/154.49 ! [V_N_2,V_M_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2)) % 154.70/154.49 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_M_2))) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Max__mono,axiom, % 154.70/154.49 ! [V_N_2,V_M_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2)) % 154.70/154.49 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_N_2))) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Min_Oremove,axiom, % 154.70/154.49 ! [V_x_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.49 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) % 154.70/154.49 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Max_Oremove,axiom, % 154.70/154.49 ! [V_x_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.49 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) % 154.70/154.49 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setsum__cases,axiom, % 154.70/154.49 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_a,T_b] : % 154.70/154.49 ( class_Groups_Ocomm__monoid__add(T_b) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),V_P_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2))))) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod_Oremove,axiom, % 154.70/154.49 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 154.70/154.49 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_card__partition,axiom, % 154.70/154.49 ! [V_k_2,V_C_2,T_a] : % 154.70/154.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_C_2)) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))) % 154.70/154.49 => ( ! [B_c] : % 154.70/154.49 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c),V_C_2)) % 154.70/154.49 => hAPP(c_Finite__Set_Ocard(T_a),B_c) = V_k_2 ) % 154.70/154.49 => ( ! [B_c1] : % 154.70/154.49 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c1),V_C_2)) % 154.70/154.49 => ! [B_c2] : % 154.70/154.49 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c2),V_C_2)) % 154.70/154.49 => ( B_c1 != B_c2 % 154.70/154.49 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_c1),B_c2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) % 154.70/154.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_inj__uminus,axiom, % 154.70/154.49 ! [V_A_2,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add(T_a) % 154.70/154.49 => c_Fun_Oinj__on(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a),V_A_2) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_ComplI,axiom, % 154.70/154.49 ! [V_A_2,V_c_2,T_a] : % 154.70/154.49 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_sup__max,axiom, % 154.70/154.49 ! [T_a] : % 154.70/154.49 ( ( class_Lattices_Osemilattice__sup(T_a) % 154.70/154.49 & class_Orderings_Olinorder(T_a) ) % 154.70/154.49 => c_Lattices_Osemilattice__sup__class_Osup(T_a) = c_Orderings_Oord__class_Omax(T_a) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_max__0L,axiom, % 154.70/154.49 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 154.70/154.49 % 154.70/154.49 fof(fact_max__0R,axiom, % 154.70/154.49 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ). % 154.70/154.49 % 154.70/154.49 fof(fact_inf__min,axiom, % 154.70/154.49 ! [T_a] : % 154.70/154.49 ( ( class_Lattices_Osemilattice__inf(T_a) % 154.70/154.49 & class_Orderings_Olinorder(T_a) ) % 154.70/154.49 => c_Lattices_Osemilattice__inf__class_Oinf(T_a) = c_Orderings_Oord__class_Omin(T_a) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__0L,axiom, % 154.70/154.49 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__0R,axiom, % 154.70/154.49 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.70/154.49 % 154.70/154.49 fof(fact_max__Suc__Suc,axiom, % 154.70/154.49 ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m),V_n)) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__Suc__Suc,axiom, % 154.70/154.49 ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Compl__anti__mono,axiom, % 154.70/154.49 ! [V_B_2,V_A_2,T_a] : % 154.70/154.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Compl__subset__Compl__iff,axiom, % 154.70/154.49 ! [V_B_2,V_A_2,T_a] : % 154.70/154.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2))) % 154.70/154.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_max__diff__distrib__left,axiom, % 154.70/154.49 ! [V_z,V_y,V_x,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add(T_a) % 154.70/154.49 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_of__nat__setprod,axiom, % 154.70/154.49 ! [V_A_2,V_f_2,T_b,T_a] : % 154.70/154.49 ( ( class_Groups_Ocomm__monoid__mult(T_a) % 154.70/154.49 & class_Rings_Osemiring__1(T_a) ) % 154.70/154.49 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_a)),V_f_2)),V_A_2) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_int__setprod,axiom, % 154.70/154.49 ! [V_A_2,V_f_2,T_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ). % 154.70/154.49 % 154.70/154.49 fof(fact_minus__minus,axiom, % 154.70/154.49 ! [V_a,T_a] : % 154.70/154.49 ( class_Groups_Ogroup__add(T_a) % 154.70/154.49 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_minus__max__eq__min,axiom, % 154.70/154.49 ! [V_y,V_x,T_a] : % 154.70/154.49 ( class_Groups_Olinordered__ab__group__add(T_a) % 154.70/154.49 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_minus__min__eq__max,axiom, % 154.70/154.49 ! [V_y,V_x,T_a] : % 154.70/154.49 ( class_Groups_Olinordered__ab__group__add(T_a) % 154.70/154.49 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_equation__minus__iff,axiom, % 154.70/154.49 ! [V_b_2,V_a_2,T_a] : % 154.70/154.49 ( class_Groups_Ogroup__add(T_a) % 154.70/154.49 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 154.70/154.49 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_minus__equation__iff,axiom, % 154.70/154.49 ! [V_b_2,V_a_2,T_a] : % 154.70/154.49 ( class_Groups_Ogroup__add(T_a) % 154.70/154.49 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_b_2 % 154.70/154.49 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) = V_a_2 ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_neg__equal__iff__equal,axiom, % 154.70/154.49 ! [V_b_2,V_a_2,T_a] : % 154.70/154.49 ( class_Groups_Ogroup__add(T_a) % 154.70/154.49 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 154.70/154.49 <=> V_a_2 = V_b_2 ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_double__complement,axiom, % 154.70/154.49 ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = V_A_2 ). % 154.70/154.49 % 154.70/154.49 fof(fact_double__compl,axiom, % 154.70/154.49 ! [V_x,T_a] : % 154.70/154.49 ( class_Lattices_Oboolean__algebra(T_a) % 154.70/154.49 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Osup_Oidem,axiom, % 154.70/154.49 ! [V_a,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Oinf_Oidem,axiom, % 154.70/154.49 ! [V_a,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_uminus__apply,axiom, % 154.70/154.49 ! [V_x_2,V_A_2,T_b,T_a] : % 154.70/154.49 ( class_Groups_Ouminus(T_a) % 154.70/154.49 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_A_2,V_x_2)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Osup_Ocommute,axiom, % 154.70/154.49 ! [V_b,V_a,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_a) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Osup__commute,axiom, % 154.70/154.49 ! [V_y,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Oinf_Ocommute,axiom, % 154.70/154.49 ! [V_b,V_a,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_a) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Oinf__commute,axiom, % 154.70/154.49 ! [V_y,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Osup__inf__absorb,axiom, % 154.70/154.49 ! [V_y,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = V_x ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Oinf__sup__absorb,axiom, % 154.70/154.49 ! [V_y,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = V_x ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Osup_Oleft__idem,axiom, % 154.70/154.49 ! [V_b,V_a,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Osup__left__idem,axiom, % 154.70/154.49 ! [V_y,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Oinf_Oleft__idem,axiom, % 154.70/154.49 ! [V_b,V_a,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Oinf__left__idem,axiom, % 154.70/154.49 ! [V_y,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Osup_Oleft__commute,axiom, % 154.70/154.49 ! [V_c,V_a,V_b,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Osup__left__commute,axiom, % 154.70/154.49 ! [V_z,V_y,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Oinf_Oleft__commute,axiom, % 154.70/154.49 ! [V_c,V_a,V_b,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Oinf__left__commute,axiom, % 154.70/154.49 ! [V_z,V_y,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Osup__inf__distrib1,axiom, % 154.70/154.49 ! [V_z,V_y,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Oinf__sup__distrib1,axiom, % 154.70/154.49 ! [V_z,V_y,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Compl__eq__Compl__iff,axiom, % 154.70/154.49 ! [V_B_2,V_A_2,T_a] : % 154.70/154.49 ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2) % 154.70/154.49 <=> V_A_2 = V_B_2 ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_compl__eq__compl__iff,axiom, % 154.70/154.49 ! [V_y_2,V_x_2,T_a] : % 154.70/154.49 ( class_Lattices_Oboolean__algebra(T_a) % 154.70/154.49 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2) % 154.70/154.49 <=> V_x_2 = V_y_2 ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Osup_Oassoc,axiom, % 154.70/154.49 ! [V_c,V_b,V_a,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Osup__assoc,axiom, % 154.70/154.49 ! [V_z,V_y,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Oinf_Oassoc,axiom, % 154.70/154.49 ! [V_c,V_b,V_a,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Oinf__assoc,axiom, % 154.70/154.49 ! [V_z,V_y,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Osup__inf__distrib2,axiom, % 154.70/154.49 ! [V_x,V_z,V_y,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_z),V_x)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Oinf__sup__distrib2,axiom, % 154.70/154.49 ! [V_x,V_z,V_y,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_z),V_x)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Max_Oidem,axiom, % 154.70/154.49 ! [V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Min_Oidem,axiom, % 154.70/154.49 ! [V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_fun__Compl__def,axiom, % 154.70/154.49 ! [V_x_2,V_A_2,T_b,T_a] : % 154.70/154.49 ( class_Groups_Ouminus(T_a) % 154.70/154.49 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_A_2,V_x_2)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Odistrib__sup__le,axiom, % 154.70/154.49 ! [V_z,V_y,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)))) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Odistrib__inf__le,axiom, % 154.70/154.49 ! [V_z,V_y,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)))) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Oless__infI2,axiom, % 154.70/154.49 ! [V_a,V_x,V_b,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Oless__infI1,axiom, % 154.70/154.49 ! [V_b,V_x,V_a,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__less__iff__disj,axiom, % 154.70/154.49 ! [V_z_2,V_y_2,V_x_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2)),V_z_2)) % 154.70/154.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) % 154.70/154.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__less__iff__conj,axiom, % 154.70/154.49 ! [V_y_2,V_x_2,V_z_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2))) % 154.70/154.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) % 154.70/154.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_neg__less__iff__less,axiom, % 154.70/154.49 ! [V_a_2,V_b_2,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 154.70/154.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_minus__less__iff,axiom, % 154.70/154.49 ! [V_b_2,V_a_2,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) % 154.70/154.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_less__minus__iff,axiom, % 154.70/154.49 ! [V_b_2,V_a_2,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))) % 154.70/154.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Oless__supI2,axiom, % 154.70/154.49 ! [V_a,V_b,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Oless__supI1,axiom, % 154.70/154.49 ! [V_b,V_a,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_max__less__iff__conj,axiom, % 154.70/154.49 ! [V_z_2,V_y_2,V_x_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)),V_z_2)) % 154.70/154.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) % 154.70/154.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_less__max__iff__disj,axiom, % 154.70/154.49 ! [V_y_2,V_x_2,V_z_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2))) % 154.70/154.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) % 154.70/154.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_neg__equal__zero,axiom, % 154.70/154.49 ! [V_a_2,T_a] : % 154.70/154.49 ( class_Groups_Olinordered__ab__group__add(T_a) % 154.70/154.49 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_a_2 % 154.70/154.49 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_neg__equal__0__iff__equal,axiom, % 154.70/154.49 ! [V_a_2,T_a] : % 154.70/154.49 ( class_Groups_Ogroup__add(T_a) % 154.70/154.49 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.49 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_equal__neg__zero,axiom, % 154.70/154.49 ! [V_a_2,T_a] : % 154.70/154.49 ( class_Groups_Olinordered__ab__group__add(T_a) % 154.70/154.49 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) % 154.70/154.49 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_neg__0__equal__iff__equal,axiom, % 154.70/154.49 ! [V_a_2,T_a] : % 154.70/154.49 ( class_Groups_Ogroup__add(T_a) % 154.70/154.49 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) % 154.70/154.49 <=> c_Groups_Ozero__class_Ozero(T_a) = V_a_2 ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_minus__zero,axiom, % 154.70/154.49 ! [T_a] : % 154.70/154.49 ( class_Groups_Ogroup__add(T_a) % 154.70/154.49 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Ole__infE,axiom, % 154.70/154.49 ! [V_b,V_a,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b))) % 154.70/154.49 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 154.70/154.49 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Oinf__mono,axiom, % 154.70/154.49 ! [V_d,V_b,V_c,V_a,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_c),V_d))) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Oinf__greatest,axiom, % 154.70/154.49 ! [V_z,V_y,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Ole__infI,axiom, % 154.70/154.49 ! [V_b,V_a,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b))) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Oinf__absorb2,axiom, % 154.70/154.49 ! [V_x,V_y,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Oinf__absorb1,axiom, % 154.70/154.49 ! [V_y,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Ole__infI2,axiom, % 154.70/154.49 ! [V_a,V_x,V_b,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Ole__infI1,axiom, % 154.70/154.49 ! [V_b,V_x,V_a,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__le__iff__disj,axiom, % 154.70/154.49 ! [V_z_2,V_y_2,V_x_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2)),V_z_2)) % 154.70/154.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 154.70/154.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Ole__inf__iff,axiom, % 154.70/154.49 ! [V_z_2,V_y_2,V_x_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y_2),V_z_2))) % 154.70/154.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 154.70/154.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Ole__iff__inf,axiom, % 154.70/154.49 ! [V_y_2,V_x_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 154.70/154.49 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2) = V_x_2 ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Oinf__le2,axiom, % 154.70/154.49 ! [V_y,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_y)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Oinf__le1,axiom, % 154.70/154.49 ! [V_y,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_x)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_compl__mono,axiom, % 154.70/154.49 ! [V_y,V_x,T_a] : % 154.70/154.49 ( class_Lattices_Oboolean__algebra(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_compl__le__compl__iff,axiom, % 154.70/154.49 ! [V_y_2,V_x_2,T_a] : % 154.70/154.49 ( class_Lattices_Oboolean__algebra(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2))) % 154.70/154.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_le__imp__neg__le,axiom, % 154.70/154.49 ! [V_b,V_a,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_neg__le__iff__le,axiom, % 154.70/154.49 ! [V_a_2,V_b_2,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 154.70/154.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_minus__le__iff,axiom, % 154.70/154.49 ! [V_b_2,V_a_2,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) % 154.70/154.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_le__minus__iff,axiom, % 154.70/154.49 ! [V_b_2,V_a_2,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))) % 154.70/154.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Ole__supE,axiom, % 154.70/154.49 ! [V_x,V_b,V_a,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x)) % 154.70/154.49 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 154.70/154.49 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Osup__mono,axiom, % 154.70/154.49 ! [V_d,V_b,V_c,V_a,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_c),V_d))) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Osup__least,axiom, % 154.70/154.49 ! [V_z,V_x,V_y,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Ole__supI,axiom, % 154.70/154.49 ! [V_b,V_x,V_a,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Osup__absorb1,axiom, % 154.70/154.49 ! [V_x,V_y,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Osup__absorb2,axiom, % 154.70/154.49 ! [V_y,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Ole__supI2,axiom, % 154.70/154.49 ! [V_a,V_b,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Ole__supI1,axiom, % 154.70/154.49 ! [V_b,V_a,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Ole__sup__iff,axiom, % 154.70/154.49 ! [V_z_2,V_y_2,V_x_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)),V_z_2)) % 154.70/154.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 154.70/154.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_le__max__iff__disj,axiom, % 154.70/154.49 ! [V_y_2,V_x_2,V_z_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2))) % 154.70/154.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_x_2)) % 154.70/154.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_y_2)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Ole__iff__sup,axiom, % 154.70/154.49 ! [V_y_2,V_x_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 154.70/154.49 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2) = V_y_2 ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_le__maxI2,axiom, % 154.70/154.49 ! [V_x,V_y,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_le__maxI1,axiom, % 154.70/154.49 ! [V_y,V_x,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom, % 154.70/154.49 ! [V_A_2,V_f_2,T_a] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Int__atLeastLessThan,axiom, % 154.70/154.49 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Int__greaterThanLessThan,axiom, % 154.70/154.49 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Int__greaterThanAtMost,axiom, % 154.70/154.49 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Int__atLeastAtMost,axiom, % 154.70/154.49 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Compl__iff,axiom, % 154.70/154.49 ! [V_A_2,V_c_2,T_a] : % 154.70/154.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 154.70/154.49 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_ComplD,axiom, % 154.70/154.49 ! [V_A_2,V_c_2,T_a] : % 154.70/154.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 154.70/154.49 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_ComplE,axiom, % 154.70/154.49 ! [V_A_2,V_c_2,T_a] : % 154.70/154.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 154.70/154.49 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__add__distrib__left,axiom, % 154.70/154.49 ! [V_z,V_y,V_x,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 154.70/154.49 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_square__eq__iff,axiom, % 154.70/154.49 ! [V_b_2,V_a_2,T_a] : % 154.70/154.49 ( class_Rings_Oidom(T_a) % 154.70/154.49 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2) % 154.70/154.49 <=> ( V_a_2 = V_b_2 % 154.70/154.49 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_minus__mult__minus,axiom, % 154.70/154.49 ! [V_b,V_a,T_a] : % 154.70/154.49 ( class_Rings_Oring(T_a) % 154.70/154.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_minus__mult__commute,axiom, % 154.70/154.49 ! [V_b,V_a,T_a] : % 154.70/154.49 ( class_Rings_Oring(T_a) % 154.70/154.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_minus__mult__left,axiom, % 154.70/154.49 ! [V_b,V_a,T_a] : % 154.70/154.49 ( class_Rings_Oring(T_a) % 154.70/154.49 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_minus__mult__right,axiom, % 154.70/154.49 ! [V_b,V_a,T_a] : % 154.70/154.49 ( class_Rings_Oring(T_a) % 154.70/154.49 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_minus__add__distrib,axiom, % 154.70/154.49 ! [V_b,V_a,T_a] : % 154.70/154.49 ( class_Groups_Oab__group__add(T_a) % 154.70/154.49 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_minus__add,axiom, % 154.70/154.49 ! [V_b,V_a,T_a] : % 154.70/154.49 ( class_Groups_Ogroup__add(T_a) % 154.70/154.49 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_add__minus__cancel,axiom, % 154.70/154.49 ! [V_b,V_a,T_a] : % 154.70/154.49 ( class_Groups_Ogroup__add(T_a) % 154.70/154.49 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) = V_b ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_minus__add__cancel,axiom, % 154.70/154.49 ! [V_b,V_a,T_a] : % 154.70/154.49 ( class_Groups_Ogroup__add(T_a) % 154.70/154.49 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = V_b ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_max__add__distrib__left,axiom, % 154.70/154.49 ! [V_z,V_y,V_x,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 154.70/154.49 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__diff__distrib__left,axiom, % 154.70/154.49 ! [V_z,V_y,V_x,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add(T_a) % 154.70/154.49 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_minus__diff__eq,axiom, % 154.70/154.49 ! [V_b,V_a,T_a] : % 154.70/154.49 ( class_Groups_Oab__group__add(T_a) % 154.70/154.49 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__diff,axiom, % 154.70/154.49 ! [V_n,V_i,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_i)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)),V_i) ). % 154.70/154.49 % 154.70/154.49 fof(fact_abs__minus__cancel,axiom, % 154.70/154.49 ! [V_a,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.49 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_vimage__Compl,axiom, % 154.70/154.49 ! [V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod__timesf,axiom, % 154.70/154.49 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 154.70/154.49 ( class_Groups_Ocomm__monoid__mult(T_a) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_g_2),V_A_2)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod__1,axiom, % 154.70/154.49 ! [V_A_2,T_b,T_a] : % 154.70/154.49 ( class_Groups_Ocomm__monoid__mult(T_a) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Oone__class_Oone(T_a))),V_A_2) = c_Groups_Oone__class_Oone(T_a) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_abs__setprod,axiom, % 154.70/154.49 ! [V_A_2,V_f_2,T_b,T_a] : % 154.70/154.49 ( class_Fields_Olinordered__field(T_a) % 154.70/154.49 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom, % 154.70/154.49 ! [T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom, % 154.70/154.49 ! [T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setsum__negf,axiom, % 154.70/154.49 ! [V_A_2,V_f_2,T_b,T_a] : % 154.70/154.49 ( class_Groups_Oab__group__add(T_a) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Ouminus__class_Ouminus(T_a)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Collect__neg__eq,axiom, % 154.70/154.49 ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)) ). % 154.70/154.49 % 154.70/154.49 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom, % 154.70/154.49 ! [V_A_2,V_f_2,T_a] : % 154.70/154.49 ( ( class_Groups_Ocomm__monoid__add(T_a) % 154.70/154.49 & class_Groups_Ocomm__monoid__mult(T_a) ) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod__zero,axiom, % 154.70/154.49 ! [V_f_2,V_A_2,T_a,T_b] : % 154.70/154.49 ( class_Rings_Ocomm__semiring__1(T_b) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( ? [B_x] : % 154.70/154.49 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.49 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod__zero__iff,axiom, % 154.70/154.49 ! [V_f_2,V_A_2,T_a,T_b] : % 154.70/154.49 ( ( class_Rings_Ocomm__semiring__1(T_b) % 154.70/154.49 & class_Rings_Ono__zero__divisors(T_b) ) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) % 154.70/154.49 <=> ? [B_x] : % 154.70/154.49 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.49 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod__empty,axiom, % 154.70/154.49 ! [V_f_2,T_b,T_a] : % 154.70/154.49 ( class_Groups_Ocomm__monoid__mult(T_a) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_a) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod_Oempty,axiom, % 154.70/154.49 ! [V_g_2,T_b,T_a] : % 154.70/154.49 ( class_Groups_Ocomm__monoid__mult(T_a) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_a) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod_Oinfinite,axiom, % 154.70/154.49 ! [V_g_2,V_A_2,T_a,T_b] : % 154.70/154.49 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.70/154.49 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod__infinite,axiom, % 154.70/154.49 ! [V_f_2,V_A_2,T_a,T_b] : % 154.70/154.49 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.70/154.49 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod__eq__1__iff,axiom, % 154.70/154.49 ! [V_f_2,V_F_2,T_a] : % 154.70/154.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 154.70/154.49 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 154.70/154.49 <=> ! [B_x] : % 154.70/154.49 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2)) % 154.70/154.49 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_neg__0__le__iff__le,axiom, % 154.70/154.49 ! [V_a_2,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 154.70/154.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_le__minus__self__iff,axiom, % 154.70/154.49 ! [V_a_2,T_a] : % 154.70/154.49 ( class_Groups_Olinordered__ab__group__add(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 154.70/154.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_neg__le__0__iff__le,axiom, % 154.70/154.49 ! [V_a_2,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_minus__le__self__iff,axiom, % 154.70/154.49 ! [V_a_2,T_a] : % 154.70/154.49 ( class_Groups_Olinordered__ab__group__add(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2)) % 154.70/154.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_neg__0__less__iff__less,axiom, % 154.70/154.49 ! [V_a_2,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 154.70/154.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_neg__less__0__iff__less,axiom, % 154.70/154.49 ! [V_a_2,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_neg__less__nonneg,axiom, % 154.70/154.49 ! [V_a_2,T_a] : % 154.70/154.49 ( class_Groups_Olinordered__ab__group__add(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2)) % 154.70/154.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_less__minus__self__iff,axiom, % 154.70/154.49 ! [V_a_2,T_a] : % 154.70/154.49 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 154.70/154.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_minus__unique,axiom, % 154.70/154.49 ! [V_b,V_a,T_a] : % 154.70/154.49 ( class_Groups_Ogroup__add(T_a) % 154.70/154.49 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.49 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_ab__left__minus,axiom, % 154.70/154.49 ! [V_a,T_a] : % 154.70/154.49 ( class_Groups_Oab__group__add(T_a) % 154.70/154.49 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_left__minus,axiom, % 154.70/154.49 ! [V_a,T_a] : % 154.70/154.49 ( class_Groups_Ogroup__add(T_a) % 154.70/154.49 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_eq__neg__iff__add__eq__0,axiom, % 154.70/154.49 ! [V_b_2,V_a_2,T_a] : % 154.70/154.49 ( class_Groups_Ogroup__add(T_a) % 154.70/154.49 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 154.70/154.49 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_right__minus,axiom, % 154.70/154.49 ! [V_a,T_a] : % 154.70/154.49 ( class_Groups_Ogroup__add(T_a) % 154.70/154.49 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_diff__0,axiom, % 154.70/154.49 ! [V_a,T_a] : % 154.70/154.49 ( class_Groups_Ogroup__add(T_a) % 154.70/154.49 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom, % 154.70/154.49 ! [V_y,V_x,T_a] : % 154.70/154.49 ( class_Rings_Ocomm__ring__1(T_a) % 154.70/154.49 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_diff__minus__eq__add,axiom, % 154.70/154.49 ! [V_b,V_a,T_a] : % 154.70/154.49 ( class_Groups_Ogroup__add(T_a) % 154.70/154.49 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_ab__diff__minus,axiom, % 154.70/154.49 ! [V_b,V_a,T_a] : % 154.70/154.49 ( class_Groups_Oab__group__add(T_a) % 154.70/154.49 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_diff__def,axiom, % 154.70/154.49 ! [V_b,V_a,T_a] : % 154.70/154.49 ( class_Groups_Ogroup__add(T_a) % 154.70/154.49 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_square__eq__1__iff,axiom, % 154.70/154.49 ! [V_x_2,T_a] : % 154.70/154.49 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 154.70/154.49 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a) % 154.70/154.49 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a) % 154.70/154.49 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom, % 154.70/154.49 ! [V_x,T_a] : % 154.70/154.49 ( class_Rings_Ocomm__ring__1(T_a) % 154.70/154.49 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_x) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_inf__compl__bot,axiom, % 154.70/154.49 ! [V_x,T_a] : % 154.70/154.49 ( class_Lattices_Oboolean__algebra(T_a) % 154.70/154.49 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_compl__inf__bot,axiom, % 154.70/154.49 ! [V_x,T_a] : % 154.70/154.49 ( class_Lattices_Oboolean__algebra(T_a) % 154.70/154.49 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_diff__eq,axiom, % 154.70/154.49 ! [V_y,V_x,T_a] : % 154.70/154.49 ( class_Lattices_Oboolean__algebra(T_a) % 154.70/154.49 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_compl__top__eq,axiom, % 154.70/154.49 ! [T_a] : % 154.70/154.49 ( class_Lattices_Oboolean__algebra(T_a) % 154.70/154.49 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_compl__bot__eq,axiom, % 154.70/154.49 ! [T_a] : % 154.70/154.49 ( class_Lattices_Oboolean__algebra(T_a) % 154.70/154.49 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_compl__sup,axiom, % 154.70/154.49 ! [V_y,V_x,T_a] : % 154.70/154.49 ( class_Lattices_Oboolean__algebra(T_a) % 154.70/154.49 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_compl__inf,axiom, % 154.70/154.49 ! [V_y,V_x,T_a] : % 154.70/154.49 ( class_Lattices_Oboolean__algebra(T_a) % 154.70/154.49 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_compl__sup__top,axiom, % 154.70/154.49 ! [V_x,T_a] : % 154.70/154.49 ( class_Lattices_Oboolean__algebra(T_a) % 154.70/154.49 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Otop__class_Otop(T_a) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_sup__compl__top,axiom, % 154.70/154.49 ! [V_x,T_a] : % 154.70/154.49 ( class_Lattices_Oboolean__algebra(T_a) % 154.70/154.49 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_abs__ge__minus__self,axiom, % 154.70/154.49 ! [V_a,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_abs__le__iff,axiom, % 154.70/154.49 ! [V_b_2,V_a_2,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2)) % 154.70/154.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 154.70/154.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_abs__leI,axiom, % 154.70/154.49 ! [V_b,V_a,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_abs__le__D2,axiom, % 154.70/154.49 ! [V_b,V_a,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_abs__less__iff,axiom, % 154.70/154.49 ! [V_b_2,V_a_2,T_a] : % 154.70/154.49 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2)) % 154.70/154.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 154.70/154.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_subset__Compl__self__eq,axiom, % 154.70/154.49 ! [V_A_2,T_a] : % 154.70/154.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 154.70/154.49 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Compl__UNIV__eq,axiom, % 154.70/154.49 ! [T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Compl__empty__eq,axiom, % 154.70/154.49 ! [T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 154.70/154.49 % 154.70/154.49 fof(fact_finite__compl,axiom, % 154.70/154.49 ! [V_A_2,T_a] : % 154.70/154.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 154.70/154.49 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Compl__disjoint2,axiom, % 154.70/154.49 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Compl__disjoint,axiom, % 154.70/154.49 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 154.70/154.49 % 154.70/154.49 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom, % 154.70/154.49 ! [V_f_2,V_A_2,T_a] : % 154.70/154.49 ( ( class_Groups_Ocomm__monoid__add(T_a) % 154.70/154.49 & class_Groups_Ocomm__monoid__mult(T_a) ) % 154.70/154.49 => ( c_Nat__Transfer_Onat__set(V_A_2) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_nat__minus__add__max,axiom, % 154.70/154.49 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)),V_m) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),V_m) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Compl__partition2,axiom, % 154.70/154.49 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Compl__partition,axiom, % 154.70/154.49 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Compl__Un,axiom, % 154.70/154.49 ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Compl__Int,axiom, % 154.70/154.49 ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) ). % 154.70/154.49 % 154.70/154.49 fof(fact_image__uminus__atLeastAtMost,axiom, % 154.70/154.49 ! [V_y_2,V_x_2,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add(T_a) % 154.70/154.49 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Compl__eq__Diff__UNIV,axiom, % 154.70/154.49 ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_A_2) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Compl__Diff__eq,axiom, % 154.70/154.49 ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Diff__eq,axiom, % 154.70/154.49 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Diff__Compl,axiom, % 154.70/154.49 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod_Odistrib,axiom, % 154.70/154.49 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 154.70/154.49 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Groups_Otimes__class_Otimes(T_b)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_h_2),V_A_2)) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Ints__minus,axiom, % 154.70/154.49 ! [V_a_2,T_a] : % 154.70/154.49 ( class_Rings_Oring__1(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_image__uminus__greaterThanLessThan,axiom, % 154.70/154.49 ! [V_y_2,V_x_2,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add(T_a) % 154.70/154.49 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Compl__eq,axiom, % 154.70/154.49 ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Compl__lessThan,axiom, % 154.70/154.49 ! [V_k_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Compl__atLeast,axiom, % 154.70/154.49 ! [V_k_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Collect__imp__eq,axiom, % 154.70/154.49 ! [V_Q_2,V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2))),hAPP(c_Set_OCollect(T_a),V_Q_2)) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Compl__greaterThan,axiom, % 154.70/154.49 ! [V_k_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Compl__atMost,axiom, % 154.70/154.49 ! [V_k_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Compl__INT,axiom, % 154.70/154.49 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Compl__UN,axiom, % 154.70/154.49 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod__pos__nat__iff,axiom, % 154.70/154.49 ! [V_f_2,V_S_2,T_a] : % 154.70/154.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_S_2))) % 154.70/154.49 <=> ! [B_x] : % 154.70/154.49 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod__reindex,axiom, % 154.70/154.49 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] : % 154.70/154.49 ( class_Groups_Ocomm__monoid__mult(T_c) % 154.70/154.49 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)),V_B_2) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod__reindex__cong,axiom, % 154.70/154.49 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 154.70/154.49 ( class_Groups_Ocomm__monoid__mult(T_c) % 154.70/154.49 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.49 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 154.70/154.49 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),V_g_2),V_A_2) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_abs__of__nonpos,axiom, % 154.70/154.49 ! [V_a,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.49 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_abs__minus__le__zero,axiom, % 154.70/154.49 ! [V_a,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_abs__if,axiom, % 154.70/154.49 ! [V_a,T_a] : % 154.70/154.49 ( class_Groups_Oabs__if(T_a) % 154.70/154.49 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.49 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) % 154.70/154.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.49 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_abs__of__neg,axiom, % 154.70/154.49 ! [V_a,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.49 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_max__Suc2,axiom, % 154.70/154.49 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),V_n_2)),V_m_2) ). % 154.70/154.49 % 154.70/154.49 fof(fact_max__Suc1,axiom, % 154.70/154.49 ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),V_m_2) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod__delta,axiom, % 154.70/154.49 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 154.70/154.49 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 154.70/154.49 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(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_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 154.70/154.49 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(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_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = c_Groups_Oone__class_Oone(T_b) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod__delta_H,axiom, % 154.70/154.49 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 154.70/154.49 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 154.70/154.49 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(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_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 154.70/154.49 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(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_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = c_Groups_Oone__class_Oone(T_b) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_disjoint__eq__subset__Compl,axiom, % 154.70/154.49 ! [V_B_2,V_A_2,T_a] : % 154.70/154.49 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2))) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_surj__Compl__image__subset,axiom, % 154.70/154.49 ! [V_A_2,V_f_2,T_a,T_b] : % 154.70/154.49 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Ofold__sup__insert,axiom, % 154.70/154.49 ! [V_a_2,V_b_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_b_2),V_A_2)) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Ofold__inf__insert,axiom, % 154.70/154.49 ! [V_a_2,V_b_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_b_2),V_A_2)) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Max_Oin__idem,axiom, % 154.70/154.49 ! [V_x_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Min_Oin__idem,axiom, % 154.70/154.49 ! [V_x_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Int__atLeastAtMostL1,axiom, % 154.70/154.49 ! [V_d_2,V_b_2,V_a_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Int__atLeastAtMostR1,axiom, % 154.70/154.49 ! [V_d_2,V_c_2,V_b_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_image__uminus__atLeastLessThan,axiom, % 154.70/154.49 ! [V_y_2,V_x_2,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add(T_a) % 154.70/154.49 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_image__uminus__greaterThanAtMost,axiom, % 154.70/154.49 ! [V_y_2,V_x_2,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add(T_a) % 154.70/154.49 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Int__atLeastAtMostL2,axiom, % 154.70/154.49 ! [V_c_2,V_b_2,V_a_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),V_b_2) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Int__atLeastAtMostR2,axiom, % 154.70/154.49 ! [V_d_2,V_c_2,V_a_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),V_d_2) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Max_OF__eq,axiom, % 154.70/154.49 ! [V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omax(T_a)),V_A_2) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Min_OF__eq,axiom, % 154.70/154.49 ! [V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_image__uminus__lessThan,axiom, % 154.70/154.49 ! [V_x_2,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add(T_a) % 154.70/154.49 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_image__uminus__greaterThan,axiom, % 154.70/154.49 ! [V_x_2,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add(T_a) % 154.70/154.49 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_image__uminus__atMost,axiom, % 154.70/154.49 ! [V_x_2,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add(T_a) % 154.70/154.49 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_image__uminus__atLeast,axiom, % 154.70/154.49 ! [V_x_2,T_a] : % 154.70/154.49 ( class_Groups_Oordered__ab__group__add(T_a) % 154.70/154.49 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod__insert,axiom, % 154.70/154.49 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 154.70/154.49 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod_Oinsert,axiom, % 154.70/154.49 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 154.70/154.49 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod__Un__Int,axiom, % 154.70/154.49 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 154.70/154.49 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.70/154.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod_Ounion__inter,axiom, % 154.70/154.49 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 154.70/154.49 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.70/154.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod_Oreindex,axiom, % 154.70/154.49 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] : % 154.70/154.49 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,T_b,T_a,V_g_2),V_h_2)),V_A_2) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod_OF__eq,axiom, % 154.70/154.49 ! [V_g_2,V_A_2,T_a,T_b] : % 154.70/154.49 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.70/154.49 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2) ) % 154.70/154.49 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod_Oeq__fold,axiom, % 154.70/154.49 ! [V_g_2,V_A_2,T_a,T_b] : % 154.70/154.49 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_compl__unique,axiom, % 154.70/154.49 ! [V_y,V_x,T_a] : % 154.70/154.49 ( class_Lattices_Oboolean__algebra(T_a) % 154.70/154.49 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a) % 154.70/154.49 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a) % 154.70/154.49 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__Suc2,axiom, % 154.70/154.49 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),V_n_2)),V_m_2) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__Suc1,axiom, % 154.70/154.49 ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),V_m_2) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Osup__le__fold__sup,axiom, % 154.70/154.49 ! [V_b_2,V_a_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_b_2),V_A_2))) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Ofold__inf__le__inf,axiom, % 154.70/154.49 ! [V_b_2,V_a_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a_2),V_b_2))) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Ofold1__belowI,axiom, % 154.70/154.49 ! [V_a_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_a_2)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_fold1__below__iff,axiom, % 154.70/154.49 ! [V_x_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_x_2)) % 154.70/154.49 <=> ? [B_x] : % 154.70/154.49 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_x_2)) ) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_min__max_Obelow__fold1__iff,axiom, % 154.70/154.49 ! [V_x_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2))) % 154.70/154.49 <=> ! [B_x] : % 154.70/154.49 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_strict__below__fold1__iff,axiom, % 154.70/154.49 ! [V_x_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2))) % 154.70/154.49 <=> ! [B_x] : % 154.70/154.49 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_fold1__strict__below__iff,axiom, % 154.70/154.49 ! [V_x_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_x_2)) % 154.70/154.49 <=> ? [B_x] : % 154.70/154.49 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_x_2)) ) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Max__insert,axiom, % 154.70/154.49 ! [V_x_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Min__insert,axiom, % 154.70/154.49 ! [V_x_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Max_Osubset__idem,axiom, % 154.70/154.49 ! [V_B_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Min_Osubset__idem,axiom, % 154.70/154.49 ! [V_B_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_inj__image__Compl__subset,axiom, % 154.70/154.49 ! [V_A_2,V_f_2,T_b,T_a] : % 154.70/154.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Max__Un,axiom, % 154.70/154.49 ! [V_B_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.70/154.49 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)) ) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Min__Un,axiom, % 154.70/154.49 ! [V_B_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.70/154.49 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)) ) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Max_Oeq__fold__idem_H,axiom, % 154.70/154.49 ! [V_a_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_a_2),V_A_2) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Min_Oeq__fold__idem_H,axiom, % 154.70/154.49 ! [V_a_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_a_2),V_A_2) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_vimage__if,axiom, % 154.70/154.49 ! [V_B_2,T_b,V_d_2,V_A_2,V_c_2,T_a] : % 154.70/154.49 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 154.70/154.49 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 154.70/154.49 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 154.70/154.49 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 154.70/154.49 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = V_B_2 ) ) ) % 154.70/154.49 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 154.70/154.49 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 154.70/154.49 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2) ) % 154.70/154.49 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 154.70/154.49 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod_Oinsert__remove,axiom, % 154.70/154.49 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] : % 154.70/154.49 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod__Un__disjoint,axiom, % 154.70/154.49 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 154.70/154.49 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.70/154.49 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_setprod_Ounion__disjoint,axiom, % 154.70/154.49 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 154.70/154.49 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.70/154.49 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Max_Oinsert,axiom, % 154.70/154.49 ! [V_x_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Min_Oinsert,axiom, % 154.70/154.49 ! [V_x_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_fold1__antimono,axiom, % 154.70/154.49 ! [V_B_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.70/154.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2))) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Max_Oinsert__remove,axiom, % 154.70/154.49 ! [V_x_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 154.70/154.49 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Max_Ounion__inter,axiom, % 154.70/154.49 ! [V_B_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.70/154.49 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Max_Ounion__disjoint,axiom, % 154.70/154.49 ! [V_B_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.70/154.49 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.49 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)) ) ) ) ) ) ) ). % 154.70/154.49 % 154.70/154.49 fof(fact_Min_Oinsert__remove,axiom, % 154.70/154.49 ! [V_x_2,V_A_2,T_a] : % 154.70/154.49 ( class_Orderings_Olinorder(T_a) % 154.70/154.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 154.70/154.50 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Min_Ounion__inter,axiom, % 154.70/154.50 ! [V_B_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.70/154.50 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Min_Ounion__disjoint,axiom, % 154.70/154.50 ! [V_B_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.70/154.50 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)) ) ) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Max_Oeq__fold_H,axiom, % 154.70/154.50 ! [V_x_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.50 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_x_2),V_A_2) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Min_Oeq__fold_H,axiom, % 154.70/154.50 ! [V_x_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.50 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_x_2),V_A_2) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_minus__Max__eq__Min,axiom, % 154.70/154.50 ! [V_S_2,T_a] : % 154.70/154.50 ( class_Groups_Olinordered__ab__group__add(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 154.70/154.50 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),V_S_2)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_minus__Min__eq__Max,axiom, % 154.70/154.50 ! [V_S_2,T_a] : % 154.70/154.50 ( class_Groups_Olinordered__ab__group__add(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 154.70/154.50 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),V_S_2)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_dual__min,axiom, % 154.70/154.50 ! [T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => c_Orderings_Oord_Omin(T_a,hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a))) = c_Orderings_Oord__class_Omax(T_a) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_dual__max,axiom, % 154.70/154.50 ! [T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => c_Orderings_Oord_Omax(T_a,hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a))) = c_Orderings_Oord__class_Omin(T_a) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_max__ord__max,axiom, % 154.70/154.50 ! [T_a] : % 154.70/154.50 ( class_Orderings_Oord(T_a) % 154.70/154.50 => c_Orderings_Oord__class_Omax(T_a) = c_Orderings_Oord_Omax(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__ord__min,axiom, % 154.70/154.50 ! [T_a] : % 154.70/154.50 ( class_Orderings_Oord(T_a) % 154.70/154.50 => c_Orderings_Oord__class_Omin(T_a) = c_Orderings_Oord_Omin(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_Oinf__Sup2__distrib,axiom, % 154.70/154.50 ! [V_B_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.70/154.50 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Orderings_Oord__class_Omin(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_negative__zle,axiom, % 154.70/154.50 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))) ). % 154.70/154.50 % 154.70/154.50 fof(fact_negative__zless,axiom, % 154.70/154.50 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zmult__zminus,axiom, % 154.70/154.50 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_w) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zminus__0,axiom, % 154.70/154.50 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 154.70/154.50 % 154.70/154.50 fof(fact_inf__nat__def,axiom, % 154.70/154.50 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ). % 154.70/154.50 % 154.70/154.50 fof(fact_sup__nat__def,axiom, % 154.70/154.50 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zminus__zadd__distrib,axiom, % 154.70/154.50 ! [V_w,V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zadd__zminus__inverse2,axiom, % 154.70/154.50 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 154.70/154.50 % 154.70/154.50 fof(fact_negative__eq__positive,axiom, % 154.70/154.50 ! [V_m_2,V_n_2] : % 154.70/154.50 ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) % 154.70/154.50 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.50 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_not__int__zless__negative,axiom, % 154.70/154.50 ! [V_m,V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)))) ). % 154.70/154.50 % 154.70/154.50 fof(fact_diff__int__def__symmetric,axiom, % 154.70/154.50 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) ). % 154.70/154.50 % 154.70/154.50 fof(fact_diff__int__def,axiom, % 154.70/154.50 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ). % 154.70/154.50 % 154.70/154.50 fof(fact_int__zle__neg,axiom, % 154.70/154.50 ! [V_m_2,V_n_2] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)))) % 154.70/154.50 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.50 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_negative__zle__0,axiom, % 154.70/154.50 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 154.70/154.50 % 154.70/154.50 fof(fact_nat__zminus__int,axiom, % 154.70/154.50 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zabs__def,axiom, % 154.70/154.50 ! [V_i] : % 154.70/154.50 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.50 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) % 154.70/154.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.50 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_neg__zminus__int,axiom, % 154.70/154.50 ! [V_n] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OSup__fin_Oin__idem,axiom, % 154.70/154.50 ! [V_x_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.50 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OSup__fin_Osingleton,axiom, % 154.70/154.50 ! [V_x_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OSup__fin_OF__eq,axiom, % 154.70/154.50 ! [V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omax(T_a)),V_A_2) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_not__zle__0__negative,axiom, % 154.70/154.50 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))) ). % 154.70/154.50 % 154.70/154.50 fof(fact_negative__zless__0,axiom, % 154.70/154.50 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom, % 154.70/154.50 ! [V_x_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OSup__fin_Osubset__idem,axiom, % 154.70/154.50 ! [V_B_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 154.70/154.50 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_Oinf__Sup__absorb,axiom, % 154.70/154.50 ! [V_a_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.70/154.50 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = V_a_2 ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OSup__fin_Ounion__idem,axiom, % 154.70/154.50 ! [V_B_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.70/154.50 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) ) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom, % 154.70/154.50 ! [V_a_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_a_2),V_A_2) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_nat__mult__distrib__neg,axiom, % 154.70/154.50 ! [V_z_H,V_z] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.50 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_H))) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OSup__fin_Oinsert,axiom, % 154.70/154.50 ! [V_x_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom, % 154.70/154.50 ! [V_x_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 154.70/154.50 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom, % 154.70/154.50 ! [V_B_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.70/154.50 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) ) ) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OSup__fin_Ounion__inter,axiom, % 154.70/154.50 ! [V_B_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.70/154.50 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom, % 154.70/154.50 ! [V_x_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.50 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_x_2),V_A_2) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OSup__fin_Oremove,axiom, % 154.70/154.50 ! [V_x_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.50 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = V_x_2 ) % 154.70/154.50 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_Oinf__Sup1__distrib,axiom, % 154.70/154.50 ! [V_x_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom, % 154.70/154.50 ! [V_f_2,V_A_2,T_a] : % 154.70/154.50 ( ! [B_x] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.50 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 154.70/154.50 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_a),c_Int_Onat),V_f_2)),V_A_2)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_Osup__Inf1__distrib,axiom, % 154.70/154.50 ! [V_x_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_Osup__Inf2__distrib,axiom, % 154.70/154.50 ! [V_B_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.70/154.50 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Orderings_Oord__class_Omax(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OSup__fin_Oclosed,axiom, % 154.70/154.50 ! [V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),V_A_2)) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zminus__zminus,axiom, % 154.70/154.50 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OInf__fin_Oin__idem,axiom, % 154.70/154.50 ! [V_x_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.50 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OInf__fin_Osingleton,axiom, % 154.70/154.50 ! [V_x_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OInf__fin_OF__eq,axiom, % 154.70/154.50 ! [V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom, % 154.70/154.50 ! [V_x_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OInf__fin_Osubset__idem,axiom, % 154.70/154.50 ! [V_B_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 154.70/154.50 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_Osup__Inf__absorb,axiom, % 154.70/154.50 ! [V_a_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.70/154.50 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = V_a_2 ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OInf__fin_Ounion__idem,axiom, % 154.70/154.50 ! [V_B_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.70/154.50 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) ) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom, % 154.70/154.50 ! [V_a_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_a_2),V_A_2) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OInf__fin_Oinsert,axiom, % 154.70/154.50 ! [V_x_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom, % 154.70/154.50 ! [V_x_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 154.70/154.50 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OInf__fin_Ounion__inter,axiom, % 154.70/154.50 ! [V_B_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.70/154.50 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom, % 154.70/154.50 ! [V_B_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.70/154.50 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) ) ) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom, % 154.70/154.50 ! [V_x_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.50 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_x_2),V_A_2) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OInf__fin_Oremove,axiom, % 154.70/154.50 ! [V_x_2,V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.50 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = V_x_2 ) % 154.70/154.50 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OInf__le__Sup,axiom, % 154.70/154.50 ! [V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OInf__fin_Oclosed,axiom, % 154.70/154.50 ! [V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),V_A_2)) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Max_Oclosed,axiom, % 154.70/154.50 ! [V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Min_Oclosed,axiom, % 154.70/154.50 ! [V_A_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_setprod_Ounion__inter__neutral,axiom, % 154.70/154.50 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 154.70/154.50 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.70/154.50 => ( ! [B_x] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.70/154.50 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 154.70/154.50 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_setprod__Un__one,axiom, % 154.70/154.50 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 154.70/154.50 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 154.70/154.50 => ( ! [B_x] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))) % 154.70/154.50 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 154.70/154.50 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2)) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_setprod__gen__delta,axiom, % 154.70/154.50 ! [V_c_2,V_b_2,V_a_2,V_S_2,T_a,T_b] : % 154.70/154.50 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 154.70/154.50 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 154.70/154.50 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(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_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) % 154.70/154.50 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 154.70/154.50 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(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_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_c_2),hAPP(c_Finite__Set_Ocard(T_a),V_S_2)) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_of__int__of__nat,axiom, % 154.70/154.50 ! [V_k,T_a] : % 154.70/154.50 ( class_Rings_Oring__1(T_a) % 154.70/154.50 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.50 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)))) ) % 154.70/154.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.50 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_k)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_setprod__diff1,axiom, % 154.70/154.50 ! [V_a_2,V_f_2,V_A_2,T_a,T_b] : % 154.70/154.50 ( class_Fields_Ofield(T_b) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_b) % 154.70/154.50 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.70/154.50 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 154.70/154.50 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.70/154.50 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) ) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom, % 154.70/154.50 ! [V_n,V_x] : % 154.70/154.50 ( c_Nat__Transfer_Ois__nat(V_x) % 154.70/154.50 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_of__int__int__eq,axiom, % 154.70/154.50 ! [V_n] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n) ). % 154.70/154.50 % 154.70/154.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom, % 154.70/154.50 ! [V_x,T_a] : % 154.70/154.50 ( class_Rings_Ocomm__semiring__1(T_a) % 154.70/154.50 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__1,axiom, % 154.70/154.50 ! [V_a,T_a] : % 154.70/154.50 ( class_Rings_Odivision__ring(T_a) % 154.70/154.50 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom, % 154.70/154.50 ! [V_n,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x),V_n)) ). % 154.70/154.50 % 154.70/154.50 fof(fact_int__power,axiom, % 154.70/154.50 ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zpower__int,axiom, % 154.70/154.50 ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) ). % 154.70/154.50 % 154.70/154.50 fof(fact_of__int__power,axiom, % 154.70/154.50 ! [V_n,V_z,T_a] : % 154.70/154.50 ( class_Rings_Oring__1(T_a) % 154.70/154.50 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)),V_n) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_of__int__eq__iff,axiom, % 154.70/154.50 ! [V_z_2,V_w_2,T_a] : % 154.70/154.50 ( class_Int_Oring__char__0(T_a) % 154.70/154.50 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) % 154.70/154.50 <=> V_w_2 = V_z_2 ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_times__divide__eq__right,axiom, % 154.70/154.50 ! [V_c,V_b,V_a,T_a] : % 154.70/154.50 ( class_Rings_Odivision__ring(T_a) % 154.70/154.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_add__divide__distrib,axiom, % 154.70/154.50 ! [V_c,V_b,V_a,T_a] : % 154.70/154.50 ( class_Rings_Odivision__ring(T_a) % 154.70/154.50 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__zero__left,axiom, % 154.70/154.50 ! [V_a,T_a] : % 154.70/154.50 ( class_Rings_Odivision__ring(T_a) % 154.70/154.50 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__zero,axiom, % 154.70/154.50 ! [V_a,T_a] : % 154.70/154.50 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom, % 154.70/154.50 ! [V_q,V_y,V_x,T_a] : % 154.70/154.50 ( class_Rings_Ocomm__semiring__1(T_a) % 154.70/154.50 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_diff__divide__distrib,axiom, % 154.70/154.50 ! [V_c,V_b,V_a,T_a] : % 154.70/154.50 ( class_Rings_Odivision__ring(T_a) % 154.70/154.50 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom, % 154.70/154.50 ! [V_q,V_p,V_x,T_a] : % 154.70/154.50 ( class_Rings_Ocomm__semiring__1(T_a) % 154.70/154.50 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zpower__zpower,axiom, % 154.70/154.50 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)) ). % 154.70/154.50 % 154.70/154.50 fof(fact_minus__divide__left,axiom, % 154.70/154.50 ! [V_b,V_a,T_a] : % 154.70/154.50 ( class_Rings_Odivision__ring(T_a) % 154.70/154.50 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_nat__power__eq,axiom, % 154.70/154.50 ! [V_n,V_z] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 154.70/154.50 => hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),V_n) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom, % 154.70/154.50 ! [V_n,V_x] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 154.70/154.50 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_setsum__divide__distrib,axiom, % 154.70/154.50 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] : % 154.70/154.50 ( class_Fields_Ofield(T_a) % 154.70/154.50 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Rings_Oinverse__class_Odivide(T_a)),V_f_2)),V_r_2)),V_A_2) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_nonzero__eq__divide__eq,axiom, % 154.70/154.50 ! [V_b_2,V_a_2,V_c_2,T_a] : % 154.70/154.50 ( class_Rings_Odivision__ring(T_a) % 154.70/154.50 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) % 154.70/154.50 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2 ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_nonzero__divide__eq__eq,axiom, % 154.70/154.50 ! [V_a_2,V_b_2,V_c_2,T_a] : % 154.70/154.50 ( class_Rings_Odivision__ring(T_a) % 154.70/154.50 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = V_a_2 % 154.70/154.50 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__eq__imp,axiom, % 154.70/154.50 ! [V_a,V_b,V_c,T_a] : % 154.70/154.50 ( class_Rings_Odivision__ring(T_a) % 154.70/154.50 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) % 154.70/154.50 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_eq__divide__imp,axiom, % 154.70/154.50 ! [V_b,V_a,V_c,T_a] : % 154.70/154.50 ( class_Rings_Odivision__ring(T_a) % 154.70/154.50 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b % 154.70/154.50 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__self__if,axiom, % 154.70/154.50 ! [V_a,T_a] : % 154.70/154.50 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 154.70/154.50 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) % 154.70/154.50 & ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__self,axiom, % 154.70/154.50 ! [V_a,T_a] : % 154.70/154.50 ( class_Rings_Odivision__ring(T_a) % 154.70/154.50 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_right__inverse__eq,axiom, % 154.70/154.50 ! [V_a_2,V_b_2,T_a] : % 154.70/154.50 ( class_Rings_Odivision__ring(T_a) % 154.70/154.50 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_a) % 154.70/154.50 <=> V_a_2 = V_b_2 ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_nonzero__minus__divide__divide,axiom, % 154.70/154.50 ! [V_a,V_b,T_a] : % 154.70/154.50 ( class_Rings_Odivision__ring(T_a) % 154.70/154.50 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_nonzero__minus__divide__right,axiom, % 154.70/154.50 ! [V_a,V_b,T_a] : % 154.70/154.50 ( class_Rings_Odivision__ring(T_a) % 154.70/154.50 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom, % 154.70/154.50 ! [V_q,V_x,T_a] : % 154.70/154.50 ( class_Rings_Ocomm__semiring__1(T_a) % 154.70/154.50 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom, % 154.70/154.50 ! [V_q,V_x,T_a] : % 154.70/154.50 ( class_Rings_Ocomm__semiring__1(T_a) % 154.70/154.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom, % 154.70/154.50 ! [V_q,V_x,T_a] : % 154.70/154.50 ( class_Rings_Ocomm__semiring__1(T_a) % 154.70/154.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom, % 154.70/154.50 ! [V_x,T_a] : % 154.70/154.50 ( class_Rings_Ocomm__semiring__1(T_a) % 154.70/154.50 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom, % 154.70/154.50 ! [V_q,V_p,V_x,T_a] : % 154.70/154.50 ( class_Rings_Ocomm__semiring__1(T_a) % 154.70/154.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_p),V_q)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom, % 154.70/154.50 ! [V_n,V_x] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zpower__zadd__distrib,axiom, % 154.70/154.50 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Ints__power,axiom, % 154.70/154.50 ! [V_n_2,V_a_2,T_a] : % 154.70/154.50 ( class_Rings_Oring__1(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_of__int__0,axiom, % 154.70/154.50 ! [T_a] : % 154.70/154.50 ( class_Rings_Oring__1(T_a) % 154.70/154.50 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_of__int__0__eq__iff,axiom, % 154.70/154.50 ! [V_z_2,T_a] : % 154.70/154.50 ( class_Int_Oring__char__0(T_a) % 154.70/154.50 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) % 154.70/154.50 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_of__int__eq__0__iff,axiom, % 154.70/154.50 ! [V_z_2,T_a] : % 154.70/154.50 ( class_Int_Oring__char__0(T_a) % 154.70/154.50 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) = c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_of__int__le__iff,axiom, % 154.70/154.50 ! [V_z_2,V_w_2,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2))) % 154.70/154.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_of__int__less__iff,axiom, % 154.70/154.50 ! [V_z_2,V_w_2,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2))) % 154.70/154.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_of__int__add,axiom, % 154.70/154.50 ! [V_z,V_w,T_a] : % 154.70/154.50 ( class_Rings_Oring__1(T_a) % 154.70/154.50 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_of__int__mult,axiom, % 154.70/154.50 ! [V_z,V_w,T_a] : % 154.70/154.50 ( class_Rings_Oring__1(T_a) % 154.70/154.50 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_setprod__dividef,axiom, % 154.70/154.50 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] : % 154.70/154.50 ( class_Fields_Ofield__inverse__zero(T_b) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_of__int__1,axiom, % 154.70/154.50 ! [T_a] : % 154.70/154.50 ( class_Rings_Oring__1(T_a) % 154.70/154.50 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(T_a) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_of__int__diff,axiom, % 154.70/154.50 ! [V_z,V_w,T_a] : % 154.70/154.50 ( class_Rings_Oring__1(T_a) % 154.70/154.50 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_of__int__of__nat__eq,axiom, % 154.70/154.50 ! [V_n,T_a] : % 154.70/154.50 ( class_Rings_Oring__1(T_a) % 154.70/154.50 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_of__int__minus,axiom, % 154.70/154.50 ! [V_z,T_a] : % 154.70/154.50 ( class_Rings_Oring__1(T_a) % 154.70/154.50 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Ints__of__int,axiom, % 154.70/154.50 ! [V_z_2,T_a] : % 154.70/154.50 ( class_Rings_Oring__1(T_a) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_geometric__sum,axiom, % 154.70/154.50 ! [V_n_2,V_x_2,T_a] : % 154.70/154.50 ( class_Fields_Ofield(T_a) % 154.70/154.50 => ( V_x_2 != c_Groups_Oone__class_Oone(T_a) % 154.70/154.50 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(c_Power_Opower__class_Opower(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x_2),c_Groups_Oone__class_Oone(T_a))) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zero__le__zpower__abs,axiom, % 154.70/154.50 ! [V_n,V_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),V_n))) ). % 154.70/154.50 % 154.70/154.50 fof(fact_of__int__setsum,axiom, % 154.70/154.50 ! [V_A_2,V_f_2,T_b,T_a] : % 154.70/154.50 ( class_Rings_Oring__1(T_a) % 154.70/154.50 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,T_b),c_Int_Oring__1__class_Oof__int(T_a)),V_f_2)),V_A_2) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_setprod__constant,axiom, % 154.70/154.50 ! [V_y_2,V_A_2,T_a,T_b] : % 154.70/154.50 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(c_COMBK(T_b,T_a),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_of__int__setprod,axiom, % 154.70/154.50 ! [V_A_2,V_f_2,T_b,T_a] : % 154.70/154.50 ( ( class_Groups_Ocomm__monoid__mult(T_a) % 154.70/154.50 & class_Rings_Oring__1(T_a) ) % 154.70/154.50 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,T_b),c_Int_Oring__1__class_Oof__int(T_a)),V_f_2)),V_A_2) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__eq__if,axiom, % 154.70/154.50 ! [V_p,V_m] : % 154.70/154.50 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.50 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 154.70/154.50 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.50 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zero__less__zpower__abs__iff,axiom, % 154.70/154.50 ! [V_n_2,V_x_2] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2)),V_n_2))) % 154.70/154.50 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.50 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_of__int__0__le__iff,axiom, % 154.70/154.50 ! [V_z_2,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2))) % 154.70/154.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_of__int__le__0__iff,axiom, % 154.70/154.50 ! [V_z_2,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_of__int__0__less__iff,axiom, % 154.70/154.50 ! [V_z_2,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2))) % 154.70/154.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_of__int__less__0__iff,axiom, % 154.70/154.50 ! [V_z_2,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_of__nat__nat,axiom, % 154.70/154.50 ! [V_z,T_a] : % 154.70/154.50 ( class_Rings_Oring__1(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 154.70/154.50 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__strict__mono,axiom, % 154.70/154.50 ! [V_n,V_b,V_a,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__diff,axiom, % 154.70/154.50 ! [V_m,V_n,V_a,T_a] : % 154.70/154.50 ( class_Fields_Ofield(T_a) % 154.70/154.50 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 154.70/154.50 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_one__less__power,axiom, % 154.70/154.50 ! [V_n,V_a,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__increasing__iff,axiom, % 154.70/154.50 ! [V_y_2,V_x_2,V_b_2,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))) % 154.70/154.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_field__power__not__zero,axiom, % 154.70/154.50 ! [V_n,V_a,T_a] : % 154.70/154.50 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 154.70/154.50 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_nat__power__eq__Suc__0__iff,axiom, % 154.70/154.50 ! [V_m_2,V_x_2] : % 154.70/154.50 ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 154.70/154.50 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.50 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__Suc__0,axiom, % 154.70/154.50 ! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 154.70/154.50 % 154.70/154.50 fof(fact_nat__power__less__imp__less,axiom, % 154.70/154.50 ! [V_n,V_m,V_i] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_nat__zero__less__power__iff,axiom, % 154.70/154.50 ! [V_n_2,V_x_2] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))) % 154.70/154.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) % 154.70/154.50 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__mult__distrib,axiom, % 154.70/154.50 ! [V_n,V_b,V_a,T_a] : % 154.70/154.50 ( class_Groups_Ocomm__monoid__mult(T_a) % 154.70/154.50 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__commutes,axiom, % 154.70/154.50 ! [V_n,V_a,T_a] : % 154.70/154.50 ( class_Groups_Omonoid__mult(T_a) % 154.70/154.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__one,axiom, % 154.70/154.50 ! [V_n,T_a] : % 154.70/154.50 ( class_Groups_Omonoid__mult(T_a) % 154.70/154.50 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_of__nat__power,axiom, % 154.70/154.50 ! [V_n,V_m,T_a] : % 154.70/154.50 ( class_Rings_Osemiring__1(T_a) % 154.70/154.50 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),V_n) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__mult,axiom, % 154.70/154.50 ! [V_n,V_m,V_a,T_a] : % 154.70/154.50 ( class_Groups_Omonoid__mult(T_a) % 154.70/154.50 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__divide,axiom, % 154.70/154.50 ! [V_n,V_b,V_a,T_a] : % 154.70/154.50 ( class_Fields_Ofield__inverse__zero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__abs,axiom, % 154.70/154.50 ! [V_n,V_a,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.50 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__one__right,axiom, % 154.70/154.50 ! [V_a,T_a] : % 154.70/154.50 ( class_Groups_Omonoid__mult(T_a) % 154.70/154.50 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__mono,axiom, % 154.70/154.50 ! [V_n,V_b,V_a,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zero__le__power,axiom, % 154.70/154.50 ! [V_n,V_a,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zero__less__power,axiom, % 154.70/154.50 ! [V_n,V_a,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__eq__0__iff,axiom, % 154.70/154.50 ! [V_n_2,V_a_2,T_a] : % 154.70/154.50 ( ( class_Power_Opower(T_a) % 154.70/154.50 & class_Rings_Omult__zero(T_a) % 154.70/154.50 & class_Rings_Ono__zero__divisors(T_a) % 154.70/154.50 & class_Rings_Ozero__neq__one(T_a) ) % 154.70/154.50 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_one__le__power,axiom, % 154.70/154.50 ! [V_n,V_a,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__0__Suc,axiom, % 154.70/154.50 ! [V_n,T_a] : % 154.70/154.50 ( ( class_Power_Opower(T_a) % 154.70/154.50 & class_Rings_Osemiring__0(T_a) ) % 154.70/154.50 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_OSuc,V_n)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__inject__exp,axiom, % 154.70/154.50 ! [V_n_2,V_m_2,V_a_2,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)) % 154.70/154.50 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) % 154.70/154.50 <=> V_m_2 = V_n_2 ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__Suc2,axiom, % 154.70/154.50 ! [V_n,V_a,T_a] : % 154.70/154.50 ( class_Groups_Omonoid__mult(T_a) % 154.70/154.50 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__Suc,axiom, % 154.70/154.50 ! [V_n,V_a,T_a] : % 154.70/154.50 ( class_Power_Opower(T_a) % 154.70/154.50 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_nat__one__le__power,axiom, % 154.70/154.50 ! [V_n,V_i] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__0,axiom, % 154.70/154.50 ! [V_a,T_a] : % 154.70/154.50 ( class_Power_Opower(T_a) % 154.70/154.50 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__add,axiom, % 154.70/154.50 ! [V_n,V_m,V_a,T_a] : % 154.70/154.50 ( class_Groups_Omonoid__mult(T_a) % 154.70/154.50 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_nonzero__power__divide,axiom, % 154.70/154.50 ! [V_n,V_a,V_b,T_a] : % 154.70/154.50 ( class_Fields_Ofield(T_a) % 154.70/154.50 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__one__over,axiom, % 154.70/154.50 ! [V_n,V_a,T_a] : % 154.70/154.50 ( class_Fields_Ofield__inverse__zero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)),V_n) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_abs__power__minus,axiom, % 154.70/154.50 ! [V_n,V_a,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.50 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__less__imp__less__base,axiom, % 154.70/154.50 ! [V_b,V_n,V_a,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__inject__base,axiom, % 154.70/154.50 ! [V_b,V_n,V_a,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.50 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 154.70/154.50 => V_a = V_b ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__le__imp__le__base,axiom, % 154.70/154.50 ! [V_b,V_n,V_a,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n)))) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__gt1__lemma,axiom, % 154.70/154.50 ! [V_n,V_a,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__less__power__Suc,axiom, % 154.70/154.50 ! [V_n,V_a,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__0__left,axiom, % 154.70/154.50 ! [V_n,T_a] : % 154.70/154.50 ( ( class_Power_Opower(T_a) % 154.70/154.50 & class_Rings_Osemiring__0(T_a) ) % 154.70/154.50 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.50 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) % 154.70/154.50 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.50 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__gt1,axiom, % 154.70/154.50 ! [V_n,V_a,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)))) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__strict__increasing__iff,axiom, % 154.70/154.50 ! [V_y_2,V_x_2,V_b_2,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))) % 154.70/154.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__less__imp__less__exp,axiom, % 154.70/154.50 ! [V_n,V_m,V_a,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__strict__increasing,axiom, % 154.70/154.50 ! [V_a,V_N,V_n,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zero__le__power__abs,axiom, % 154.70/154.50 ! [V_n,V_a,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n))) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__increasing,axiom, % 154.70/154.50 ! [V_a,V_N,V_n,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__minus,axiom, % 154.70/154.50 ! [V_n,V_a,T_a] : % 154.70/154.50 ( class_Rings_Oring__1(T_a) % 154.70/154.50 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__Suc__less,axiom, % 154.70/154.50 ! [V_n,V_a,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__eq__imp__eq__base,axiom, % 154.70/154.50 ! [V_b,V_n,V_a,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.50 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 154.70/154.50 => V_a = V_b ) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__Suc__less__one,axiom, % 154.70/154.50 ! [V_n,V_a,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),c_Groups_Oone__class_Oone(T_a))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__strict__decreasing,axiom, % 154.70/154.50 ! [V_a,V_N,V_n,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__decreasing,axiom, % 154.70/154.50 ! [V_a,V_N,V_n,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__le__imp__le__exp,axiom, % 154.70/154.50 ! [V_n,V_m,V_a,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_le__divide__eq,axiom, % 154.70/154.50 ! [V_c_2,V_b_2,V_a_2,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) % 154.70/154.50 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) % 154.70/154.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 154.70/154.50 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) % 154.70/154.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__le__eq,axiom, % 154.70/154.50 ! [V_a_2,V_c_2,V_b_2,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2)) % 154.70/154.50 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) % 154.70/154.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 154.70/154.50 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) % 154.70/154.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_pos__le__divide__eq,axiom, % 154.70/154.50 ! [V_b_2,V_a_2,V_c_2,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) % 154.70/154.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_pos__divide__le__eq,axiom, % 154.70/154.50 ! [V_a_2,V_b_2,V_c_2,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2)) % 154.70/154.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_times__divide__times__eq,axiom, % 154.70/154.50 ! [V_w,V_z,V_y,V_x,T_a] : % 154.70/154.50 ( class_Fields_Ofield__inverse__zero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_z),V_w)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_w)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_minus__divide__right,axiom, % 154.70/154.50 ! [V_b,V_a,T_a] : % 154.70/154.50 ( class_Fields_Ofield__inverse__zero(T_a) % 154.70/154.50 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_minus__divide__divide,axiom, % 154.70/154.50 ! [V_b,V_a,T_a] : % 154.70/154.50 ( class_Fields_Ofield__inverse__zero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_abs__divide,axiom, % 154.70/154.50 ! [V_b,V_a,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 154.70/154.50 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zero__le__divide__iff,axiom, % 154.70/154.50 ! [V_b_2,V_a_2,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2))) % 154.70/154.50 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 154.70/154.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 154.70/154.50 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__le__0__iff,axiom, % 154.70/154.50 ! [V_b_2,V_a_2,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 154.70/154.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 154.70/154.50 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__right__mono,axiom, % 154.70/154.50 ! [V_c,V_b,V_a,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__right__mono__neg,axiom, % 154.70/154.50 ! [V_c,V_b,V_a,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zero__less__divide__iff,axiom, % 154.70/154.50 ! [V_b_2,V_a_2,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2))) % 154.70/154.50 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 154.70/154.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 154.70/154.50 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__less__0__iff,axiom, % 154.70/154.50 ! [V_b_2,V_a_2,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 154.70/154.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 154.70/154.50 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__pos__pos,axiom, % 154.70/154.50 ! [V_y,V_x,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__pos__neg,axiom, % 154.70/154.50 ! [V_y,V_x,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__neg__pos,axiom, % 154.70/154.50 ! [V_y,V_x,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__neg__neg,axiom, % 154.70/154.50 ! [V_y,V_x,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__strict__right__mono,axiom, % 154.70/154.50 ! [V_c,V_b,V_a,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__strict__right__mono__neg,axiom, % 154.70/154.50 ! [V_c,V_a,V_b,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_eq__divide__eq,axiom, % 154.70/154.50 ! [V_c_2,V_b_2,V_a_2,T_a] : % 154.70/154.50 ( class_Fields_Ofield__inverse__zero(T_a) % 154.70/154.50 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) % 154.70/154.50 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2 ) % 154.70/154.50 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__eq__eq,axiom, % 154.70/154.50 ! [V_a_2,V_c_2,V_b_2,T_a] : % 154.70/154.50 ( class_Fields_Ofield__inverse__zero(T_a) % 154.70/154.50 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = V_a_2 % 154.70/154.50 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) ) % 154.70/154.50 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mult__divide__mult__cancel__right,axiom, % 154.70/154.50 ! [V_b,V_a,V_c,T_a] : % 154.70/154.50 ( class_Fields_Ofield__inverse__zero(T_a) % 154.70/154.50 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mult__divide__mult__cancel__left,axiom, % 154.70/154.50 ! [V_b,V_a,V_c,T_a] : % 154.70/154.50 ( class_Fields_Ofield__inverse__zero(T_a) % 154.70/154.50 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_frac__eq__eq,axiom, % 154.70/154.50 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_a] : % 154.70/154.50 ( class_Fields_Ofield(T_a) % 154.70/154.50 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w_2),V_z_2) % 154.70/154.50 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_nonzero__abs__divide,axiom, % 154.70/154.50 ! [V_a,V_b,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__nonneg__pos,axiom, % 154.70/154.50 ! [V_y,V_x,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__nonneg__neg,axiom, % 154.70/154.50 ! [V_y,V_x,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_frac__less2,axiom, % 154.70/154.50 ! [V_z,V_w,V_y,V_x,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_frac__less,axiom, % 154.70/154.50 ! [V_z,V_w,V_y,V_x,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_frac__le,axiom, % 154.70/154.50 ! [V_z,V_w,V_y,V_x,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__nonpos__pos,axiom, % 154.70/154.50 ! [V_y,V_x,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__nonpos__neg,axiom, % 154.70/154.50 ! [V_y,V_x,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__strict__left__mono__neg,axiom, % 154.70/154.50 ! [V_c,V_b,V_a,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__strict__left__mono,axiom, % 154.70/154.50 ! [V_c,V_a,V_b,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_neg__divide__less__eq,axiom, % 154.70/154.50 ! [V_a_2,V_b_2,V_c_2,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2)) % 154.70/154.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_neg__less__divide__eq,axiom, % 154.70/154.50 ! [V_b_2,V_a_2,V_c_2,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) % 154.70/154.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mult__imp__less__div__pos,axiom, % 154.70/154.50 ! [V_x,V_z,V_y,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mult__imp__div__pos__less,axiom, % 154.70/154.50 ! [V_z,V_x,V_y,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_pos__divide__less__eq,axiom, % 154.70/154.50 ! [V_a_2,V_b_2,V_c_2,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2)) % 154.70/154.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_pos__less__divide__eq,axiom, % 154.70/154.50 ! [V_b_2,V_a_2,V_c_2,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) % 154.70/154.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__less__eq,axiom, % 154.70/154.50 ! [V_a_2,V_c_2,V_b_2,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2)) % 154.70/154.50 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) % 154.70/154.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 154.70/154.50 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) % 154.70/154.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_less__divide__eq,axiom, % 154.70/154.50 ! [V_c_2,V_b_2,V_a_2,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) % 154.70/154.50 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) % 154.70/154.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 154.70/154.50 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) % 154.70/154.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_add__frac__eq,axiom, % 154.70/154.50 ! [V_w,V_x,V_z,V_y,T_a] : % 154.70/154.50 ( class_Fields_Ofield(T_a) % 154.70/154.50 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__add__eq__iff,axiom, % 154.70/154.50 ! [V_y,V_x,V_z,T_a] : % 154.70/154.50 ( class_Fields_Ofield(T_a) % 154.70/154.50 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_add__frac__num,axiom, % 154.70/154.50 ! [V_z,V_x,V_y,T_a] : % 154.70/154.50 ( class_Fields_Ofield__inverse__zero(T_a) % 154.70/154.50 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_add__divide__eq__iff,axiom, % 154.70/154.50 ! [V_y,V_x,V_z,T_a] : % 154.70/154.50 ( class_Fields_Ofield(T_a) % 154.70/154.50 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_add__num__frac,axiom, % 154.70/154.50 ! [V_x,V_z,V_y,T_a] : % 154.70/154.50 ( class_Fields_Ofield__inverse__zero(T_a) % 154.70/154.50 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_diff__divide__eq__iff,axiom, % 154.70/154.50 ! [V_y,V_x,V_z,T_a] : % 154.70/154.50 ( class_Fields_Ofield(T_a) % 154.70/154.50 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__diff__eq__iff,axiom, % 154.70/154.50 ! [V_y,V_x,V_z,T_a] : % 154.70/154.50 ( class_Fields_Ofield(T_a) % 154.70/154.50 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_diff__frac__eq,axiom, % 154.70/154.50 ! [V_w,V_x,V_z,V_y,T_a] : % 154.70/154.50 ( class_Fields_Ofield(T_a) % 154.70/154.50 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_gt__half__sum,axiom, % 154.70/154.50 ! [V_b,V_a,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))),V_b)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_less__half__sum,axiom, % 154.70/154.50 ! [V_b,V_a,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))))) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_abs__div__pos,axiom, % 154.70/154.50 ! [V_x,V_y,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 154.70/154.50 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)),V_y) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__left__mono__neg,axiom, % 154.70/154.50 ! [V_c,V_b,V_a,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divide__left__mono,axiom, % 154.70/154.50 ! [V_c,V_a,V_b,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_neg__divide__le__eq,axiom, % 154.70/154.50 ! [V_a_2,V_b_2,V_c_2,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2)) % 154.70/154.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_neg__le__divide__eq,axiom, % 154.70/154.50 ! [V_b_2,V_a_2,V_c_2,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) % 154.70/154.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mult__imp__le__div__pos,axiom, % 154.70/154.50 ! [V_x,V_z,V_y,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mult__imp__div__pos__le,axiom, % 154.70/154.50 ! [V_z,V_x,V_y,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_setprod__Un,axiom, % 154.70/154.50 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 154.70/154.50 ( class_Fields_Ofield(T_b) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 154.70/154.50 => ( ! [B_x] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 154.70/154.50 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_b) ) % 154.70/154.50 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_card__Pow,axiom, % 154.70/154.50 ! [V_A_2,T_a] : % 154.70/154.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.50 => hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power__power__power,axiom, % 154.70/154.50 ! [T_a] : % 154.70/154.50 ( class_Power_Opower(T_a) % 154.70/154.50 => c_Power_Opower__class_Opower(T_a) = c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_int__power__div__base,axiom, % 154.70/154.50 ! [V_k,V_m] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m)),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_PowI,axiom, % 154.70/154.50 ! [V_B_2,V_A_2,T_a] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zdiv__zminus2,axiom, % 154.70/154.50 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zdiv__zminus__zminus,axiom, % 154.70/154.50 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zdiv__zero,axiom, % 154.70/154.50 ! [V_b] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom, % 154.70/154.50 ! [V_y,V_x] : % 154.70/154.50 ( c_Nat__Transfer_Ois__nat(V_x) % 154.70/154.50 => ( c_Nat__Transfer_Ois__nat(V_y) % 154.70/154.50 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__by__1,axiom, % 154.70/154.50 ! [V_a,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__by__0,axiom, % 154.70/154.50 ! [V_a,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__0,axiom, % 154.70/154.50 ! [V_a,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Pow__top,axiom, % 154.70/154.50 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_A_2))) ). % 154.70/154.50 % 154.70/154.50 fof(fact_image__Pow__surj,axiom, % 154.70/154.50 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] : % 154.70/154.50 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_B_2 % 154.70/154.50 => hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_f_2)),hAPP(c_Set_OPow(T_b),V_A_2)) = hAPP(c_Set_OPow(T_a),V_B_2) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Union__Pow__eq,axiom, % 154.70/154.50 ! [V_A_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_OPow(T_a),V_A_2)) = V_A_2 ). % 154.70/154.50 % 154.70/154.50 fof(fact_Cantors__paradox,axiom, % 154.70/154.50 ! [V_A_2,T_a] : % 154.70/154.50 ~ ? [B_f] : hAPP(c_Set_Oimage(T_a,tc_fun(T_a,tc_HOL_Obool),B_f),V_A_2) = hAPP(c_Set_OPow(T_a),V_A_2) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Pow__not__empty,axiom, % 154.70/154.50 ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Pow__INT__eq,axiom, % 154.70/154.50 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_b),c_Set_OPow(T_a)),V_B_2)) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom, % 154.70/154.50 ! [V_y,V_x] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y))) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_pos__imp__zdiv__neg__iff,axiom, % 154.70/154.50 ! [V_a_2,V_b_2] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_neg__imp__zdiv__neg__iff,axiom, % 154.70/154.50 ! [V_a_2,V_b_2] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__neg__pos__less0,axiom, % 154.70/154.50 ! [V_b,V_a] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zdiv__self,axiom, % 154.70/154.50 ! [V_a] : % 154.70/154.50 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__mult__mult1__if,axiom, % 154.70/154.50 ! [V_b,V_a,V_c,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a) ) % 154.70/154.50 & ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__mult__self2__is__id,axiom, % 154.70/154.50 ! [V_a,V_b,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_b) = V_a ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__mult__self1__is__id,axiom, % 154.70/154.50 ! [V_a,V_b,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),V_b) = V_a ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__mult__mult2,axiom, % 154.70/154.50 ! [V_b,V_a,V_c,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__mult__mult1,axiom, % 154.70/154.50 ! [V_b,V_a,V_c,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__self,axiom, % 154.70/154.50 ! [V_a,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Pow__bottom,axiom, % 154.70/154.50 ! [V_B_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_Set_OPow(T_a),V_B_2))) ). % 154.70/154.50 % 154.70/154.50 fof(fact_PowD,axiom, % 154.70/154.50 ! [V_B_2,V_A_2,T_a] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Pow__iff,axiom, % 154.70/154.50 ! [V_B_2,V_A_2,T_a] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) % 154.70/154.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Pow__mono,axiom, % 154.70/154.50 ! [V_B_2,V_A_2,T_a] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2))) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zdiv__mono1__neg,axiom, % 154.70/154.50 ! [V_b,V_a_H,V_a] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zdiv__mono1,axiom, % 154.70/154.50 ! [V_b,V_a_H,V_a] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b))) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__neg__neg__trivial,axiom, % 154.70/154.50 ! [V_b,V_a] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zdiv__mono2__neg,axiom, % 154.70/154.50 ! [V_b,V_b_H,V_a] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__nonpos__pos__le0,axiom, % 154.70/154.50 ! [V_b,V_a] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_neg__imp__zdiv__nonneg__iff,axiom, % 154.70/154.50 ! [V_a_2,V_b_2] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) % 154.70/154.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__pos__pos__trivial,axiom, % 154.70/154.50 ! [V_b,V_a] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__nonneg__neg__le0,axiom, % 154.70/154.50 ! [V_b,V_a] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zdiv__mono2,axiom, % 154.70/154.50 ! [V_b,V_b_H,V_a] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H))) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom, % 154.70/154.50 ! [V_b_2,V_a_2] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) % 154.70/154.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) % 154.70/154.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_pos__imp__zdiv__pos__iff,axiom, % 154.70/154.50 ! [V_i_2,V_k_2] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2))) % 154.70/154.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_pos__imp__zdiv__nonneg__iff,axiom, % 154.70/154.50 ! [V_a_2,V_b_2] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) % 154.70/154.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zdiv__eq__0__iff,axiom, % 154.70/154.50 ! [V_k_2,V_i_2] : % 154.70/154.50 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.50 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.50 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) % 154.70/154.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) ) % 154.70/154.50 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_int__div__less__self,axiom, % 154.70/154.50 ! [V_k,V_x] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_k)),V_x)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zdiv__zmult2__eq,axiom, % 154.70/154.50 ! [V_b,V_a,V_c] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_c) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Pow__def,axiom, % 154.70/154.50 ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),V_A_2)) ). % 154.70/154.50 % 154.70/154.50 fof(fact_finite__Pow__iff,axiom, % 154.70/154.50 ! [V_A_2,T_a] : % 154.70/154.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2))) % 154.70/154.50 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_subset__Pow__Union,axiom, % 154.70/154.50 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)))) ). % 154.70/154.50 % 154.70/154.50 fof(fact_power_Opower_Opower__0,axiom, % 154.70/154.50 ! [V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2 ). % 154.70/154.50 % 154.70/154.50 fof(fact_power_Opower_Opower__Suc,axiom, % 154.70/154.50 ! [V_n_2,V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2)) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Pow__insert,axiom, % 154.70/154.50 ! [V_A_2,V_a_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_a),V_a_2)),hAPP(c_Set_OPow(T_a),V_A_2))) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Pow__UNIV,axiom, % 154.70/154.50 ! [T_a] : hAPP(c_Set_OPow(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__mult__self2,axiom, % 154.70/154.50 ! [V_c,V_a,V_b,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__mult__self1,axiom, % 154.70/154.50 ! [V_c,V_a,V_b,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__add__self2,axiom, % 154.70/154.50 ! [V_a,V_b,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__add__self1,axiom, % 154.70/154.50 ! [V_a,V_b,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_UN__Pow__subset,axiom, % 154.70/154.50 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_b),c_Set_OPow(T_a)),V_B_2))),hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Pow__Int__eq,axiom, % 154.70/154.50 ! [V_B_2,V_A_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2)) ). % 154.70/154.50 % 154.70/154.50 fof(fact_image__Pow__mono,axiom, % 154.70/154.50 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),V_B_2)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_f_2)),hAPP(c_Set_OPow(T_b),V_A_2))),hAPP(c_Set_OPow(T_a),V_B_2))) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Pow__Compl,axiom, % 154.70/154.50 ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_COMBS(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_a))))) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Pow__empty,axiom, % 154.70/154.50 ! [T_a] : hAPP(c_Set_OPow(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Un__Pow__subset,axiom, % 154.70/154.50 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2))),hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Powp__Pow__eq,axiom, % 154.70/154.50 ! [V_x_2,V_A_2,T_a] : % 154.70/154.50 ( hBOOL(hAPP(c_Predicate_OPowp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),V_x_2)) % 154.70/154.50 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_a),V_A_2))) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_divmod__int__rel__div__eq,axiom, % 154.70/154.50 ! [V_r_1,V_y,V_b_1,V_a_1] : % 154.70/154.50 ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1) % 154.70/154.50 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) % 154.70/154.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) ) % 154.70/154.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) % 154.70/154.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 154.70/154.50 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_split__zdiv,axiom, % 154.70/154.50 ! [V_k_2,V_n_2,V_P_2] : % 154.70/154.50 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2))) % 154.70/154.50 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.50 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 154.70/154.50 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 154.70/154.50 => ! [B_i] : % 154.70/154.50 ( ? [B_j] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 154.70/154.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 154.70/154.50 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 154.70/154.50 => hBOOL(hAPP(V_P_2,B_i)) ) ) % 154.70/154.50 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.50 => ! [B_i] : % 154.70/154.50 ( ? [B_j] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 154.70/154.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.50 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 154.70/154.50 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_z3div__def,axiom, % 154.70/154.50 ! [V_k,V_l] : % 154.70/154.50 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 154.70/154.50 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) ) % 154.70/154.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 154.70/154.50 => c_SMT_Oz3div(V_k,V_l) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l))) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OSup__fin_Ohom__commute,axiom, % 154.70/154.50 ! [V_N_2,V_h_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 154.70/154.50 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_min__max_OInf__fin_Ohom__commute,axiom, % 154.70/154.50 ! [V_N_2,V_h_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 154.70/154.50 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Max_Ohom__commute,axiom, % 154.70/154.50 ! [V_N_2,V_h_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 154.70/154.50 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__le__dividend,axiom, % 154.70/154.50 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__le__mono,axiom, % 154.70/154.50 ! [V_k,V_n,V_m] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),V_k))) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__mult2__eq,axiom, % 154.70/154.50 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)),V_c) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__1,axiom, % 154.70/154.50 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__less,axiom, % 154.70/154.50 ! [V_n,V_m] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_nat__mult__div__cancel__disj,axiom, % 154.70/154.50 ! [V_n,V_m,V_k] : % 154.70/154.50 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 154.70/154.50 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zdiv__int,axiom, % 154.70/154.50 ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom, % 154.70/154.50 ! [V_y,V_x] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_x),V_y)) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__le__mono2,axiom, % 154.70/154.50 ! [V_k,V_n,V_m] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_n)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_m))) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__mult__self1__is__m,axiom, % 154.70/154.50 ! [V_m,V_n] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)),V_n) = V_m ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__mult__self__is__m,axiom, % 154.70/154.50 ! [V_m,V_n] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_nat__mult__div__cancel1,axiom, % 154.70/154.50 ! [V_n,V_m,V_k] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__less__dividend,axiom, % 154.70/154.50 ! [V_m,V_n] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__if,axiom, % 154.70/154.50 ! [V_m,V_n] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 154.70/154.50 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 154.70/154.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_div__geq,axiom, % 154.70/154.50 ! [V_m,V_n] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 154.70/154.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_split__div,axiom, % 154.70/154.50 ! [V_k_2,V_n_2,V_P_2] : % 154.70/154.50 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2))) % 154.70/154.50 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.50 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 154.70/154.50 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.50 => ! [B_i,B_j] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 154.70/154.50 => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j) % 154.70/154.50 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom, % 154.70/154.50 ! [V_y,V_x] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_nat__div__distrib,axiom, % 154.70/154.50 ! [V_y,V_x] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 154.70/154.50 => hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_le__div__geq,axiom, % 154.70/154.50 ! [V_m,V_n] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 154.70/154.50 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_split__div__lemma,axiom, % 154.70/154.50 ! [V_m_2,V_q_2,V_n_2] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 154.70/154.50 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2)) % 154.70/154.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_q_2)))) ) % 154.70/154.50 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_split__div_H,axiom, % 154.70/154.50 ! [V_n_2,V_m_2,V_P_2] : % 154.70/154.50 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2))) % 154.70/154.50 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.50 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 154.70/154.50 | ? [B_q] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2)) % 154.70/154.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,B_q)))) % 154.70/154.50 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Nitpick_Onat__lcm__def,axiom, % 154.70/154.50 ! [V_y,V_x] : c_Nitpick_Onat__lcm(V_x,V_y) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)),c_Nitpick_Onat__gcd(V_x,V_y)) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Min_Ohom__commute,axiom, % 154.70/154.50 ! [V_N_2,V_h_2,T_a] : % 154.70/154.50 ( class_Orderings_Olinorder(T_a) % 154.70/154.50 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 154.70/154.50 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.50 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_negD,axiom, % 154.70/154.50 ! [V_x] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.50 => ? [B_n] : V_x = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_strong__setprod__reindex__cong,axiom, % 154.70/154.50 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 154.70/154.50 ( class_Groups_Ocomm__monoid__mult(T_c) % 154.70/154.50 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.50 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 154.70/154.50 => ( ! [B_x] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.50 => hAPP(V_g_2,B_x) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2),B_x) ) % 154.70/154.50 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),V_g_2),V_A_2) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Nitpick_Oint__gcd__def,axiom, % 154.70/154.50 ! [V_y,V_x] : hAPP(hAPP(c_Nitpick_Oint__gcd,V_x),V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))) ). % 154.70/154.50 % 154.70/154.50 fof(fact_setprod__mono__one__left,axiom, % 154.70/154.50 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 154.70/154.50 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 154.70/154.50 => ( ! [B_x] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2))) % 154.70/154.50 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 154.70/154.50 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_setprod__mono__one__right,axiom, % 154.70/154.50 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 154.70/154.50 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.70/154.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 154.70/154.50 => ( ! [B_x] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2))) % 154.70/154.50 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 154.70/154.50 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_field__le__mult__one__interval,axiom, % 154.70/154.50 ! [V_y,V_x,T_a] : % 154.70/154.50 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 154.70/154.50 => ( ! [B_z] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a))) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_z),V_x)),V_y)) ) ) % 154.70/154.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom, % 154.70/154.50 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] : % 154.70/154.50 ( ( class_Groups_Ocomm__monoid__add(T_a) % 154.70/154.50 & class_Groups_Ocomm__monoid__mult(T_a) ) % 154.70/154.50 => ( V_A_2 = V_B_2 % 154.70/154.50 => ( c_Nat__Transfer_Onat__set(V_B_2) % 154.70/154.50 => ( ! [B_x] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 154.70/154.50 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 154.70/154.50 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),V_g_2),V_B_2) ) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_split__pos__lemma,axiom, % 154.70/154.50 ! [V_n_2,V_P_2,V_k_2] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 154.70/154.50 <=> ! [B_i,B_j] : % 154.70/154.50 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 154.70/154.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 154.70/154.50 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 154.70/154.50 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_split__neg__lemma,axiom, % 154.70/154.50 ! [V_n_2,V_P_2,V_k_2] : % 154.70/154.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 154.70/154.50 <=> ! [B_i,B_j] : % 154.70/154.50 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 154.70/154.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.50 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 154.70/154.50 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_sgn__neg,axiom, % 154.70/154.50 ! [V_a,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.50 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zmod__zminus2,axiom, % 154.70/154.50 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mod__minus__eq,axiom, % 154.70/154.50 ! [V_b,V_a,T_a] : % 154.70/154.50 ( class_Divides_Oring__div(T_a) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zmod__zminus__zminus,axiom, % 154.70/154.50 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zminus__zmod,axiom, % 154.70/154.50 ! [V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_x),V_m) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mod__minus__cong,axiom, % 154.70/154.50 ! [V_a_H,V_b,V_a,T_a] : % 154.70/154.50 ( class_Divides_Oring__div(T_a) % 154.70/154.50 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_H),V_b) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zmod__zmult1__eq,axiom, % 154.70/154.50 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zmod__simps_I3_J,axiom, % 154.70/154.50 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mod__add__cong,axiom, % 154.70/154.50 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 154.70/154.50 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zmod__simps_I1_J,axiom, % 154.70/154.50 ! [V_b,V_c,V_a,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zmod__simps_I2_J,axiom, % 154.70/154.50 ! [V_c,V_b,V_a,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mod__add__eq,axiom, % 154.70/154.50 ! [V_c,V_b,V_a,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mod__add__left__eq,axiom, % 154.70/154.50 ! [V_c,V_b,V_a,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mod__add__right__eq,axiom, % 154.70/154.50 ! [V_c,V_b,V_a,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mod__add__self1,axiom, % 154.70/154.50 ! [V_a,V_b,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mod__add__self2,axiom, % 154.70/154.50 ! [V_b,V_a,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mod__mult__right__eq,axiom, % 154.70/154.50 ! [V_c,V_b,V_a,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mod__mult__left__eq,axiom, % 154.70/154.50 ! [V_c,V_b,V_a,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mod__mult__eq,axiom, % 154.70/154.50 ! [V_c,V_b,V_a,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mod__mult__mult1,axiom, % 154.70/154.50 ! [V_b,V_a,V_c,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mod__mult__mult2,axiom, % 154.70/154.50 ! [V_b,V_c,V_a,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zmod__simps_I4_J,axiom, % 154.70/154.50 ! [V_b,V_c,V_a,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mod__mult__cong,axiom, % 154.70/154.50 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 154.70/154.50 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b_H),V_c) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mod__diff__cong,axiom, % 154.70/154.50 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 154.70/154.50 ( class_Divides_Oring__div(T_a) % 154.70/154.50 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 154.70/154.50 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_H),V_b_H),V_c) ) ) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mod__diff__eq,axiom, % 154.70/154.50 ! [V_c,V_b,V_a,T_a] : % 154.70/154.50 ( class_Divides_Oring__div(T_a) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mod__diff__left__eq,axiom, % 154.70/154.50 ! [V_c,V_b,V_a,T_a] : % 154.70/154.50 ( class_Divides_Oring__div(T_a) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mod__diff__right__eq,axiom, % 154.70/154.50 ! [V_c,V_b,V_a,T_a] : % 154.70/154.50 ( class_Divides_Oring__div(T_a) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mod__mod__trivial,axiom, % 154.70/154.50 ! [V_b,V_a,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_sgn__sgn,axiom, % 154.70/154.50 ! [V_a,T_a] : % 154.70/154.50 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.50 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mod__0,axiom, % 154.70/154.50 ! [V_a,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mod__by__0,axiom, % 154.70/154.50 ! [V_a,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_mod__self,axiom, % 154.70/154.50 ! [V_a,T_a] : % 154.70/154.50 ( class_Divides_Osemiring__div(T_a) % 154.70/154.50 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zmod__zero,axiom, % 154.70/154.50 ! [V_b] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zmod__self,axiom, % 154.70/154.50 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zdiff__zmod__left,axiom, % 154.70/154.50 ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m) ). % 154.70/154.50 % 154.70/154.50 fof(fact_zdiff__zmod__right,axiom, % 154.70/154.50 ! [V_m,V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m) ). % 154.70/154.50 % 154.70/154.50 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom, % 154.70/154.50 ! [V_y,V_x] : % 154.70/154.50 ( c_Nat__Transfer_Ois__nat(V_x) % 154.70/154.51 => ( c_Nat__Transfer_Ois__nat(V_y) % 154.70/154.51 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zpower__zmod,axiom, % 154.70/154.51 ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y),V_m) ). % 154.70/154.51 % 154.70/154.51 fof(fact_sgn0,axiom, % 154.70/154.51 ! [T_a] : % 154.70/154.51 ( class_Groups_Osgn__if(T_a) % 154.70/154.51 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_sgn__0__0,axiom, % 154.70/154.51 ! [V_a_2,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.51 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.51 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_sgn__times,axiom, % 154.70/154.51 ! [V_b,V_a,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.51 => c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__mult__self2__is__0,axiom, % 154.70/154.51 ! [V_b,V_a,T_a] : % 154.70/154.51 ( class_Divides_Osemiring__div(T_a) % 154.70/154.51 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__mult__self1__is__0,axiom, % 154.70/154.51 ! [V_a,V_b,T_a] : % 154.70/154.51 ( class_Divides_Osemiring__div(T_a) % 154.70/154.51 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__mult__self2,axiom, % 154.70/154.51 ! [V_c,V_b,V_a,T_a] : % 154.70/154.51 ( class_Divides_Osemiring__div(T_a) % 154.70/154.51 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__mult__self1,axiom, % 154.70/154.51 ! [V_b,V_c,V_a,T_a] : % 154.70/154.51 ( class_Divides_Osemiring__div(T_a) % 154.70/154.51 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__by__1,axiom, % 154.70/154.51 ! [V_a,T_a] : % 154.70/154.51 ( class_Divides_Osemiring__div(T_a) % 154.70/154.51 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__div__trivial,axiom, % 154.70/154.51 ! [V_b,V_a,T_a] : % 154.70/154.51 ( class_Divides_Osemiring__div(T_a) % 154.70/154.51 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zmod__le__nonneg__dividend,axiom, % 154.70/154.51 ! [V_k,V_m] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k)),V_m)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom, % 154.70/154.51 ! [V_y,V_x] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_pos__mod__bound,axiom, % 154.70/154.51 ! [V_a,V_b] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_neg__mod__bound,axiom, % 154.70/154.51 ! [V_a,V_b] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zmod__eq__0__iff,axiom, % 154.70/154.51 ! [V_d_2,V_m_2] : % 154.70/154.51 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zmod__zminus2__not__zero,axiom, % 154.70/154.51 ! [V_l,V_k] : % 154.70/154.51 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zmod__zminus1__not__zero,axiom, % 154.70/154.51 ! [V_l,V_k] : % 154.70/154.51 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_DIVISION__BY__ZERO,axiom, % 154.70/154.51 ! [V_a] : % 154.70/154.51 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zmod__zdiv__trivial,axiom, % 154.70/154.51 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zdiv__zadd1__eq,axiom, % 154.70/154.51 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_div__mod__equality,axiom, % 154.70/154.51 ! [V_c,V_b,V_a,T_a] : % 154.70/154.51 ( class_Divides_Osemiring__div(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_div__mod__equality2,axiom, % 154.70/154.51 ! [V_c,V_a,V_b,T_a] : % 154.70/154.51 ( class_Divides_Osemiring__div(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__div__equality,axiom, % 154.70/154.51 ! [V_b,V_a,T_a] : % 154.70/154.51 ( class_Divides_Osemiring__div(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__div__equality2,axiom, % 154.70/154.51 ! [V_a,V_b,T_a] : % 154.70/154.51 ( class_Divides_Osemiring__div(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_semiring__div__class_Omod__div__equality_H,axiom, % 154.70/154.51 ! [V_b,V_a,T_a] : % 154.70/154.51 ( class_Divides_Osemiring__div(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)) = V_a ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__neg__neg__trivial,axiom, % 154.70/154.51 ! [V_b,V_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_neg__mod__conj,axiom, % 154.70/154.51 ! [V_a,V_b] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_neg__mod__sign,axiom, % 154.70/154.51 ! [V_a,V_b] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__pos__pos__trivial,axiom, % 154.70/154.51 ! [V_b,V_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_pos__mod__conj,axiom, % 154.70/154.51 ! [V_a,V_b] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) % 154.70/154.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_pos__mod__sign,axiom, % 154.70/154.51 ! [V_a,V_b] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_sgn__less,axiom, % 154.70/154.51 ! [V_a_2,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_sgn__greater,axiom, % 154.70/154.51 ! [V_a_2,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Osgn__class_Osgn(T_a,V_a_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zmod__zminus1__eq__if,axiom, % 154.70/154.51 ! [V_b,V_a] : % 154.70/154.51 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 154.70/154.51 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zmod__zminus2__eq__if,axiom, % 154.70/154.51 ! [V_b,V_a] : % 154.70/154.51 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 154.70/154.51 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zmod__zdiv__equality,axiom, % 154.70/154.51 ! [V_b,V_a] : V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zdiv__zmult1__eq,axiom, % 154.70/154.51 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zdiv__zmod__equality,axiom, % 154.70/154.51 ! [V_k,V_a,V_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zdiv__zmod__equality2,axiom, % 154.70/154.51 ! [V_k,V_b,V_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zmod__zdiv__equality_H,axiom, % 154.70/154.51 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)),V_n)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zmult__div__cancel,axiom, % 154.70/154.51 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_abs__sgn,axiom, % 154.70/154.51 ! [V_k,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.51 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mult__sgn__abs,axiom, % 154.70/154.51 ! [V_x,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)) = V_x ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__pos__neg__trivial,axiom, % 154.70/154.51 ! [V_b,V_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_sgn__pos,axiom, % 154.70/154.51 ! [V_a,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 154.70/154.51 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_sgn__1__pos,axiom, % 154.70/154.51 ! [V_a_2,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.51 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_divmod__int__rel__mod__eq,axiom, % 154.70/154.51 ! [V_y,V_q_1,V_b_1,V_a_1] : % 154.70/154.51 ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_q_1)),V_y) % 154.70/154.51 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 154.70/154.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) % 154.70/154.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 154.70/154.51 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zmult2__lemma__aux2,axiom, % 154.70/154.51 ! [V_q,V_r,V_b,V_c] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zmult2__lemma__aux1,axiom, % 154.70/154.51 ! [V_q,V_r,V_b,V_c] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zmult2__lemma__aux4,axiom, % 154.70/154.51 ! [V_q,V_b,V_r,V_c] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zmult2__lemma__aux3,axiom, % 154.70/154.51 ! [V_q,V_b,V_r,V_c] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_split__zmod,axiom, % 154.70/154.51 ! [V_k_2,V_n_2,V_P_2] : % 154.70/154.51 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 154.70/154.51 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => hBOOL(hAPP(V_P_2,V_n_2)) ) % 154.70/154.51 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 154.70/154.51 => ! [B_i,B_j] : % 154.70/154.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 154.70/154.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 154.70/154.51 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 154.70/154.51 => hBOOL(hAPP(V_P_2,B_j)) ) ) % 154.70/154.51 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.51 => ! [B_i,B_j] : % 154.70/154.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 154.70/154.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.51 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 154.70/154.51 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zmod__zmult2__eq,axiom, % 154.70/154.51 ! [V_b,V_a,V_c] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zdiv__zminus2__eq__if,axiom, % 154.70/154.51 ! [V_a,V_b] : % 154.70/154.51 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) ) % 154.70/154.51 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zdiv__zminus1__eq__if,axiom, % 154.70/154.51 ! [V_a,V_b] : % 154.70/154.51 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) ) % 154.70/154.51 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zsgn__def,axiom, % 154.70/154.51 ! [V_i] : % 154.70/154.51 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 154.70/154.51 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 154.70/154.51 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 154.70/154.51 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_sgn__if,axiom, % 154.70/154.51 ! [V_x,T_a] : % 154.70/154.51 ( class_Groups_Osgn__if(T_a) % 154.70/154.51 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.51 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) % 154.70/154.51 & ( V_x != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.51 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 154.70/154.51 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 154.70/154.51 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_sgn__1__neg,axiom, % 154.70/154.51 ! [V_a_2,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.51 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_z3mod__def,axiom, % 154.70/154.51 ! [V_k,V_l] : % 154.70/154.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 154.70/154.51 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 154.70/154.51 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_setprod__pos__nat,axiom, % 154.70/154.51 ! [V_f_2,V_S_2,T_a] : % 154.70/154.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 154.70/154.51 => ( ! [B_x] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_S_2))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_card__quotient__disjoint,axiom, % 154.70/154.51 ! [V_r_2,V_A_2,T_a] : % 154.70/154.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.51 => ( c_Fun_Oinj__on(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),T_a),c_Equiv__Relations_Oquotient(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_r_2),V_A_2) % 154.70/154.51 => hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_fold__image__1,axiom, % 154.70/154.51 ! [V_f_2,V_S_2,T_a,T_b] : % 154.70/154.51 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.70/154.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 154.70/154.51 => ( ! [B_x] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 154.70/154.51 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 154.70/154.51 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),V_S_2) = c_Groups_Oone__class_Oone(T_b) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__mult__distrib2,axiom, % 154.70/154.51 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__mult__distrib,axiom, % 154.70/154.51 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_k) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__less__eq__dividend,axiom, % 154.70/154.51 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_m)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__less,axiom, % 154.70/154.51 ! [V_n,V_m] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__Suc__eq__Suc__mod,axiom, % 154.70/154.51 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n) ). % 154.70/154.51 % 154.70/154.51 fof(fact_quotient__empty,axiom, % 154.70/154.51 ! [V_r_2,T_a] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_quotient__is__empty2,axiom, % 154.70/154.51 ! [V_r_2,V_A_2,T_a] : % 154.70/154.51 ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2) % 154.70/154.51 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_quotient__is__empty,axiom, % 154.70/154.51 ! [V_r_2,V_A_2,T_a] : % 154.70/154.51 ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 154.70/154.51 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__Suc,axiom, % 154.70/154.51 ! [V_n,V_m] : % 154.70/154.51 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 154.70/154.51 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__1,axiom, % 154.70/154.51 ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__less__divisor,axiom, % 154.70/154.51 ! [V_m,V_n] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__eq__0__iff,axiom, % 154.70/154.51 ! [V_d_2,V_m_2] : % 154.70/154.51 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.51 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__if,axiom, % 154.70/154.51 ! [V_n,V_m] : % 154.70/154.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__geq,axiom, % 154.70/154.51 ! [V_n,V_m] : % 154.70/154.51 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__mult__self3,axiom, % 154.70/154.51 ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) ). % 154.70/154.51 % 154.70/154.51 fof(fact_le__mod__geq,axiom, % 154.70/154.51 ! [V_m,V_n] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zmod__int,axiom, % 154.70/154.51 ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom, % 154.70/154.51 ! [V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_div__add1__eq,axiom, % 154.70/154.51 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__gcd_Osimps,axiom, % 154.70/154.51 ! [V_x,V_y] : % 154.70/154.51 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.51 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x ) % 154.70/154.51 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.51 => c_Nitpick_Onat__gcd(V_x,V_y) = c_Nitpick_Onat__gcd(V_y,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__le__divisor,axiom, % 154.70/154.51 ! [V_m,V_n] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__mult__self4,axiom, % 154.70/154.51 ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m)),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__mult2__eq,axiom, % 154.70/154.51 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_div__mult1__eq,axiom, % 154.70/154.51 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Divides_Omod__div__equality_H,axiom, % 154.70/154.51 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mult__div__cancel,axiom, % 154.70/154.51 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_div__mod__equality_H,axiom, % 154.70/154.51 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_quotient__diff1,axiom, % 154.70/154.51 ! [V_a_2,V_A_2,V_r_2,T_a] : % 154.70/154.51 ( c_Fun_Oinj__on(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),T_a),c_Equiv__Relations_Oquotient(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_r_2),V_A_2) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.70/154.51 => hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__lemma,axiom, % 154.70/154.51 ! [V_q,V_b,V_r,V_c] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_split__mod,axiom, % 154.70/154.51 ! [V_k_2,V_n_2,V_P_2] : % 154.70/154.51 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) % 154.70/154.51 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.51 => hBOOL(hAPP(V_P_2,V_n_2)) ) % 154.70/154.51 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.51 => ! [B_i,B_j] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 154.70/154.51 => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j) % 154.70/154.51 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Suc__times__mod__eq,axiom, % 154.70/154.51 ! [V_m,V_k] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k)) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),V_k) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom, % 154.70/154.51 ! [V_y,V_x] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__mod__distrib,axiom, % 154.70/154.51 ! [V_y,V_x] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 154.70/154.51 => hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_quotient__def,axiom, % 154.70/154.51 ! [V_r_2,V_A_2,T_a] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),T_a),c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),c_Relation_OImage(T_a,T_a,V_r_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_singleton__quotient,axiom, % 154.70/154.51 ! [V_r_2,V_x_2,T_a] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_quotientI,axiom, % 154.70/154.51 ! [V_r_2,V_A_2,V_x_2,T_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_card_Oneutral,axiom, % 154.70/154.51 ! [V_A_2,T_a] : % 154.70/154.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.51 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.51 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 154.70/154.51 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Image__eq__UN,axiom, % 154.70/154.51 ! [V_B_2,V_r_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Relation_OImage(T_b,T_a,V_r_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Image__INT__subset,axiom, % 154.70/154.51 ! [V_B_2,V_A_2,T_c,V_r_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Relation_OImage(T_b,T_a,V_r_2)),V_B_2)))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Image__Int__subset,axiom, % 154.70/154.51 ! [V_B_2,V_A_2,V_R_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_B_2)))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Image__UN,axiom, % 154.70/154.51 ! [V_B_2,V_A_2,T_c,V_r_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Relation_OImage(T_b,T_a,V_r_2)),V_B_2)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Image__empty,axiom, % 154.70/154.51 ! [V_R_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_R_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)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Image__mono,axiom, % 154.70/154.51 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_b,T_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_H_2),V_A_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_b,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Image__Un,axiom, % 154.70/154.51 ! [V_B_2,V_A_2,V_R_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_B_2)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Un__Image,axiom, % 154.70/154.51 ! [V_A_2,V_S_2,V_R_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_S_2),V_A_2)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_quotientE,axiom, % 154.70/154.51 ! [V_r_2,V_A_2,V_X_2,T_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 154.70/154.51 => ~ ! [B_x] : % 154.70/154.51 ( V_X_2 = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 154.70/154.51 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__mod__eq__lemma,axiom, % 154.70/154.51 ! [V_y,V_n,V_x] : % 154.70/154.51 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x)) % 154.70/154.51 => ? [B_q] : V_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),B_q)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_min__max_Ofold__sup__le__sup,axiom, % 154.70/154.51 ! [V_c_2,V_b_2,V_A_2,T_a] : % 154.70/154.51 ( class_Orderings_Olinorder(T_a) % 154.70/154.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.51 => ( ! [B_x] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b_2),V_c_2))) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_min__max_Oinf__le__fold__inf,axiom, % 154.70/154.51 ! [V_c_2,V_b_2,V_A_2,T_a] : % 154.70/154.51 ( class_Orderings_Olinorder(T_a) % 154.70/154.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.51 => ( ! [B_x] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_c_2),V_A_2))) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_less__by__empty,axiom, % 154.70/154.51 ! [V_B_2,T_a,V_A_2] : % 154.70/154.51 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__induct__0,axiom, % 154.70/154.51 ! [V_i_2,V_P_2,V_p_2] : % 154.70/154.51 ( ! [B_i] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) % 154.70/154.51 => ( hBOOL(hAPP(V_P_2,B_i)) % 154.70/154.51 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) ) % 154.70/154.51 => ( hBOOL(hAPP(V_P_2,V_i_2)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2)) % 154.70/154.51 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_InterI,axiom, % 154.70/154.51 ! [V_A_2,V_C_2,T_a] : % 154.70/154.51 ( ! [B_X] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) ) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_fold__image__cong,axiom, % 154.70/154.51 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_a,T_b] : % 154.70/154.51 ( class_Groups_Oab__semigroup__mult(T_b) % 154.70/154.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.51 => ( ! [B_x] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.51 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 154.70/154.51 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_h_2),V_z_2),V_A_2) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Max__eqI,axiom, % 154.70/154.51 ! [V_x_2,V_A_2,T_a] : % 154.70/154.51 ( class_Orderings_Olinorder(T_a) % 154.70/154.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.51 => ( ! [B_y] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_y),V_x_2)) ) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.51 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Min__eqI,axiom, % 154.70/154.51 ! [V_x_2,V_A_2,T_a] : % 154.70/154.51 ( class_Orderings_Olinorder(T_a) % 154.70/154.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.51 => ( ! [B_y] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_y)) ) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.51 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_inf__le__fold__inf,axiom, % 154.70/154.51 ! [V_c_2,V_b_2,V_A_2,T_a] : % 154.70/154.51 ( class_Lattices_Osemilattice__inf(T_a) % 154.70/154.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.51 => ( ! [B_x] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_c_2),V_A_2))) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_fold__sup__le__sup,axiom, % 154.70/154.51 ! [V_c_2,V_b_2,V_A_2,T_a] : % 154.70/154.51 ( class_Lattices_Osemilattice__sup(T_a) % 154.70/154.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.51 => ( ! [B_x] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b_2),V_c_2))) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_expand__Suc,axiom, % 154.70/154.51 ! [V_v] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v))) % 154.70/154.51 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_eq__number__of,axiom, % 154.70/154.51 ! [V_y_2,V_x_2,T_a] : % 154.70/154.51 ( ( class_Int_Onumber__ring(T_a) % 154.70/154.51 & class_Int_Oring__char__0(T_a) ) % 154.70/154.51 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 154.70/154.51 <=> V_x_2 = V_y_2 ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_number__of__reorient,axiom, % 154.70/154.51 ! [V_x_2,V_w_2,T_a] : % 154.70/154.51 ( class_Int_Onumber(T_a) % 154.70/154.51 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = V_x_2 % 154.70/154.51 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_of__nat__number__of__eq,axiom, % 154.70/154.51 ! [V_v,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.51 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.51 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_of__int__number__of__eq,axiom, % 154.70/154.51 ! [V_v,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_number__of__eq,axiom, % 154.70/154.51 ! [V_k,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_of__nat__number__of__lemma,axiom, % 154.70/154.51 ! [V_v,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.51 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.51 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_le__number__of__eq__not__less,axiom, % 154.70/154.51 ! [V_w_2,V_v_2,T_a] : % 154.70/154.51 ( ( class_Int_Onumber(T_a) % 154.70/154.51 & class_Orderings_Olinorder(T_a) ) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 154.70/154.51 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_left__distrib__number__of,axiom, % 154.70/154.51 ! [V_v,V_b,V_a,T_b] : % 154.70/154.51 ( ( class_Int_Onumber(T_b) % 154.70/154.51 & class_Rings_Osemiring(T_b) ) % 154.70/154.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_right__distrib__number__of,axiom, % 154.70/154.51 ! [V_c,V_b,V_v,T_b] : % 154.70/154.51 ( ( class_Int_Onumber(T_b) % 154.70/154.51 & class_Rings_Osemiring(T_b) ) % 154.70/154.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_right__diff__distrib__number__of,axiom, % 154.70/154.51 ! [V_c,V_b,V_v,T_b] : % 154.70/154.51 ( ( class_Int_Onumber(T_b) % 154.70/154.51 & class_Rings_Oring(T_b) ) % 154.70/154.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_left__diff__distrib__number__of,axiom, % 154.70/154.51 ! [V_v,V_b,V_a,T_b] : % 154.70/154.51 ( ( class_Int_Onumber(T_b) % 154.70/154.51 & class_Rings_Oring(T_b) ) % 154.70/154.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_le__number__of,axiom, % 154.70/154.51 ! [V_y_2,V_x_2,T_a] : % 154.70/154.51 ( ( class_Int_Onumber__ring(T_a) % 154.70/154.51 & class_Rings_Olinordered__idom(T_a) ) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_less__number__of,axiom, % 154.70/154.51 ! [V_y_2,V_x_2,T_a] : % 154.70/154.51 ( ( class_Int_Onumber__ring(T_a) % 154.70/154.51 & class_Rings_Olinordered__idom(T_a) ) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_min__number__of,axiom, % 154.70/154.51 ! [V_v,V_u,T_b] : % 154.70/154.51 ( ( class_Int_Onumber(T_b) % 154.70/154.51 & class_Orderings_Oord(T_b) ) % 154.70/154.51 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) % 154.70/154.51 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) % 154.70/154.51 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_max__number__of,axiom, % 154.70/154.51 ! [V_v,V_u,T_b] : % 154.70/154.51 ( ( class_Int_Onumber(T_b) % 154.70/154.51 & class_Orderings_Oord(T_b) ) % 154.70/154.51 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) % 154.70/154.51 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) % 154.70/154.51 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_add__number__of__left,axiom, % 154.70/154.51 ! [V_z,V_w,V_v,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_z) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_add__number__of__eq,axiom, % 154.70/154.51 ! [V_w,V_v,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_number__of__add,axiom, % 154.70/154.51 ! [V_w,V_v,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mult__number__of__left,axiom, % 154.70/154.51 ! [V_z,V_w,V_v,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))),V_z) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_arith__simps_I32_J,axiom, % 154.70/154.51 ! [V_w,V_v,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_number__of__mult,axiom, % 154.70/154.51 ! [V_w,V_v,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_number__of__diff,axiom, % 154.70/154.51 ! [V_w,V_v,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_number__of__minus,axiom, % 154.70/154.51 ! [V_w,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_arith__simps_I30_J,axiom, % 154.70/154.51 ! [V_w,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Ints__number__of,axiom, % 154.70/154.51 ! [V_w_2,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_eq__divide__eq__number__of1,axiom, % 154.70/154.51 ! [V_w_2,V_b_2,V_a_2,T_a] : % 154.70/154.51 ( ( class_Fields_Ofield__inverse__zero(T_a) % 154.70/154.51 & class_Int_Onumber(T_a) ) % 154.70/154.51 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) % 154.70/154.51 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) = V_b_2 ) % 154.70/154.51 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.51 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_eq__divide__eq__number__of,axiom, % 154.70/154.51 ! [V_c_2,V_b_2,V_w_2,T_a] : % 154.70/154.51 ( ( class_Fields_Ofield__inverse__zero(T_a) % 154.70/154.51 & class_Int_Onumber(T_a) ) % 154.70/154.51 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) % 154.70/154.51 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2) = V_b_2 ) % 154.70/154.51 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.51 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_divide__eq__eq__number__of,axiom, % 154.70/154.51 ! [V_w_2,V_c_2,V_b_2,T_a] : % 154.70/154.51 ( ( class_Fields_Ofield__inverse__zero(T_a) % 154.70/154.51 & class_Int_Onumber(T_a) ) % 154.70/154.51 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) % 154.70/154.51 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.51 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2) ) % 154.70/154.51 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.51 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_divide__eq__eq__number__of1,axiom, % 154.70/154.51 ! [V_a_2,V_w_2,V_b_2,T_a] : % 154.70/154.51 ( ( class_Fields_Ofield__inverse__zero(T_a) % 154.70/154.51 & class_Int_Onumber(T_a) ) % 154.70/154.51 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) = V_a_2 % 154.70/154.51 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.51 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) ) % 154.70/154.51 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.51 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_add__number__of__diff1,axiom, % 154.70/154.51 ! [V_c,V_w,V_v,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_c) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_minus__number__of__mult,axiom, % 154.70/154.51 ! [V_z,V_w,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),V_z) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))),V_z) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_diff__number__of__eq,axiom, % 154.70/154.51 ! [V_w,V_v,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_less__divide__eq__number__of1,axiom, % 154.70/154.51 ! [V_w_2,V_b_2,V_a_2,T_a] : % 154.70/154.51 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 154.70/154.51 & class_Int_Onumber(T_a) ) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) % 154.70/154.51 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 154.70/154.51 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_less__divide__eq__number__of,axiom, % 154.70/154.51 ! [V_c_2,V_b_2,V_w_2,T_a] : % 154.70/154.51 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 154.70/154.51 & class_Int_Onumber(T_a) ) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) % 154.70/154.51 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2)) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 154.70/154.51 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2))) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_divide__less__eq__number__of,axiom, % 154.70/154.51 ! [V_w_2,V_c_2,V_b_2,T_a] : % 154.70/154.51 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 154.70/154.51 & class_Int_Onumber(T_a) ) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 154.70/154.51 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2))) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 154.70/154.51 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2)) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) ) ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_divide__less__eq__number__of1,axiom, % 154.70/154.51 ! [V_a_2,V_w_2,V_b_2,T_a] : % 154.70/154.51 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 154.70/154.51 & class_Int_Onumber(T_a) ) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_a_2)) % 154.70/154.51 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 154.70/154.51 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_abs__number__of,axiom, % 154.70/154.51 ! [V_x,T_a] : % 154.70/154.51 ( ( class_Int_Onumber__ring(T_a) % 154.70/154.51 & class_Rings_Olinordered__idom(T_a) ) % 154.70/154.51 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.51 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.51 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_add__number__of__diff2,axiom, % 154.70/154.51 ! [V_w,V_c,V_v,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)))),V_c) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_divide__le__eq__number__of1,axiom, % 154.70/154.51 ! [V_a_2,V_w_2,V_b_2,T_a] : % 154.70/154.51 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 154.70/154.51 & class_Int_Onumber(T_a) ) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_a_2)) % 154.70/154.51 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 154.70/154.51 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_divide__le__eq__number__of,axiom, % 154.70/154.51 ! [V_w_2,V_c_2,V_b_2,T_a] : % 154.70/154.51 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 154.70/154.51 & class_Int_Onumber(T_a) ) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 154.70/154.51 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2))) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 154.70/154.51 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2)) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) ) ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_le__divide__eq__number__of,axiom, % 154.70/154.51 ! [V_c_2,V_b_2,V_w_2,T_a] : % 154.70/154.51 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 154.70/154.51 & class_Int_Onumber(T_a) ) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) % 154.70/154.51 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2)) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 154.70/154.51 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2))) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_le__divide__eq__number__of1,axiom, % 154.70/154.51 ! [V_w_2,V_b_2,V_a_2,T_a] : % 154.70/154.51 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 154.70/154.51 & class_Int_Onumber(T_a) ) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) % 154.70/154.51 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 154.70/154.51 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_one__mod__nat__number__of,axiom, % 154.70/154.51 ! [V_v_H] : % 154.70/154.51 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_one__div__nat__number__of,axiom, % 154.70/154.51 ! [V_v_H] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power__number__of__odd__number__of,axiom, % 154.70/154.51 ! [V_v_2,V_w_2,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)))),c_COMBI(T_a))) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power__nat__number__of,axiom, % 154.70/154.51 ! [V_n,V_v] : % 154.70/154.51 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),V_n)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_minus__numeral__code_I5_J,axiom, % 154.70/154.51 ! [V_w] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_plus__numeral__code_I9_J,axiom, % 154.70/154.51 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_less__number__of__int__code,axiom, % 154.70/154.51 ! [V_l_2,V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_number__of__is__id,axiom, % 154.70/154.51 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ). % 154.70/154.51 % 154.70/154.51 fof(fact_neg__number__of__Bit1,axiom, % 154.70/154.51 ! [V_w_2] : % 154.70/154.51 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2)))) % 154.70/154.51 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_times__numeral__code_I5_J,axiom, % 154.70/154.51 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_less__eq__number__of__int__code,axiom, % 154.70/154.51 ! [V_l_2,V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I34_J,axiom, % 154.70/154.51 ! [V_l_2,V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_less__eq__int__code_I16_J,axiom, % 154.70/154.51 ! [V_k2_2,V_k1_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I51_J,axiom, % 154.70/154.51 ! [V_l_2,V_k_2] : % 154.70/154.51 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2) % 154.70/154.51 <=> V_k_2 = V_l_2 ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_less__int__code_I16_J,axiom, % 154.70/154.51 ! [V_k2_2,V_k1_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I17_J,axiom, % 154.70/154.51 ! [V_l_2,V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_int__number__of__def,axiom, % 154.70/154.51 ! [V_w] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),V_w) ). % 154.70/154.51 % 154.70/154.51 fof(fact_bin__less__0__simps_I4_J,axiom, % 154.70/154.51 ! [V_w_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Bit1__def,axiom, % 154.70/154.51 ! [V_k] : c_Int_OBit1(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)),V_k) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__number__of,axiom, % 154.70/154.51 ! [V_w] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__number__of__def,axiom, % 154.70/154.51 ! [V_v] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__number__of__Bit1,axiom, % 154.70/154.51 ! [V_w_2] : % 154.70/154.51 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 154.70/154.51 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 154.70/154.51 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_number__of__Bit1,axiom, % 154.70/154.51 ! [V_w,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power__number__of__odd,axiom, % 154.70/154.51 ! [V_z_2,V_w_2,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z_2))),c_COMBI(T_a))) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zpower__number__of__odd,axiom, % 154.70/154.51 ! [V_z_2,V_w_2] : % 154.70/154.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z_2))),c_COMBI(tc_Int_Oint))) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_minus__numeral__code_I6_J,axiom, % 154.70/154.51 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_neg__imp__number__of__eq__0,axiom, % 154.70/154.51 ! [V_v] : % 154.70/154.51 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.51 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_int__eq__iff__number__of,axiom, % 154.70/154.51 ! [V_v_2,V_m_2] : % 154.70/154.51 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) % 154.70/154.51 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) % 154.70/154.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_eq__nat__number__of,axiom, % 154.70/154.51 ! [V_v_H_2,V_v_2] : % 154.70/154.51 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2) % 154.70/154.51 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 154.70/154.51 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 154.70/154.51 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 154.70/154.51 => V_v_2 = V_v_H_2 ) ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__number__of__add__left,axiom, % 154.70/154.51 ! [V_k,V_v_H,V_v] : % 154.70/154.51 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.51 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 154.70/154.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_k) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 154.70/154.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H))),V_k) ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_int__nat__number__of,axiom, % 154.70/154.51 ! [V_v] : % 154.70/154.51 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.51 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.51 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__nat__number__of,axiom, % 154.70/154.51 ! [V_v_H,V_v] : % 154.70/154.51 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.51 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_div__nat__number__of,axiom, % 154.70/154.51 ! [V_v_H,V_v] : % 154.70/154.51 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.51 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.51 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power__nat__number__of__number__of,axiom, % 154.70/154.51 ! [V_w,V_v] : % 154.70/154.51 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Suc__nat__number__of__add,axiom, % 154.70/154.51 ! [V_n,V_v] : % 154.70/154.51 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.51 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.51 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v))),V_n) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_diff__nat__number__of,axiom, % 154.70/154.51 ! [V_v_2,V_v_H_2] : % 154.70/154.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 154.70/154.51 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 154.70/154.51 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_v_H_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_min__Suc__number__of,axiom, % 154.70/154.51 ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_succ__Pls,axiom, % 154.70/154.51 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I39_J,axiom, % 154.70/154.51 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I46_J,axiom, % 154.70/154.51 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ). % 154.70/154.51 % 154.70/154.51 fof(fact_minus__Pls,axiom, % 154.70/154.51 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ). % 154.70/154.51 % 154.70/154.51 fof(fact_Pls__def,axiom, % 154.70/154.51 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 154.70/154.51 % 154.70/154.51 fof(fact_succ__pred,axiom, % 154.70/154.51 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ). % 154.70/154.51 % 154.70/154.51 fof(fact_mult__Pls,axiom, % 154.70/154.51 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ). % 154.70/154.51 % 154.70/154.51 fof(fact_add__Pls,axiom, % 154.70/154.51 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ). % 154.70/154.51 % 154.70/154.51 fof(fact_add__Pls__right,axiom, % 154.70/154.51 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I2_J,axiom, % 154.70/154.51 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_diff__bin__simps_I1_J,axiom, % 154.70/154.51 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I19_J,axiom, % 154.70/154.51 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_number__of__Pls,axiom, % 154.70/154.51 ! [T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_semiring__norm_I112_J,axiom, % 154.70/154.51 ! [T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_add__numeral__0__right,axiom, % 154.70/154.51 ! [V_a,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = V_a ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_add__numeral__0,axiom, % 154.70/154.51 ! [V_a,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)),V_a) = V_a ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_bin__less__0__simps_I1_J,axiom, % 154.70/154.51 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_semiring__norm_I113_J,axiom, % 154.70/154.51 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__number__of__Pls,axiom, % 154.70/154.51 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zero__is__num__zero,axiom, % 154.70/154.51 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I22_J,axiom, % 154.70/154.51 ! [V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I12_J,axiom, % 154.70/154.51 ! [V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Suc__diff__number__of,axiom, % 154.70/154.51 ! [V_m,V_v] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v)) % 154.70/154.51 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_not__neg__number__of__Pls,axiom, % 154.70/154.51 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__1__add__number__of,axiom, % 154.70/154.51 ! [V_v] : % 154.70/154.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 154.70/154.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 154.70/154.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__number__of__add__1,axiom, % 154.70/154.51 ! [V_v] : % 154.70/154.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 154.70/154.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 154.70/154.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_le__iff__pred__less,axiom, % 154.70/154.51 ! [V_l_2,V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_minus__Bit1,axiom, % 154.70/154.51 ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(V_k)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_pred__def,axiom, % 154.70/154.51 ! [V_k] : c_Int_Opred(V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__number__of__diff__1,axiom, % 154.70/154.51 ! [V_v] : % 154.70/154.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 154.70/154.51 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 154.70/154.51 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mult__numeral__1,axiom, % 154.70/154.51 ! [V_a,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))),V_a) = V_a ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mult__numeral__1__right,axiom, % 154.70/154.51 ! [V_a,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_divide__Numeral0,axiom, % 154.70/154.51 ! [V_x,T_a] : % 154.70/154.51 ( ( class_Fields_Ofield__inverse__zero(T_a) % 154.70/154.51 & class_Int_Onumber__ring(T_a) ) % 154.70/154.51 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_semiring__norm_I110_J,axiom, % 154.70/154.51 ! [T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_numeral__1__eq__1,axiom, % 154.70/154.51 ! [T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_eq__number__of__0,axiom, % 154.70/154.51 ! [V_v_2] : % 154.70/154.51 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_eq__0__number__of,axiom, % 154.70/154.51 ! [V_v_2] : % 154.70/154.51 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_number__of2,axiom, % 154.70/154.51 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I5_J,axiom, % 154.70/154.51 ! [V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I29_J,axiom, % 154.70/154.51 ! [V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_less__nat__number__of,axiom, % 154.70/154.51 ! [V_v_H_2,V_v_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2))) % 154.70/154.51 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) % 154.70/154.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_divide__Numeral1,axiom, % 154.70/154.51 ! [V_x,T_a] : % 154.70/154.51 ( ( class_Fields_Ofield(T_a) % 154.70/154.51 & class_Int_Onumber__ring(T_a) ) % 154.70/154.51 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_x ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_divide__numeral__1,axiom, % 154.70/154.51 ! [V_a,T_a] : % 154.70/154.51 ( ( class_Fields_Ofield(T_a) % 154.70/154.51 & class_Int_Onumber__ring(T_a) ) % 154.70/154.51 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_le__nat__number__of,axiom, % 154.70/154.51 ! [V_v_H_2,V_v_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2))) % 154.70/154.51 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_one__is__num__one,axiom, % 154.70/154.51 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__numeral__1__eq__1,axiom, % 154.70/154.51 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Numeral1__eq1__nat,axiom, % 154.70/154.51 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom, % 154.70/154.51 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_succ__def,axiom, % 154.70/154.51 ! [V_k] : c_Int_Osucc(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_le__special_I3_J,axiom, % 154.70/154.51 ! [V_x_2,T_a] : % 154.70/154.51 ( ( class_Int_Onumber__ring(T_a) % 154.70/154.51 & class_Rings_Olinordered__idom(T_a) ) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_le__special_I1_J,axiom, % 154.70/154.51 ! [V_y_2,T_a] : % 154.70/154.51 ( ( class_Int_Onumber__ring(T_a) % 154.70/154.51 & class_Rings_Olinordered__idom(T_a) ) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_less__special_I1_J,axiom, % 154.70/154.51 ! [V_y_2,T_a] : % 154.70/154.51 ( ( class_Int_Onumber__ring(T_a) % 154.70/154.51 & class_Rings_Olinordered__idom(T_a) ) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_less__special_I3_J,axiom, % 154.70/154.51 ! [V_x_2,T_a] : % 154.70/154.51 ( ( class_Int_Onumber__ring(T_a) % 154.70/154.51 & class_Rings_Olinordered__idom(T_a) ) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_less__0__number__of,axiom, % 154.70/154.51 ! [V_v_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_numeral__1__eq__Suc__0,axiom, % 154.70/154.51 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_numeral__3__eq__3,axiom, % 154.70/154.51 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power3__eq__cube,axiom, % 154.70/154.51 ! [V_a,T_a] : % 154.70/154.51 ( class_Groups_Omonoid__mult(T_a) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),V_a) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom, % 154.70/154.51 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Suc3__eq__add__3,axiom, % 154.70/154.51 ! [V_n] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n) ). % 154.70/154.51 % 154.70/154.51 fof(fact_add__nat__number__of,axiom, % 154.70/154.51 ! [V_v_H,V_v] : % 154.70/154.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 154.70/154.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 154.70/154.51 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 154.70/154.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 154.70/154.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H)) ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_transfer__int__nat__numerals_I4_J,axiom, % 154.70/154.51 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_transfer__nat__int__numerals_I4_J,axiom, % 154.70/154.51 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_number__of__succ,axiom, % 154.70/154.51 ! [V_k,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Osucc(V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_number__of__pred,axiom, % 154.70/154.51 ! [V_w,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Opred(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_le__special_I4_J,axiom, % 154.70/154.51 ! [V_x_2,T_a] : % 154.70/154.51 ( ( class_Int_Onumber__ring(T_a) % 154.70/154.51 & class_Rings_Olinordered__idom(T_a) ) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Oone__class_Oone(T_a))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_le__special_I2_J,axiom, % 154.70/154.51 ! [V_y_2,T_a] : % 154.70/154.51 ( ( class_Int_Onumber__ring(T_a) % 154.70/154.51 & class_Rings_Olinordered__idom(T_a) ) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_less__special_I2_J,axiom, % 154.70/154.51 ! [V_y_2,T_a] : % 154.70/154.51 ( ( class_Int_Onumber__ring(T_a) % 154.70/154.51 & class_Rings_Olinordered__idom(T_a) ) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_less__special_I4_J,axiom, % 154.70/154.51 ! [V_x_2,T_a] : % 154.70/154.51 ( ( class_Int_Onumber__ring(T_a) % 154.70/154.51 & class_Rings_Olinordered__idom(T_a) ) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Oone__class_Oone(T_a))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_add__special_I3_J,axiom, % 154.70/154.51 ! [V_v,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),c_Int_OBit1(c_Int_OPls))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_add__special_I2_J,axiom, % 154.70/154.51 ! [V_w,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_w)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Suc__diff__eq__diff__pred,axiom, % 154.70/154.51 ! [V_m,V_n] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),V_n)) % 154.70/154.51 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__number__of__mult__left,axiom, % 154.70/154.51 ! [V_k,V_v_H,V_v] : % 154.70/154.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 154.70/154.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 154.70/154.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H))),V_k) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mult__nat__number__of,axiom, % 154.70/154.51 ! [V_v_H,V_v] : % 154.70/154.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 154.70/154.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 154.70/154.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_neg__number__of__pred__iff__0,axiom, % 154.70/154.51 ! [V_v_2] : % 154.70/154.51 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2)))) % 154.70/154.51 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod__Suc__eq__mod__add3,axiom, % 154.70/154.51 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Suc__mod__eq__add3__mod,axiom, % 154.70/154.51 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),V_n) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom, % 154.70/154.51 ! [V_v,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_div__Suc__eq__div__add3,axiom, % 154.70/154.51 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Suc__div__eq__add3__div,axiom, % 154.70/154.51 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),V_n) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Suc__div__eq__add3__div__number__of,axiom, % 154.70/154.51 ! [V_v,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_diff__special_I1_J,axiom, % 154.70/154.51 ! [V_w,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_diff__special_I2_J,axiom, % 154.70/154.51 ! [V_v,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_eq__number__of__Suc,axiom, % 154.70/154.51 ! [V_n_2,V_v_2] : % 154.70/154.51 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Suc__eq__number__of,axiom, % 154.70/154.51 ! [V_v_2,V_n_2] : % 154.70/154.51 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__case__number__of,axiom, % 154.70/154.51 ! [V_v_2,V_f_2,V_a_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_a_2,V_f_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),V_f_2),c_Int_Onat))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_less__Suc__number__of,axiom, % 154.70/154.51 ! [V_v_2,V_n_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_less__number__of__Suc,axiom, % 154.70/154.51 ! [V_n_2,V_v_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_le__number__of__Suc,axiom, % 154.70/154.51 ! [V_n_2,V_v_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_le__Suc__number__of,axiom, % 154.70/154.51 ! [V_v_2,V_n_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Suc__nat__number__of,axiom, % 154.70/154.51 ! [V_v] : % 154.70/154.51 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.51 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.51 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_max__Suc__number__of,axiom, % 154.70/154.51 ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_max__number__of__Suc,axiom, % 154.70/154.51 ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),c_Int_Onat)))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__case__add__eq__if,axiom, % 154.70/154.51 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_a_2,V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_a,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_min__number__of__Suc,axiom, % 154.70/154.51 ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),c_Int_Onat)))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__rec__add__eq__if,axiom, % 154.70/154.51 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,T_a),tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_eq__special_I4_J,axiom, % 154.70/154.51 ! [V_x_2,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Oone__class_Oone(T_a) % 154.70/154.51 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_eq__special_I2_J,axiom, % 154.70/154.51 ! [V_y_2,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => ( c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 154.70/154.51 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_iszero__def,axiom, % 154.70/154.51 ! [V_z_2,T_a] : % 154.70/154.51 ( class_Rings_Osemiring__1(T_a) % 154.70/154.51 => ( c_Int_Oiszero(T_a,V_z_2) % 154.70/154.51 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_iszero__0,axiom, % 154.70/154.51 ! [T_a] : % 154.70/154.51 ( class_Rings_Osemiring__1(T_a) % 154.70/154.51 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_not__iszero__1,axiom, % 154.70/154.51 ! [T_a] : % 154.70/154.51 ( class_Rings_Osemiring__1(T_a) % 154.70/154.51 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__rec__0,axiom, % 154.70/154.51 ! [V_f2_2,V_f1_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__rec__Suc,axiom, % 154.70/154.51 ! [V_nat_2,V_f2_2,V_f1_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,V_f1_2,V_f2_2),hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(hAPP(V_f2_2,V_nat_2),hAPP(c_Nat_Onat_Onat__rec(T_a,V_f1_2,V_f2_2),V_nat_2)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_iszero__Numeral0,axiom, % 154.70/154.51 ! [T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_iszero__number__of__Bit1,axiom, % 154.70/154.51 ! [V_w,T_a] : % 154.70/154.51 ( ( class_Int_Onumber__ring(T_a) % 154.70/154.51 & class_Int_Oring__char__0(T_a) ) % 154.70/154.51 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_not__iszero__Numeral1,axiom, % 154.70/154.51 ! [T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_eq__number__of__eq,axiom, % 154.70/154.51 ! [V_y_2,V_x_2,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 154.70/154.51 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_eq__special_I1_J,axiom, % 154.70/154.51 ! [V_y_2,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 154.70/154.51 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_eq__special_I3_J,axiom, % 154.70/154.51 ! [V_x_2,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.51 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__rec__number__of,axiom, % 154.70/154.51 ! [V_v_2,V_f_2,V_a_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,T_a),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2)),c_Int_Onat)))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_neg__zmod__mult__2,axiom, % 154.70/154.51 ! [V_b,V_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_a))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zmod__number__of__Bit1,axiom, % 154.70/154.51 ! [V_v,V_w] : % 154.70/154.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_arith__series__int,axiom, % 154.70/154.51 ! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I49_J,axiom, % 154.70/154.51 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I50_J,axiom, % 154.70/154.51 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ). % 154.70/154.51 % 154.70/154.51 fof(fact_minus__Bit0,axiom, % 154.70/154.51 ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(V_k)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mult__Bit0,axiom, % 154.70/154.51 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(V_k)),V_l) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I48_J,axiom, % 154.70/154.51 ! [V_l_2,V_k_2] : % 154.70/154.51 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2) % 154.70/154.51 <=> V_k_2 = V_l_2 ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Bit0__def,axiom, % 154.70/154.51 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ). % 154.70/154.51 % 154.70/154.51 fof(fact_add__Bit0__Bit0,axiom, % 154.70/154.51 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I14_J,axiom, % 154.70/154.51 ! [V_l_2,V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_less__int__code_I13_J,axiom, % 154.70/154.51 ! [V_k2_2,V_k1_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_diff__bin__simps_I7_J,axiom, % 154.70/154.51 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_less__eq__int__code_I13_J,axiom, % 154.70/154.51 ! [V_k2_2,V_k1_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I31_J,axiom, % 154.70/154.51 ! [V_l_2,V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Bit0__Pls,axiom, % 154.70/154.51 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I38_J,axiom, % 154.70/154.51 ! [V_l_2] : % 154.70/154.51 ( c_Int_OPls = c_Int_OBit0(V_l_2) % 154.70/154.51 <=> c_Int_OPls = V_l_2 ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I44_J,axiom, % 154.70/154.51 ! [V_k_2] : % 154.70/154.51 ( c_Int_OBit0(V_k_2) = c_Int_OPls % 154.70/154.51 <=> V_k_2 = c_Int_OPls ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_bin__less__0__simps_I3_J,axiom, % 154.70/154.51 ! [V_w_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I21_J,axiom, % 154.70/154.51 ! [V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I27_J,axiom, % 154.70/154.51 ! [V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I32_J,axiom, % 154.70/154.51 ! [V_l_2,V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_less__eq__int__code_I14_J,axiom, % 154.70/154.51 ! [V_k2_2,V_k1_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I10_J,axiom, % 154.70/154.51 ! [V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I4_J,axiom, % 154.70/154.51 ! [V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_less__int__code_I15_J,axiom, % 154.70/154.51 ! [V_k2_2,V_k1_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I16_J,axiom, % 154.70/154.51 ! [V_l_2,V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_add__Bit0__Bit1,axiom, % 154.70/154.51 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_add__Bit1__Bit0,axiom, % 154.70/154.51 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_diff__bin__simps_I3_J,axiom, % 154.70/154.51 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),V_l)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_diff__bin__simps_I10_J,axiom, % 154.70/154.51 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_diff__bin__simps_I9_J,axiom, % 154.70/154.51 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zdiv__number__of__Bit0,axiom, % 154.70/154.51 ! [V_w,V_v] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_neg__number__of__Bit0,axiom, % 154.70/154.51 ! [V_w_2] : % 154.70/154.51 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2)))) % 154.70/154.51 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_pred__Bit1,axiom, % 154.70/154.51 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ). % 154.70/154.51 % 154.70/154.51 fof(fact_pred__Bit0,axiom, % 154.70/154.51 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_iszero__number__of__Bit0,axiom, % 154.70/154.51 ! [V_w_2,T_a] : % 154.70/154.51 ( ( class_Int_Onumber__ring(T_a) % 154.70/154.51 & class_Int_Oring__char__0(T_a) ) % 154.70/154.51 => ( c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w_2))) % 154.70/154.51 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_succ__Bit0,axiom, % 154.70/154.51 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ). % 154.70/154.51 % 154.70/154.51 fof(fact_succ__Bit1,axiom, % 154.70/154.51 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__number__of__Bit0,axiom, % 154.70/154.51 ! [V_w_2] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_number__of__Bit0,axiom, % 154.70/154.51 ! [V_w,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_less__eq__int__code_I15_J,axiom, % 154.70/154.51 ! [V_k2_2,V_k1_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I33_J,axiom, % 154.70/154.51 ! [V_l_2,V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_less__int__code_I14_J,axiom, % 154.70/154.51 ! [V_k2_2,V_k1_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I15_J,axiom, % 154.70/154.51 ! [V_l_2,V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_card__UNIV__bool,axiom, % 154.70/154.51 hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mult__Bit1,axiom, % 154.70/154.51 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(V_k)),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l))),V_l) ). % 154.70/154.51 % 154.70/154.51 fof(fact_diff__bin__simps_I8_J,axiom, % 154.70/154.51 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(V_k)),V_l)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_add__Bit1__Bit1,axiom, % 154.70/154.51 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_Osucc(V_l))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power__number__of__even,axiom, % 154.70/154.51 ! [V_w_2,V_z_2,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Otimes__class_Otimes(T_a)),c_COMBI(T_a))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zpower__number__of__even,axiom, % 154.70/154.51 ! [V_w_2,V_z_2] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_double__number__of__Bit0,axiom, % 154.70/154.51 ! [V_w,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_number__of1,axiom, % 154.70/154.51 ! [V_n] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_n)))) % 154.70/154.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_n)))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom, % 154.70/154.51 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power__number__of__even__number__of,axiom, % 154.70/154.51 ! [V_w_2,V_v_2,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Otimes__class_Otimes(T_a)),c_COMBI(T_a))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mult__2,axiom, % 154.70/154.51 ! [V_z,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mult__2__right,axiom, % 154.70/154.51 ! [V_z,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_one__add__one__is__two,axiom, % 154.70/154.51 ! [T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zero__eq__power2,axiom, % 154.70/154.51 ! [V_a_2,T_a] : % 154.70/154.51 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 154.70/154.51 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.51 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zero__power2,axiom, % 154.70/154.51 ! [T_a] : % 154.70/154.51 ( class_Rings_Osemiring__1(T_a) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_semiring__norm_I115_J,axiom, % 154.70/154.51 hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_numeral__2__eq__2,axiom, % 154.70/154.51 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom, % 154.70/154.51 ! [V_x,T_a] : % 154.70/154.51 ( class_Rings_Ocomm__semiring__1(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power2__eq__square,axiom, % 154.70/154.51 ! [V_a,T_a] : % 154.70/154.51 ( class_Groups_Omonoid__mult(T_a) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom, % 154.70/154.51 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_add__2__eq__Suc_H,axiom, % 154.70/154.51 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_add__2__eq__Suc,axiom, % 154.70/154.51 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_one__power2,axiom, % 154.70/154.51 ! [T_a] : % 154.70/154.51 ( class_Rings_Osemiring__1(T_a) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power2__minus,axiom, % 154.70/154.51 ! [V_a,T_a] : % 154.70/154.51 ( class_Rings_Oring__1(T_a) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__mult__2__right,axiom, % 154.70/154.51 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_z),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__mult__2,axiom, % 154.70/154.51 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power__even__eq,axiom, % 154.70/154.51 ! [V_n,V_a,T_a] : % 154.70/154.51 ( class_Groups_Omonoid__mult(T_a) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_transfer__int__nat__numerals_I3_J,axiom, % 154.70/154.51 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_transfer__nat__int__numerals_I3_J,axiom, % 154.70/154.51 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_abs__power2,axiom, % 154.70/154.51 ! [V_a,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.51 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power2__abs,axiom, % 154.70/154.51 ! [V_a,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__1__add__1,axiom, % 154.70/154.51 hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod2__Suc__Suc,axiom, % 154.70/154.51 ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_div2__Suc__Suc,axiom, % 154.70/154.51 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zmod__number__of__Bit0,axiom, % 154.70/154.51 ! [V_w,V_v] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_add__self__div__2,axiom, % 154.70/154.51 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_m ). % 154.70/154.51 % 154.70/154.51 fof(fact_half__gt__zero,axiom, % 154.70/154.51 ! [V_r,T_a] : % 154.70/154.51 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 154.70/154.51 & class_Int_Onumber__ring(T_a) ) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_r),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_half__gt__zero__iff,axiom, % 154.70/154.51 ! [V_r_2,T_a] : % 154.70/154.51 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 154.70/154.51 & class_Int_Onumber__ring(T_a) ) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r_2)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power2__eq__imp__eq,axiom, % 154.70/154.51 ! [V_y,V_x,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.51 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 154.70/154.51 => V_x = V_y ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power2__le__imp__le,axiom, % 154.70/154.51 ! [V_y,V_x,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zero__le__power2,axiom, % 154.70/154.51 ! [V_a,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zero__less__power2,axiom, % 154.70/154.51 ! [V_a_2,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 154.70/154.51 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power2__less__0,axiom, % 154.70/154.51 ! [V_a,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.51 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_sum__power2__eq__zero__iff,axiom, % 154.70/154.51 ! [V_y_2,V_x_2,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.51 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.51 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.51 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power2__eq__square__number__of,axiom, % 154.70/154.51 ! [V_w,T_b] : % 154.70/154.51 ( ( class_Groups_Omonoid__mult(T_b) % 154.70/154.51 & class_Int_Onumber(T_b) ) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_less__2__cases,axiom, % 154.70/154.51 ! [V_n] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) % 154.70/154.51 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.51 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__2,axiom, % 154.70/154.51 hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power2__eq__1__iff,axiom, % 154.70/154.51 ! [V_a_2,T_a] : % 154.70/154.51 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 154.70/154.51 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) % 154.70/154.51 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_a) % 154.70/154.51 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom, % 154.70/154.51 ! [V_n,V_x,T_a] : % 154.70/154.51 ( class_Rings_Ocomm__semiring__1(T_a) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power__minus__even,axiom, % 154.70/154.51 ! [V_n,V_a,T_a] : % 154.70/154.51 ( class_Rings_Oring__1(T_a) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power2__less__imp__less,axiom, % 154.70/154.51 ! [V_y,V_x,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__semidom(T_a) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_sum__power2__le__zero__iff,axiom, % 154.70/154.51 ! [V_y_2,V_x_2,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.51 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.51 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_sum__power2__ge__zero,axiom, % 154.70/154.51 ! [V_y,V_x,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.51 => hBOOL(hAPP(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),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_sum__power2__gt__zero__iff,axiom, % 154.70/154.51 ! [V_y_2,V_x_2,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.51 => ( 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),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) % 154.70/154.51 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) % 154.70/154.51 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_not__sum__power2__lt__zero,axiom, % 154.70/154.51 ! [V_y,V_x,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.51 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power2__sum,axiom, % 154.70/154.51 ! [V_y,V_x,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zero__le__even__power_H,axiom, % 154.70/154.51 ! [V_n,V_a,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom, % 154.70/154.51 ! [V_n,V_x,T_a] : % 154.70/154.51 ( class_Rings_Ocomm__semiring__1(T_a) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power__odd__eq,axiom, % 154.70/154.51 ! [V_n,V_a,T_a] : % 154.70/154.51 ( class_Groups_Omonoid__mult(T_a) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power__minus1__even,axiom, % 154.70/154.51 ! [V_n,T_a] : % 154.70/154.51 ( class_Rings_Oring__1(T_a) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zdiv__number__of__Bit1,axiom, % 154.70/154.51 ! [V_v,V_w] : % 154.70/154.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 154.70/154.51 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 154.70/154.51 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mod2__gr__0,axiom, % 154.70/154.51 ! [V_m_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 154.70/154.51 <=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_div__2__gt__zero,axiom, % 154.70/154.51 ! [V_n] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power2__diff,axiom, % 154.70/154.51 ! [V_y,V_x,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_odd__0__le__power__imp__0__le,axiom, % 154.70/154.51 ! [V_n,V_a,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_odd__power__less__zero,axiom, % 154.70/154.51 ! [V_n,V_a,T_a] : % 154.70/154.51 ( class_Rings_Olinordered__idom(T_a) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power__minus1__odd,axiom, % 154.70/154.51 ! [V_n,T_a] : % 154.70/154.51 ( class_Rings_Oring__1(T_a) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Suc__n__div__2__gt__zero,axiom, % 154.70/154.51 ! [V_n] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_of__nat__double,axiom, % 154.70/154.51 ! [V_x,T_a] : % 154.70/154.51 ( class_Rings_Osemiring__1(T_a) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 154.70/154.51 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_pos__zmod__mult__2,axiom, % 154.70/154.51 ! [V_b,V_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_a))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_neg__zdiv__mult__2,axiom, % 154.70/154.51 ! [V_b,V_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.51 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_a) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_pos__zdiv__mult__2,axiom, % 154.70/154.51 ! [V_b,V_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 154.70/154.51 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_a) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_int__of__code,axiom, % 154.70/154.51 ! [V_k] : % 154.70/154.51 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 154.70/154.51 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 154.70/154.51 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 154.70/154.51 => ( ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 154.70/154.51 => hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) % 154.70/154.51 & ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 154.70/154.51 => hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_of__int__num,axiom, % 154.70/154.51 ! [V_k_2,T_a] : % 154.70/154.51 ( class_Rings_Oring__1(T_a) % 154.70/154.51 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = c_Groups_Ozero__class_Ozero(T_a) ) % 154.70/154.51 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.51 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k_2))) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.51 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_a,T_a)),tc_fun(tc_Int_Oint,T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),T_a),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_a,T_a)),tc_fun(tc_Int_Oint,T_a)),tc_Int_Oint),c_COMBB(tc_fun(T_a,T_a),T_a,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_fun(T_a,T_a),T_a),tc_Int_Oint),c_HOL_OLet(T_a,T_a)),c_Int_Oring__1__class_Oof__int(T_a)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_a,T_a),tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,T_a)),tc_Int_Oint),c_COMBS(T_a,T_a,T_a)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_a,T_a),tc_fun(T_a,tc_fun(T_a,T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_fun(T_a,T_a))),tc_Int_Oint),c_COMBB(T_a,tc_fun(T_a,T_a),T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_COMBI(T_a))))),hAPP(hAPP(c_COMBC(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Oplus__class_Oplus(T_a)),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_COMBI(T_a)))),c_Groups_Oone__class_Oone(T_a))))),c_Divides_Odivmod__int(V_k_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power__m1__odd,axiom, % 154.70/154.51 ! [V_n,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I45_J,axiom, % 154.70/154.51 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I42_J,axiom, % 154.70/154.51 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I37_J,axiom, % 154.70/154.51 c_Int_OPls != c_Int_OMin ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I40_J,axiom, % 154.70/154.51 c_Int_OMin != c_Int_OPls ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I24_J,axiom, % 154.70/154.51 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_code__numeral__zero__minus__one,axiom, % 154.70/154.51 hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I7_J,axiom, % 154.70/154.51 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I47_J,axiom, % 154.70/154.51 ! [V_k_2] : % 154.70/154.51 ( c_Int_OBit1(V_k_2) = c_Int_OMin % 154.70/154.51 <=> V_k_2 = c_Int_OMin ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I43_J,axiom, % 154.70/154.51 ! [V_l_2] : % 154.70/154.51 ( c_Int_OMin = c_Int_OBit1(V_l_2) % 154.70/154.51 <=> c_Int_OMin = V_l_2 ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Bit1__Min,axiom, % 154.70/154.51 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ). % 154.70/154.51 % 154.70/154.51 fof(fact_bin__less__0__simps_I2_J,axiom, % 154.70/154.51 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I20_J,axiom, % 154.70/154.51 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I23_J,axiom, % 154.70/154.51 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I30_J,axiom, % 154.70/154.51 ! [V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I26_J,axiom, % 154.70/154.51 ! [V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I6_J,axiom, % 154.70/154.51 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I3_J,axiom, % 154.70/154.51 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I9_J,axiom, % 154.70/154.51 ! [V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I13_J,axiom, % 154.70/154.51 ! [V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I28_J,axiom, % 154.70/154.51 ! [V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I8_J,axiom, % 154.70/154.51 ! [V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_eq__number__of__Pls__Min,axiom, % 154.70/154.51 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Int_OMin__def,axiom, % 154.70/154.51 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mult__Min,axiom, % 154.70/154.51 ! [V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k) ). % 154.70/154.51 % 154.70/154.51 fof(fact_neg__number__of__Min,axiom, % 154.70/154.51 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_pred__Pls,axiom, % 154.70/154.51 c_Int_Opred(c_Int_OPls) = c_Int_OMin ). % 154.70/154.51 % 154.70/154.51 fof(fact_add__Min__right,axiom, % 154.70/154.51 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ). % 154.70/154.51 % 154.70/154.51 fof(fact_add__Min,axiom, % 154.70/154.51 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ). % 154.70/154.51 % 154.70/154.51 fof(fact_pred__Min,axiom, % 154.70/154.51 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nonzero__number__of__Min,axiom, % 154.70/154.51 ! [T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_succ__Min,axiom, % 154.70/154.51 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ). % 154.70/154.51 % 154.70/154.51 fof(fact_diff__bin__simps_I2_J,axiom, % 154.70/154.51 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mult__minus1__right,axiom, % 154.70/154.51 ! [V_z,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mult__minus1,axiom, % 154.70/154.51 ! [V_z,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_z) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_number__of__Min,axiom, % 154.70/154.51 ! [T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_arith__simps_I31_J,axiom, % 154.70/154.51 ! [T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_abs__minus__one,axiom, % 154.70/154.51 ! [T_a] : % 154.70/154.51 ( ( class_Int_Onumber__ring(T_a) % 154.70/154.51 & class_Rings_Olinordered__idom(T_a) ) % 154.70/154.51 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = c_Groups_Oone__class_Oone(T_a) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_divide__minus1,axiom, % 154.70/154.51 ! [V_x,T_a] : % 154.70/154.51 ( ( class_Fields_Ofield__inverse__zero(T_a) % 154.70/154.51 & class_Int_Onumber__ring(T_a) ) % 154.70/154.51 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I25_J,axiom, % 154.70/154.51 ! [V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rel__simps_I11_J,axiom, % 154.70/154.51 ! [V_k_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zmod__minus1__right,axiom, % 154.70/154.51 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 154.70/154.51 % 154.70/154.51 fof(fact_diff__bin__simps_I4_J,axiom, % 154.70/154.51 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_minus__Min,axiom, % 154.70/154.51 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ). % 154.70/154.51 % 154.70/154.51 fof(fact_pos__zmult__eq__1__iff__lemma,axiom, % 154.70/154.51 ! [V_n,V_m] : % 154.70/154.51 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 154.70/154.51 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) % 154.70/154.51 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zmult__eq__1__iff,axiom, % 154.70/154.51 ! [V_n_2,V_m_2] : % 154.70/154.51 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 154.70/154.51 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 154.70/154.51 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 154.70/154.51 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) % 154.70/154.51 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_diff__bin__simps_I6_J,axiom, % 154.70/154.51 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_diff__bin__simps_I5_J,axiom, % 154.70/154.51 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_of__int__m1,axiom, % 154.70/154.51 ! [T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zdiv__minus1__right,axiom, % 154.70/154.51 ! [V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zero__code__numeral__code,axiom, % 154.70/154.51 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls) ). % 154.70/154.51 % 154.70/154.51 fof(fact_minus1__divide,axiom, % 154.70/154.51 ! [V_x,T_a] : % 154.70/154.51 ( ( class_Fields_Ofield__inverse__zero(T_a) % 154.70/154.51 & class_Int_Onumber__ring(T_a) ) % 154.70/154.51 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_x)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_abs__power__minus__one,axiom, % 154.70/154.51 ! [V_n,T_a] : % 154.70/154.51 ( ( class_Int_Onumber__ring(T_a) % 154.70/154.51 & class_Rings_Olinordered__idom(T_a) ) % 154.70/154.51 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_div__eq__minus1,axiom, % 154.70/154.51 ! [V_b] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 154.70/154.51 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_div__pos__neg__trivial,axiom, % 154.70/154.51 ! [V_b,V_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.51 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zmod__minus1,axiom, % 154.70/154.51 ! [V_b] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_one__code__numeral__code,axiom, % 154.70/154.51 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_power__m1__even,axiom, % 154.70/154.51 ! [V_n,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Nitpick_OFrac__def,axiom, % 154.70/154.51 c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_int__ge__less__than__def,axiom, % 154.70/154.51 ! [V_d_2] : c_Int_Oint__ge__less__than(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_int__ge__less__than2__def,axiom, % 154.70/154.51 ! [V_d_2] : c_Int_Oint__ge__less__than2(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_inj__graph,axiom, % 154.70/154.51 ! [T_b,T_a] : c_Fun_Oinj__on(tc_fun(T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_a,T_b)),c_Set_OCollect(tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_a,T_b)),c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool)),hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Nitpick_Oprod__def,axiom, % 154.70/154.51 ! [V_B_2,V_A_2,T_b,T_a] : c_Nitpick_Oprod(T_a,T_b,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_nat__of__aux__code,axiom, % 154.70/154.51 ! [V_n,V_i] : % 154.70/154.51 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 154.70/154.51 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n ) % 154.70/154.51 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 154.70/154.51 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,V_n)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_divmod__int__rel__def,axiom, % 154.70/154.51 ! [V_b_2,V_a_2] : c_Divides_Odivmod__int__rel(V_a_2,V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,V_a_2))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_2)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_divmod__int__correct,axiom, % 154.70/154.51 ! [V_a,V_b] : % 154.70/154.51 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zmult2__lemma,axiom, % 154.70/154.51 ! [V_c,V_r,V_q,V_b,V_a] : % 154.70/154.51 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 154.70/154.51 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 154.70/154.51 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)))) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_code__numeral_Osize_I1_J,axiom, % 154.70/154.51 c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Nats__number__of,axiom, % 154.70/154.51 ! [V_w_2,T_a] : % 154.70/154.51 ( class_Int_Onumber__ring(T_a) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_sup__Un__eq2,axiom, % 154.70/154.51 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(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(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(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),hAPP(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(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(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),hAPP(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)),V_x_2),V_y_2)) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_bot__empty__eq2,axiom, % 154.70/154.51 ! [V_y_2,V_x_2,T_b,T_a] : % 154.70/154.51 ( 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)) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_inf__Int__eq2,axiom, % 154.70/154.51 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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(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(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),hAPP(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(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(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),hAPP(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)),V_x_2),V_y_2)) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_pred__equals__eq2,axiom, % 154.70/154.51 ! [V_S_2,V_R_2,T_b,T_a] : % 154.70/154.51 ( 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(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(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),hAPP(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(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(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),hAPP(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) % 154.70/154.51 <=> V_R_2 = V_S_2 ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_pred__subset__eq2,axiom, % 154.70/154.51 ! [V_S_2,V_R_2,T_b,T_a] : % 154.70/154.51 ( hBOOL(hAPP(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(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(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),hAPP(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(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(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),hAPP(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))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rev__ImageI,axiom, % 154.70/154.51 ! [V_r_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Image__iff,axiom, % 154.70/154.51 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2))) % 154.70/154.51 <=> ? [B_x] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 154.70/154.51 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_unique__remainder,axiom, % 154.70/154.51 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 154.70/154.51 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 154.70/154.51 => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H))) % 154.70/154.51 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => V_r = V_r_H ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_unique__quotient,axiom, % 154.70/154.51 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 154.70/154.51 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 154.70/154.51 => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H))) % 154.70/154.51 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => V_q = V_q_H ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_self__remainder,axiom, % 154.70/154.51 ! [V_r,V_q,V_a] : % 154.70/154.51 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 154.70/154.51 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_divmod__int__rel__0,axiom, % 154.70/154.51 ! [V_b] : % 154.70/154.51 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_SUP__UN__eq2,axiom, % 154.70/154.51 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_a),hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c))))),V_r_2)),V_x_2),V_y_2)) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_INF__INT__eq2,axiom, % 154.70/154.51 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_a),hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c))))),V_r_2)),V_x_2),V_y_2)) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_self__quotient,axiom, % 154.70/154.51 ! [V_r,V_q,V_a] : % 154.70/154.51 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 154.70/154.51 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_divmod__int__rel__mod,axiom, % 154.70/154.51 ! [V_r,V_q,V_b,V_a] : % 154.70/154.51 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 154.70/154.51 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_divmod__int__rel__div,axiom, % 154.70/154.51 ! [V_r,V_q,V_b,V_a] : % 154.70/154.51 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 154.70/154.51 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Nats__0,axiom, % 154.70/154.51 ! [T_a] : % 154.70/154.51 ( class_Rings_Osemiring__1(T_a) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_divmod__int__mod__div,axiom, % 154.70/154.51 ! [V_q,V_p] : c_Divides_Odivmod__int(V_p,V_q) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_p),V_q)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_p,V_q)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Nats__add,axiom, % 154.70/154.51 ! [V_b_2,V_a_2,T_a] : % 154.70/154.51 ( class_Rings_Osemiring__1(T_a) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Nats__mult,axiom, % 154.70/154.51 ! [V_b_2,V_a_2,T_a] : % 154.70/154.51 ( class_Rings_Osemiring__1(T_a) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Nats__1,axiom, % 154.70/154.51 ! [T_a] : % 154.70/154.51 ( class_Rings_Osemiring__1(T_a) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_of__nat__in__Nats,axiom, % 154.70/154.51 ! [V_n_2,T_a] : % 154.70/154.51 ( class_Rings_Osemiring__1(T_a) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Image__singleton__iff,axiom, % 154.70/154.51 ! [V_a_2,V_r_2,T_b,V_b_2,T_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 154.70/154.51 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2),V_b_2)),V_r_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_divmod__int__rel__div__mod,axiom, % 154.70/154.51 ! [V_a,V_b] : % 154.70/154.51 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Image__singleton,axiom, % 154.70/154.51 ! [V_a_2,V_r_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_b,T_a))),hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2))),V_r_2)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zadd1__lemma,axiom, % 154.70/154.51 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 154.70/154.51 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_aq),V_ar))) % 154.70/154.51 => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_bq),V_br))) % 154.70/154.51 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br),V_c)))) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zminus1__lemma,axiom, % 154.70/154.51 ! [V_r_2,V_q_2,V_b_2,V_a_2] : % 154.70/154.51 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a_2,V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2))) % 154.70/154.51 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b_2),V_r_2))))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_divmod__int__relI,axiom, % 154.70/154.51 ! [V_r,V_q,V_b,V_a] : % 154.70/154.51 ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) % 154.70/154.51 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 154.70/154.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 154.70/154.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 154.70/154.51 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_zmult1__lemma,axiom, % 154.70/154.51 ! [V_a,V_r,V_q,V_c,V_b] : % 154.70/154.51 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) % 154.70/154.51 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r),V_c)))) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_pair__imageI,axiom, % 154.70/154.51 ! [V_f_2,T_c,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_A_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_c,hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)),V_A_2))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_norm__frac_Osimps,axiom, % 154.70/154.51 ! [V_a_2,V_b_2] : % 154.70/154.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.51 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) ) % 154.70/154.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.51 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 154.70/154.51 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) % 154.70/154.51 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.51 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 154.70/154.51 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) ) ) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_adjust__eq,axiom, % 154.70/154.51 ! [V_r_2,V_q_2,V_b_2] : hAPP(c_Divides_Oadjust(V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_r_2),V_b_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),V_r_2))) ). % 154.70/154.51 % 154.70/154.51 fof(fact_sup2CI,axiom, % 154.70/154.51 ! [T_b,T_a,V_A_2,V_y_2,V_x_2,V_B_2] : % 154.70/154.51 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) % 154.70/154.51 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_sup2E,axiom, % 154.70/154.51 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 154.70/154.51 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_inf2E,axiom, % 154.70/154.51 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 154.70/154.51 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 154.70/154.51 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_inf2I,axiom, % 154.70/154.51 ! [T_b,T_a,V_B_2,V_y_2,V_x_2,V_A_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_mem__splitI,axiom, % 154.70/154.51 ! [T_c,T_b,V_b_2,V_a_2,V_c_2,V_z_2,T_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2))) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_a,tc_HOL_Obool)),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_splitI,axiom, % 154.70/154.51 ! [T_b,T_a,V_b_2,V_a_2,V_f_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_prod__caseI,axiom, % 154.70/154.51 ! [T_b,T_a,V_b_2,V_a_2,V_f1_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_bot2E,axiom, % 154.70/154.51 ! [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)) ). % 154.70/154.51 % 154.70/154.51 fof(fact_splitD_H,axiom, % 154.70/154.51 ! [V_c_2,V_b_2,V_a_2,V_R_2,T_c,T_b,T_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_c,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_c_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_swap__inj__on,axiom, % 154.70/154.51 ! [V_A_2,T_b,T_a] : c_Fun_Oinj__on(tc_prod(T_a,T_b),tc_prod(T_b,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(T_b,T_a)),hAPP(c_COMBC(T_b,T_a,tc_prod(T_b,T_a)),c_Product__Type_OPair(T_b,T_a))),V_A_2) ). % 154.70/154.51 % 154.70/154.51 fof(fact_sup2I2,axiom, % 154.70/154.51 ! [V_A_2,T_b,T_a,V_y_2,V_x_2,V_B_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_sup2I1,axiom, % 154.70/154.51 ! [V_B_2,T_b,T_a,V_y_2,V_x_2,V_A_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_rev__predicate2D,axiom, % 154.70/154.51 ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_P_2] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_P_2),V_Q_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_predicate2D,axiom, % 154.70/154.51 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_b,T_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_P_2),V_Q_2)) % 154.70/154.51 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_inf2D2,axiom, % 154.70/154.51 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_inf2D1,axiom, % 154.70/154.51 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 154.70/154.51 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 154.70/154.51 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Pair__inject,axiom, % 154.70/154.51 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] : % 154.70/154.51 ( hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H),V_b_H) % 154.70/154.51 => ~ ( V_a = V_a_H % 154.70/154.51 => V_b != V_b_H ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_Pair__eq,axiom, % 154.70/154.51 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 154.70/154.51 ( hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2) % 154.70/154.51 <=> ( V_a_2 = V_a_H_2 % 154.70/154.51 & V_b_2 = V_b_H_2 ) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_split__paired__All,axiom, % 154.70/154.51 ! [T_b,T_a,V_P_2] : % 154.70/154.51 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 154.70/154.51 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_split__weak__cong,axiom, % 154.70/154.51 ! [V_c_2,T_c,T_b,T_a,V_q_2,V_p_2] : % 154.70/154.51 ( V_p_2 = V_q_2 % 154.70/154.51 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_c_2),V_q_2) ) ). % 154.70/154.51 % 154.70/154.51 fof(fact_split__twice,axiom, % 154.70/154.51 ! [V_p_2,V_g_2,T_e,T_d,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_b,T_c)),tc_fun(T_e,T_a),T_d),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_e),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2))),V_g_2)),V_p_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_split__conv,axiom, % 154.70/154.52 ! [V_b_2,V_a_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_f_2,V_a_2),V_b_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_prod_Osimps_I2_J,axiom, % 154.70/154.52 ! [V_b_2,V_a_2,V_f1_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_splitD,axiom, % 154.70/154.52 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2))) % 154.70/154.52 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_split__eta,axiom, % 154.70/154.52 ! [V_f_2,T_c,T_b,T_a] : hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,T_c),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),T_c,T_b),V_f_2)),c_Product__Type_OPair(T_a,T_b))) = V_f_2 ). % 154.70/154.52 % 154.70/154.52 fof(fact_split__paired__The,axiom, % 154.70/154.52 ! [V_P_2,T_b,T_a] : c_HOL_OThe(tc_prod(T_a,T_b),V_P_2) = c_HOL_OThe(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b)))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_The__split__eq,axiom, % 154.70/154.52 ! [V_y_2,V_x_2,T_b,T_a] : c_HOL_OThe(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_adjust__def,axiom, % 154.70/154.52 ! [V_b_2] : c_Divides_Oadjust(V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_in__rel__def,axiom, % 154.70/154.52 ! [V_y_2,V_x_2,V_R_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2)) % 154.70/154.52 <=> 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)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_div__mod__code__numeral__def,axiom, % 154.70/154.52 ! [V_m,V_n] : c_Code__Numeral_Odiv__mod__code__numeral(V_n,V_m) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_negDivAlg__eqn__1__number__of,axiom, % 154.70/154.52 ! [V_w] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 154.70/154.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) % 154.70/154.52 => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) % 154.70/154.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) % 154.70/154.52 => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_negDivAlg__correct,axiom, % 154.70/154.52 ! [V_b,V_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 154.70/154.52 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_negDivAlg__div__mod,axiom, % 154.70/154.52 ! [V_l,V_k] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 154.70/154.52 => c_Divides_OnegDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_negDivAlg__minus1,axiom, % 154.70/154.52 ! [V_b] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_negDivAlg_Osimps,axiom, % 154.70/154.52 ! [V_b,V_a] : % 154.70/154.52 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) % 154.70/154.52 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 154.70/154.52 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)) ) % 154.70/154.52 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) % 154.70/154.52 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 154.70/154.52 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_negDivAlg__eqn,axiom, % 154.70/154.52 ! [V_a,V_b] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 154.70/154.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) % 154.70/154.52 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)) ) % 154.70/154.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) % 154.70/154.52 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_negDivAlg__eqn__number__of,axiom, % 154.70/154.52 ! [V_w,V_v] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) % 154.70/154.52 => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) % 154.70/154.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) % 154.70/154.52 => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Nitpick_Orefl_H__def,axiom, % 154.70/154.52 ! [V_r_2,T_a] : % 154.70/154.52 ( c_Nitpick_Orefl_H(T_a,V_r_2) % 154.70/154.52 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_posDivAlg__eqn__1__number__of,axiom, % 154.70/154.52 ! [V_w] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 154.70/154.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 154.70/154.52 => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) % 154.70/154.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 154.70/154.52 => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_posDivAlg_Osimps,axiom, % 154.70/154.52 ! [V_b,V_a] : % 154.70/154.52 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 154.70/154.52 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 154.70/154.52 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a) ) % 154.70/154.52 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 154.70/154.52 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 154.70/154.52 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_posDivAlg__0,axiom, % 154.70/154.52 ! [V_b] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_posDivAlg__correct,axiom, % 154.70/154.52 ! [V_b,V_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 154.70/154.52 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_posDivAlg__div__mod,axiom, % 154.70/154.52 ! [V_l,V_k] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 154.70/154.52 => c_Divides_OposDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_posDivAlg__eqn__number__of,axiom, % 154.70/154.52 ! [V_w,V_v] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.52 => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) % 154.70/154.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 154.70/154.52 => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_posDivAlg__eqn,axiom, % 154.70/154.52 ! [V_a,V_b] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 154.70/154.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 154.70/154.52 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a) ) % 154.70/154.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 154.70/154.52 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_divmod__int__def,axiom, % 154.70/154.52 ! [V_b,V_a] : % 154.70/154.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 154.70/154.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 154.70/154.52 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) ) % 154.70/154.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 154.70/154.52 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.52 => c_Divides_Odivmod__int(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) % 154.70/154.52 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.52 => c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))) ) ) ) ) ) % 154.70/154.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 154.70/154.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 154.70/154.52 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) ) % 154.70/154.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 154.70/154.52 => c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))) ) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_divmod__nat__step,axiom, % 154.70/154.52 ! [V_m,V_n] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 154.70/154.52 => c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_divmod__int__pdivmod,axiom, % 154.70/154.52 ! [V_l_2,V_k_2] : % 154.70/154.52 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.52 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) % 154.70/154.52 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.52 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.52 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2) ) % 154.70/154.52 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.52 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l_2)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))) ) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_apsnd__compose,axiom, % 154.70/154.52 ! [V_x_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_a,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_x_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_negateSnd__def,axiom, % 154.70/154.52 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_apsnd__conv,axiom, % 154.70/154.52 ! [V_y_2,V_x_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),hAPP(V_f_2,V_y_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_divmod__nat__zero,axiom, % 154.70/154.52 ! [V_m] : c_Divides_Odivmod__nat(V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) ). % 154.70/154.52 % 154.70/154.52 fof(fact_divmod__nat__base,axiom, % 154.70/154.52 ! [V_n,V_m] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 154.70/154.52 => c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_negateSnd__eq,axiom, % 154.70/154.52 ! [V_r,V_q] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_r)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_divmod__nat__div__mod,axiom, % 154.70/154.52 ! [V_n,V_m] : c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_divmod__int__rel__neg,axiom, % 154.70/154.52 ! [V_qr,V_b,V_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)),V_qr)) % 154.70/154.52 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_divmod__nat__if,axiom, % 154.70/154.52 ! [V_m_2,V_n_2] : % 154.70/154.52 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.52 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 154.70/154.52 => c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2) ) % 154.70/154.52 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.52 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 154.70/154.52 => c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2),V_n_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_pdivmod__def,axiom, % 154.70/154.52 ! [V_l,V_k] : c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_pdivmod__posDivAlg,axiom, % 154.70/154.52 ! [V_k,V_l] : % 154.70/154.52 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.52 => c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)) ) % 154.70/154.52 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.52 => c_Divides_Opdivmod(V_k,V_l) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_divmod__int__code,axiom, % 154.70/154.52 ! [V_l_2,V_k_2] : % 154.70/154.52 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.52 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) % 154.70/154.52 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.52 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.52 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2) ) % 154.70/154.52 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.52 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_k_2)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))) ) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_divmod__nat__rel__mult2__eq,axiom, % 154.70/154.52 ! [V_c,V_r,V_q,V_b,V_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 154.70/154.52 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)))) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_divmod__nat__rel__mult1__eq,axiom, % 154.70/154.52 ! [V_a,V_r,V_q,V_c,V_b] : % 154.70/154.52 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 154.70/154.52 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r),V_c)))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_negDivAlg_Opsimps,axiom, % 154.70/154.52 ! [V_b_2,V_a_2] : % 154.70/154.52 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2))) % 154.70/154.52 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) % 154.70/154.52 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 154.70/154.52 => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2)) ) % 154.70/154.52 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) % 154.70/154.52 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 154.70/154.52 => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OnegDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_divmod__nat__rel__unique,axiom, % 154.70/154.52 ! [V_qr_H,V_qr,V_n,V_m] : % 154.70/154.52 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 154.70/154.52 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H)) % 154.70/154.52 => V_qr = V_qr_H ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_divmod__nat__rel__divmod__nat,axiom, % 154.70/154.52 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_divmod__nat__eq,axiom, % 154.70/154.52 ! [V_qr,V_n,V_m] : % 154.70/154.52 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 154.70/154.52 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_divmod__nat__def,axiom, % 154.70/154.52 ! [V_n_2,V_m_2] : c_Divides_Odivmod__nat(V_m_2,V_n_2) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(V_m_2,V_n_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_mod__eq,axiom, % 154.70/154.52 ! [V_r,V_q,V_n,V_m] : % 154.70/154.52 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) % 154.70/154.52 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_div__eq,axiom, % 154.70/154.52 ! [V_r,V_q,V_n,V_m] : % 154.70/154.52 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) % 154.70/154.52 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_divmod__nat__rel,axiom, % 154.70/154.52 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_divmod__nat__rel__add1__eq,axiom, % 154.70/154.52 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_aq),V_ar))) % 154.70/154.52 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_bq),V_br))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 154.70/154.52 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br),V_c)))) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_posDivAlg_Opsimps,axiom, % 154.70/154.52 ! [V_b_2,V_a_2] : % 154.70/154.52 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2))) % 154.70/154.52 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 154.70/154.52 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 154.70/154.52 => c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2) ) % 154.70/154.52 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 154.70/154.52 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 154.70/154.52 => c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OposDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_norm__frac_Opsimps,axiom, % 154.70/154.52 ! [V_b_2,V_a_2] : % 154.70/154.52 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2))) % 154.70/154.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.52 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) ) % 154.70/154.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.52 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.52 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 154.70/154.52 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) % 154.70/154.52 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 154.70/154.52 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 154.70/154.52 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) ) ) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_negDivAlg_Opinduct,axiom, % 154.70/154.52 ! [V_P_2,V_a1_2,V_a0_2] : % 154.70/154.52 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) % 154.70/154.52 => ( ! [B_a,B_b] : % 154.70/154.52 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) % 154.70/154.52 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_a),B_b))) % 154.70/154.52 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 154.70/154.52 => hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) ) % 154.70/154.52 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 154.70/154.52 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_posDivAlg_Opinduct,axiom, % 154.70/154.52 ! [V_P_2,V_a1_2,V_a0_2] : % 154.70/154.52 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) % 154.70/154.52 => ( ! [B_a,B_b] : % 154.70/154.52 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) % 154.70/154.52 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) % 154.70/154.52 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 154.70/154.52 => hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) ) % 154.70/154.52 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 154.70/154.52 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_accp__subset,axiom, % 154.70/154.52 ! [V_R2_2,V_R1_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),V_R1_2),V_R2_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_a,V_R2_2)),c_Wellfounded_Oaccp(T_a,V_R1_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_mod__pos__neg__1__number__of,axiom, % 154.70/154.52 ! [V_w] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.52 => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_snd__eqD,axiom, % 154.70/154.52 ! [V_a,V_y,V_x,T_a,T_b] : % 154.70/154.52 ( hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x),V_y)) = V_a % 154.70/154.52 => V_y = V_a ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_snd__conv,axiom, % 154.70/154.52 ! [V_b,V_a,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a),V_b)) = V_b ). % 154.70/154.52 % 154.70/154.52 fof(fact_snd__def,axiom, % 154.70/154.52 ! [V_p_2,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,T_a),hAPP(c_COMBK(tc_fun(T_a,T_a),T_b),c_COMBI(T_a))),V_p_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_snd__apsnd,axiom, % 154.70/154.52 ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(c_Product__Type_Oapsnd(T_c,T_a,T_b,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_c),V_x_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_apsnd__eq__conv,axiom, % 154.70/154.52 ! [V_g_2,V_x_2,V_f_2,T_a,T_b,T_c] : % 154.70/154.52 ( hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_g_2),V_x_2) % 154.70/154.52 <=> hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_a,T_c),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_a,T_c),V_x_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_mod__int__def,axiom, % 154.70/154.52 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_accp__downward,axiom, % 154.70/154.52 ! [V_a_2,V_b_2,V_r_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_b_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 154.70/154.52 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_accp_Oequations,axiom, % 154.70/154.52 ! [V_a_2,V_r_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) % 154.70/154.52 <=> ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 154.70/154.52 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_accp_Osimps,axiom, % 154.70/154.52 ! [V_a_2,V_r_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) % 154.70/154.52 <=> ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 154.70/154.52 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_mod__neg__pos,axiom, % 154.70/154.52 ! [V_b,V_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 154.70/154.52 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_mod__pos__pos,axiom, % 154.70/154.52 ! [V_b,V_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 154.70/154.52 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_mod__pos__pos__1__number__of,axiom, % 154.70/154.52 ! [V_w] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 154.70/154.52 => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_mod__pos__neg,axiom, % 154.70/154.52 ! [V_b,V_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.52 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_mod__neg__neg,axiom, % 154.70/154.52 ! [V_b,V_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.52 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_nat__gcd_Opsimps,axiom, % 154.70/154.52 ! [V_y_2,V_x_2] : % 154.70/154.52 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2))) % 154.70/154.52 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.52 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) % 154.70/154.52 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.52 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = c_Nitpick_Onat__gcd(V_y_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x_2,V_y_2)) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_nat_Osize_I2_J,axiom, % 154.70/154.52 ! [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))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_in__measure,axiom, % 154.70/154.52 ! [V_f_2,V_y_2,V_x_2,T_a] : % 154.70/154.52 ( 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)),hAPP(c_Wellfounded_Omeasure(T_a),V_f_2))) % 154.70/154.52 <=> 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))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_mod__nat__def,axiom, % 154.70/154.52 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_nat_Osize_I1_J,axiom, % 154.70/154.52 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.70/154.52 % 154.70/154.52 fof(fact_irrefl__def,axiom, % 154.70/154.52 ! [V_r_2,T_a] : % 154.70/154.52 ( c_Relation_Oirrefl(T_a,V_r_2) % 154.70/154.52 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_norm__frac_Opinduct,axiom, % 154.70/154.52 ! [V_P_2,V_a1_2,V_a0_2] : % 154.70/154.52 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) % 154.70/154.52 => ( ! [B_a,B_b] : % 154.70/154.52 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) % 154.70/154.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.52 => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b))) ) % 154.70/154.52 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 154.70/154.52 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_div__pos__neg__1__number__of,axiom, % 154.70/154.52 ! [V_w] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.52 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Pair__fst__snd__eq,axiom, % 154.70/154.52 ! [T_b,T_a,V_t_2,V_s_2] : % 154.70/154.52 ( V_s_2 = V_t_2 % 154.70/154.52 <=> ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_t_2) % 154.70/154.52 & hAPP(c_Product__Type_Osnd(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_t_2) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_prod__eqI,axiom, % 154.70/154.52 ! [V_q,V_p,T_b,T_a] : % 154.70/154.52 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) % 154.70/154.52 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q) % 154.70/154.52 => V_p = V_q ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_fst__eqD,axiom, % 154.70/154.52 ! [V_a,V_y,V_x,T_b,T_a] : % 154.70/154.52 ( hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) = V_a % 154.70/154.52 => V_x = V_a ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_fst__conv,axiom, % 154.70/154.52 ! [V_b,V_a,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b)) = V_a ). % 154.70/154.52 % 154.70/154.52 fof(fact_fst__def,axiom, % 154.70/154.52 ! [V_p_2,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_a),c_COMBK(T_a,T_b)),V_p_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_fst__apsnd,axiom, % 154.70/154.52 ! [V_x_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_a,T_c),V_x_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_pair__collapse,axiom, % 154.70/154.52 ! [V_p,T_b,T_a] : hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p)) = V_p ). % 154.70/154.52 % 154.70/154.52 fof(fact_surjective__pairing,axiom, % 154.70/154.52 ! [T_b,T_a,V_t] : V_t = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_t)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_t)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_prod__case__beta,axiom, % 154.70/154.52 ! [V_p_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_div__int__def,axiom, % 154.70/154.52 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_split__comp__eq,axiom, % 154.70/154.52 ! [V_g_2,V_f_2,T_d,T_c,T_b,T_a] : hAPP(hAPP(c_COMBS(tc_prod(T_a,T_b),T_b,T_c),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,T_c),tc_prod(T_a,T_b)),V_f_2),hAPP(hAPP(c_COMBB(T_a,T_d,tc_prod(T_a,T_b)),V_g_2),c_Product__Type_Ofst(T_a,T_b)))),c_Product__Type_Osnd(T_a,T_b)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,T_c),T_a),V_f_2),V_g_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_split__beta,axiom, % 154.70/154.52 ! [V_z_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_P_2),V_z_2) = hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_z_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_z_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_split__def,axiom, % 154.70/154.52 ! [V_p_2,V_c_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_c_2),V_p_2) = hAPP(hAPP(V_c_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_split__comp,axiom, % 154.70/154.52 ! [V_x_2,V_g_2,V_f_2,T_d,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),hAPP(c_Fun_Ocomp(T_d,tc_fun(T_c,T_a),T_b,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_x_2))),hAPP(c_Product__Type_Osnd(T_b,T_c),V_x_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_The__split,axiom, % 154.70/154.52 ! [V_P_2,T_b,T_a] : c_HOL_OThe(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2)) = c_HOL_OThe(tc_prod(T_a,T_b),hAPP(hAPP(c_COMBS(tc_prod(T_a,T_b),T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),tc_prod(T_a,T_b)),V_P_2),c_Product__Type_Ofst(T_a,T_b))),c_Product__Type_Osnd(T_a,T_b))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_div__neg__pos,axiom, % 154.70/154.52 ! [V_b,V_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 154.70/154.52 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_div__pos__pos,axiom, % 154.70/154.52 ! [V_b,V_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 154.70/154.52 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_div__pos__pos__1__number__of,axiom, % 154.70/154.52 ! [V_w] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 154.70/154.52 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_div__pos__neg,axiom, % 154.70/154.52 ! [V_b,V_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.52 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_div__neg__neg,axiom, % 154.70/154.52 ! [V_b,V_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 154.70/154.52 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_prod__size__simp,axiom, % 154.70/154.52 ! [V_p_2,V_g_2,V_f_2,T_b,T_a] : c_Product__Type_Oprod_Oprod__size(T_a,T_b,V_f_2,V_g_2,V_p_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_a,T_b),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_a,T_b),V_p_2)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_exI__realizer,axiom, % 154.70/154.52 ! [T_a,T_b,V_x_2,V_y_2,V_P_2] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_conjI__realizer,axiom, % 154.70/154.52 ! [T_b,T_a,V_q_2,V_Q_2,V_p_2,V_P_2] : % 154.70/154.52 ( hBOOL(hAPP(V_P_2,V_p_2)) % 154.70/154.52 => ( hBOOL(hAPP(V_Q_2,V_q_2)) % 154.70/154.52 => ( hBOOL(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_p_2),V_q_2)))) % 154.70/154.52 & hBOOL(hAPP(V_Q_2,hAPP(c_Product__Type_Osnd(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_p_2),V_q_2)))) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_div__nat__def,axiom, % 154.70/154.52 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_divmod__nat__rel__def,axiom, % 154.70/154.52 ! [V_qr_2,V_n_2,V_m_2] : % 154.70/154.52 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2)) % 154.70/154.52 <=> ( V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)) % 154.70/154.52 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.52 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 154.70/154.52 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) % 154.70/154.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)) ) ) % 154.70/154.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) % 154.70/154.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_nat__def,axiom, % 154.70/154.52 ! [V_z_2] : hAPP(c_Int_Onat,V_z_2) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_nat__gcd_Opinduct,axiom, % 154.70/154.52 ! [V_P_2,V_a1_2,V_a0_2] : % 154.70/154.52 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a0_2),V_a1_2))) % 154.70/154.52 => ( ! [B_x,B_y] : % 154.70/154.52 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y))) % 154.70/154.52 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.52 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) ) % 154.70/154.52 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) ) % 154.70/154.52 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_inv__image__def,axiom, % 154.70/154.52 ! [V_f_2,V_r_2,T_a,T_b] : hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_b,T_b)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_b,T_b)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_prod(T_b,T_b))),T_a),c_COMBB(T_b,tc_prod(T_b,T_b),T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_prod(T_b,T_b)),T_a),c_Product__Type_OPair(T_b,T_b)),V_f_2))),V_f_2)))),V_r_2))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Rep__Integ__inject,axiom, % 154.70/154.52 ! [V_y_2,V_x_2] : % 154.70/154.52 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2) % 154.70/154.52 <=> V_x_2 = V_y_2 ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_in__inv__image,axiom, % 154.70/154.52 ! [V_f_2,V_r_2,T_b,V_y_2,V_x_2,T_a] : % 154.70/154.52 ( 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)),hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_r_2),V_f_2))) % 154.70/154.52 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_rp__inv__image__def,axiom, % 154.70/154.52 ! [T_b,T_a] : c_FunDef_Orp__inv__image(T_a,T_b) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))))),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_COMBS(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(T_b,T_a)),c_Product__Type_OPair(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),c_Relation_Oinv__image(T_a,T_b))))),c_Relation_Oinv__image(T_a,T_b))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_equiv__class__nondisjoint,axiom, % 154.70/154.52 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_subset__equiv__class,axiom, % 154.70/154.52 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Union__quotient,axiom, % 154.70/154.52 ! [V_r_2,V_A_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 154.70/154.52 => c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)) = V_A_2 ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_equiv__class__self,axiom, % 154.70/154.52 ! [V_a_2,V_r_2,V_A_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_quotient__disj,axiom, % 154.70/154.52 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 154.70/154.52 => ( V_X_2 = V_Y_2 % 154.70/154.52 | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_equiv__class__eq,axiom, % 154.70/154.52 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 154.70/154.52 => hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_quotient__eqI,axiom, % 154.70/154.52 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2)) % 154.70/154.52 => ( 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)) % 154.70/154.52 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_quotient__eq__iff,axiom, % 154.70/154.52 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2)) % 154.70/154.52 => ( V_X_2 = V_Y_2 % 154.70/154.52 <=> 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)) ) ) ) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_eq__equiv__class,axiom, % 154.70/154.52 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_a] : % 154.70/154.52 ( hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 154.70/154.52 => ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_eq__equiv__class__iff,axiom, % 154.70/154.52 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 154.70/154.52 => ( hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 154.70/154.52 <=> 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)) ) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_equiv__class__eq__iff,axiom, % 154.70/154.52 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 154.70/154.52 => ( 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)) % 154.70/154.52 <=> ( hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 154.70/154.52 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.52 & hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_equiv__class__subset,axiom, % 154.70/154.52 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_eq__equiv__class__iff2,axiom, % 154.70/154.52 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 154.70/154.52 => ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2) % 154.70/154.52 <=> 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)) ) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_UN__equiv__class,axiom, % 154.70/154.52 ! [V_a_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 154.70/154.52 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.70/154.52 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_f_2) = hAPP(V_f_2,V_a_2) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_UN__equiv__class2,axiom, % 154.70/154.52 ! [V_a2_2,V_a1_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 154.70/154.52 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 154.70/154.52 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a1_2),V_A1_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a2_2),V_A2_2)) % 154.70/154.52 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_f_2)) = hAPP(hAPP(V_f_2,V_a1_2),V_a2_2) ) ) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_in__finite__psubset,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,T_a] : % 154.70/154.52 ( 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))) % 154.70/154.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.70/154.52 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_congruent2__implies__congruent,axiom, % 154.70/154.52 ! [V_a_2,V_f_2,V_r2_2,T_c,T_b,V_r1_2,V_A_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r1_2) % 154.70/154.52 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.70/154.52 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_congruent2D,axiom, % 154.70/154.52 ! [V_z2_2,V_y2_2,V_z1_2,V_y1_2,V_f_2,V_r2_2,V_r1_2,T_c,T_b,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y1_2),V_z1_2)),V_r1_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y2_2),V_z2_2)),V_r2_2)) % 154.70/154.52 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_congruentD,axiom, % 154.70/154.52 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_b,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),V_r_2)) % 154.70/154.52 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_congruent2__implies__congruent__UN,axiom, % 154.70/154.52 ! [V_a_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 154.70/154.52 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 154.70/154.52 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A2_2)) % 154.70/154.52 => c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_c,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_f_2)) ) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_finite__psubset__def,axiom, % 154.70/154.52 ! [T_a] : c_Wellfounded_Ofinite__psubset(T_a) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_COMBS(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_a)))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_UN__equiv__class__inject,axiom, % 154.70/154.52 ! [V_Y_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 154.70/154.52 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 154.70/154.52 => ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_f_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_Y_2),V_f_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 154.70/154.52 => ( ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.52 => ! [B_y] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 154.70/154.52 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2)) ) ) ) % 154.70/154.52 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_UN__equiv__class__type2,axiom, % 154.70/154.52 ! [V_B_2,V_X2_2,V_X1_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 154.70/154.52 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 154.70/154.52 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A1_2),V_r1_2))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A2_2),V_r2_2))) % 154.70/154.52 => ( ! [B_x1] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x1),V_A1_2)) % 154.70/154.52 => ! [B_x2] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x2),V_A2_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) ) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_c,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X2_2)),V_f_2))),V_B_2)) ) ) ) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_UN__equiv__class__type,axiom, % 154.70/154.52 ! [V_B_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 154.70/154.52 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 154.70/154.52 => ( ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) ) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2)) ) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_mlex__leq,axiom, % 154.70/154.52 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 154.70/154.52 => ( 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)) % 154.70/154.52 => 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))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_code__numeral_Osize_I2_J,axiom, % 154.70/154.52 ! [V_code__numeral] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_mlex__less,axiom, % 154.70/154.52 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 154.70/154.52 ( 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))) % 154.70/154.52 => 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))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_code__numeral_Oinject,axiom, % 154.70/154.52 ! [V_code__numeral_H_2,V_code__numeral_2] : % 154.70/154.52 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) % 154.70/154.52 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_code__numeral_Osimps_I2_J,axiom, % 154.70/154.52 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ). % 154.70/154.52 % 154.70/154.52 fof(fact_code__numeral_Osimps_I3_J,axiom, % 154.70/154.52 ! [V_code__numeral_H_1] : c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_1) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Suc__code__numeral__minus__one,axiom, % 154.70/154.52 ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_n)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = V_n ). % 154.70/154.52 % 154.70/154.52 fof(fact_code__numeral_Osize_I4_J,axiom, % 154.70/154.52 ! [V_code__numeral] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_nat_Osize_I4_J,axiom, % 154.70/154.52 ! [V_nat] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_prod_Orecs,axiom, % 154.70/154.52 ! [V_b_2,V_a_2,V_f1_2,T_a,T_c,T_b] : c_Product__Type_Oprod_Oprod__rec(T_b,T_c,T_a,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_nat__size,axiom, % 154.70/154.52 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ). % 154.70/154.52 % 154.70/154.52 fof(fact_nat_Osize_I3_J,axiom, % 154.70/154.52 hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.70/154.52 % 154.70/154.52 fof(fact_code__numeral_Osize_I3_J,axiom, % 154.70/154.52 hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.70/154.52 % 154.70/154.52 fof(fact_in__lex__prod,axiom, % 154.70/154.52 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_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))) % 154.70/154.52 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_H_2)),V_r_2)) % 154.70/154.52 | ( V_a_2 = V_a_H_2 % 154.70/154.52 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_b_H_2)),V_s_2)) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_equivp__equiv,axiom, % 154.70/154.52 ! [V_A_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequiv(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_A_2) % 154.70/154.52 <=> c_Equiv__Relations_Oequivp(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(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(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),hAPP(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_A_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_apfst__apsnd,axiom, % 154.70/154.52 ! [V_x_2,V_g_2,T_d,V_f_2,T_b,T_a,T_c] : hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_c,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_apfst__compose,axiom, % 154.70/154.52 ! [V_x_2,V_g_2,T_d,V_f_2,T_b,T_a,T_c] : hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_d,T_c,T_b,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_d,T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_a,T_d,V_f_2),V_g_2)),V_x_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_identity__equivp,axiom, % 154.70/154.52 ! [T_a] : c_Equiv__Relations_Oequivp(T_a,c_fequal) ). % 154.70/154.52 % 154.70/154.52 fof(fact_equivp__def,axiom, % 154.70/154.52 ! [V_R_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 154.70/154.52 <=> ! [B_x,B_y] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 154.70/154.52 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_equivp__reflp,axiom, % 154.70/154.52 ! [V_x_2,V_R_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 154.70/154.52 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_equivp__symp,axiom, % 154.70/154.52 ! [V_y_2,V_x_2,V_R_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_equivp__transp,axiom, % 154.70/154.52 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_snd__apfst,axiom, % 154.70/154.52 ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(c_Product__Type_Oapfst(T_c,T_b,T_a,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_c,T_a),V_x_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_apfst__eq__conv,axiom, % 154.70/154.52 ! [V_g_2,V_x_2,V_f_2,T_b,T_a,T_c] : % 154.70/154.52 ( hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_g_2),V_x_2) % 154.70/154.52 <=> hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_fst__apfst,axiom, % 154.70/154.52 ! [V_x_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_apfst__conv,axiom, % 154.70/154.52 ! [V_y_2,V_x_2,V_f_2,T_b,T_a,T_c] : hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,V_x_2)),V_y_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_apsnd__apfst__commute,axiom, % 154.70/154.52 ! [V_p_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(c_Product__Type_Oapfst(T_d,T_a,T_c,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_d,T_a,T_b,V_g_2),hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_d,V_f_2),V_p_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_apsnd__apfst,axiom, % 154.70/154.52 ! [V_x_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(c_Product__Type_Oapfst(T_d,T_a,T_c,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_d,T_c),V_x_2))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_same__fstI,axiom, % 154.70/154.52 ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_P_2] : % 154.70/154.52 ( hBOOL(hAPP(V_P_2,V_x_2)) % 154.70/154.52 => ( 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))) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_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))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_pair__lessI2,axiom, % 154.70/154.52 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_ImageE,axiom, % 154.70/154.52 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2))) % 154.70/154.52 => ~ ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2)) % 154.70/154.52 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_pair__lessI1,axiom, % 154.70/154.52 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_pair__leqI2,axiom, % 154.70/154.52 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_smax__insertI,axiom, % 154.70/154.52 ! [V_X_2,V_x_2,V_Y_2,V_y_2] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),V_Y_2)),c_FunDef_Omax__strict)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_X_2)),V_Y_2)),c_FunDef_Omax__strict)) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_smin__insertI,axiom, % 154.70/154.52 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__strict)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__strict)) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_smin__emptyI,axiom, % 154.70/154.52 ! [V_X_2] : % 154.70/154.52 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_smax__emptyI,axiom, % 154.70/154.52 ! [V_Y_2] : % 154.70/154.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) % 154.70/154.52 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_Y_2)),c_FunDef_Omax__strict)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_pair__leqI1,axiom, % 154.70/154.52 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wmin__insertI,axiom, % 154.70/154.52 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__weak)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__weak)) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wmax__insertI,axiom, % 154.70/154.52 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omax__weak)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)),V_YS_2)),c_FunDef_Omax__weak)) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Field__insert,axiom, % 154.70/154.52 ! [V_r_2,V_b_2,V_a_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_a),V_r_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Field__Union,axiom, % 154.70/154.52 ! [V_R_2,T_a] : hAPP(c_Relation_OField(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Relation_OField(T_a)),V_R_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Field__empty,axiom, % 154.70/154.52 ! [T_a] : hAPP(c_Relation_OField(T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_mono__Field,axiom, % 154.70/154.52 ! [V_s_2,V_r_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_Relation_OField(T_a),V_s_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Field__Un,axiom, % 154.70/154.52 ! [V_s_2,V_r_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_Relation_OField(T_a),V_s_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_finite__Field,axiom, % 154.70/154.52 ! [V_r_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 154.70/154.52 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_OField(T_a),V_r_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wmax__emptyI,axiom, % 154.70/154.52 ! [V_X_2] : % 154.70/154.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_X_2)),c_FunDef_Omax__weak)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wmin__emptyI,axiom, % 154.70/154.52 ! [V_X_2] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_min__weak__def,axiom, % 154.70/154.52 c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_max__weak__def,axiom, % 154.70/154.52 c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Id__on__def,axiom, % 154.70/154.52 ! [V_A_2,T_a] : c_Relation_OId__on(T_a,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),T_a),c_Set_Oinsert(tc_prod(T_a,T_a))),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Id__on__def_H,axiom, % 154.70/154.52 ! [V_A_2,T_a] : c_Relation_OId__on(T_a,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),c_fequal))),V_A_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Id__on__empty,axiom, % 154.70/154.52 ! [T_a] : c_Relation_OId__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Image__Id__on,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Id__on__iff,axiom, % 154.70/154.52 ! [V_A_2,V_y_2,V_x_2,T_a] : % 154.70/154.52 ( 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_Relation_OId__on(T_a,V_A_2))) % 154.70/154.52 <=> ( V_x_2 = V_y_2 % 154.70/154.52 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Id__on__eqI,axiom, % 154.70/154.52 ! [V_A_2,T_a,V_b_2,V_a_2] : % 154.70/154.52 ( V_a_2 = V_b_2 % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Relation_OId__on(T_a,V_A_2))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_max__strict__def,axiom, % 154.70/154.52 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 154.70/154.52 % 154.70/154.52 fof(fact_max__ext__additive,axiom, % 154.70/154.52 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_a] : % 154.70/154.52 ( 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_Omax__ext(T_a,V_R_2))) % 154.70/154.52 => ( 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_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) % 154.70/154.52 => 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)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_min__strict__def,axiom, % 154.70/154.52 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 154.70/154.52 % 154.70/154.52 fof(fact_max__extp__max__ext__eq,axiom, % 154.70/154.52 ! [V_xa_2,V_x_2,V_R_2,T_a] : % 154.70/154.52 ( 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(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(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),hAPP(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) % 154.70/154.52 <=> 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))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_min__rpair__set,axiom, % 154.70/154.52 c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_max__rpair__set,axiom, % 154.70/154.52 c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_rp__inv__image__rp,axiom, % 154.70/154.52 ! [V_f_2,T_b,V_P_2,T_a] : % 154.70/154.52 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 154.70/154.52 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_FunDef_Orp__inv__image(T_a,T_b),V_P_2),V_f_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_equiv__intrel__iff,axiom, % 154.70/154.52 ! [V_y_2,V_x_2] : % 154.70/154.52 ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) % 154.70/154.52 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_Int_Ointrel)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_less__than__iff,axiom, % 154.70/154.52 ! [V_y_2,V_x_2] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Wellfounded_Oless__than)) % 154.70/154.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_intrel__iff,axiom, % 154.70/154.52 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2))),c_Int_Ointrel)) % 154.70/154.52 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_equiv__intrel,axiom, % 154.70/154.52 c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel) ). % 154.70/154.52 % 154.70/154.52 fof(fact_pair__less__def,axiom, % 154.70/154.52 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ). % 154.70/154.52 % 154.70/154.52 fof(fact_measure__def,axiom, % 154.70/154.52 ! [T_a] : c_Wellfounded_Omeasure(T_a) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_a),c_Wellfounded_Oless__than) ). % 154.70/154.52 % 154.70/154.52 fof(fact_mlex__prod__def,axiom, % 154.70/154.52 ! [V_R_2,V_f_2,T_a] : c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_a),T_a),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_a,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(tc_Nat_Onat,T_a)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,tc_prod(tc_Nat_Onat,T_a)),T_a),c_Product__Type_OPair(tc_Nat_Onat,T_a)),V_f_2)),c_COMBI(T_a))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_of__int,axiom, % 154.70/154.52 ! [V_j_2,V_i_2,T_a] : % 154.70/154.52 ( class_Rings_Oring__1(T_a) % 154.70/154.52 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_i_2),V_j_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_j_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_One__int__def,axiom, % 154.70/154.52 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_mult,axiom, % 154.70/154.52 ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_v_2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_u_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Rep__Integ__inverse,axiom, % 154.70/154.52 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ). % 154.70/154.52 % 154.70/154.52 fof(fact_minus,axiom, % 154.70/154.52 ! [V_y_2,V_x_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_y_2),V_x_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Zero__int__def,axiom, % 154.70/154.52 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_int__def,axiom, % 154.70/154.52 ! [V_m_2] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_add,axiom, % 154.70/154.52 ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y_2),V_v_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_nat,axiom, % 154.70/154.52 ! [V_y_2,V_x_2] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_minus__int__def,axiom, % 154.70/154.52 ! [V_z_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_2) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_less,axiom, % 154.70/154.52 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) % 154.70/154.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_le,axiom, % 154.70/154.52 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) % 154.70/154.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_eq__Abs__Integ,axiom, % 154.70/154.52 ! [V_z_2] : % 154.70/154.52 ~ ! [B_x,B_y] : V_z_2 != hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Integ__def,axiom, % 154.70/154.52 c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Id__onE,axiom, % 154.70/154.52 ! [V_A_2,V_c_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_c_2),c_Relation_OId__on(T_a,V_A_2))) % 154.70/154.52 => ~ ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.52 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Rep__Integ,axiom, % 154.70/154.52 ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_x_2)),c_Int_OInteg)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_type__definition__Integ,axiom, % 154.70/154.52 c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg) ). % 154.70/154.52 % 154.70/154.52 fof(fact_code__numeral_Osimps_I5_J,axiom, % 154.70/154.52 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_a] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_a,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(V_f2_2,V_code__numeral_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_accp__acc__eq,axiom, % 154.70/154.52 ! [V_x_2,V_r_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Wellfounded_Oaccp(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(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(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),hAPP(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)) % 154.70/154.52 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_acc__subset,axiom, % 154.70/154.52 ! [V_R2_2,V_R1_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R1_2),V_R2_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Oacc(T_a,V_R2_2)),c_Wellfounded_Oacc(T_a,V_R1_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_acc__downward,axiom, % 154.70/154.52 ! [V_a_2,V_r_2,V_b_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_acc_Osimps,axiom, % 154.70/154.52 ! [V_r_2,V_a_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 154.70/154.52 <=> ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_a_2)),V_r_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_code__numeral_Osimps_I4_J,axiom, % 154.70/154.52 ! [V_f2_2,V_f1_2,T_a] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_a,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ). % 154.70/154.52 % 154.70/154.52 fof(fact_type__definition_ORep__range,axiom, % 154.70/154.52 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 154.70/154.52 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 154.70/154.52 => hAPP(c_Set_Oimage(T_a,T_b,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_type__definition_OAbs__image,axiom, % 154.70/154.52 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 154.70/154.52 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 154.70/154.52 => hAPP(c_Set_Oimage(T_b,T_a,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_type__definition_OAbs__inject,axiom, % 154.70/154.52 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 154.70/154.52 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 154.70/154.52 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2) % 154.70/154.52 <=> V_x_2 = V_y_2 ) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_type__definition_ORep__inject,axiom, % 154.70/154.52 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 154.70/154.52 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 154.70/154.52 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2) % 154.70/154.52 <=> V_x_2 = V_y_2 ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_type__definition_ORep__inverse,axiom, % 154.70/154.52 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 154.70/154.52 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 154.70/154.52 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_type__definition_ORep,axiom, % 154.70/154.52 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 154.70/154.52 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_type__definition_OAbs__inverse,axiom, % 154.70/154.52 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 154.70/154.52 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 154.70/154.52 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_rel__comp__def,axiom, % 154.70/154.52 ! [V_s_2,V_r_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_a),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_a),c_COMBC(T_c,tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_a,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_c),tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_a,T_c)))),c_Product__Type_OPair(T_a,T_c)))),V_r_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_b)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_c,T_b)))),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))))),V_s_2))))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_max__extp_Oequations,axiom, % 154.70/154.52 ! [V_a2_2,V_a1_2,V_R_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Omax__extp(T_a,V_R_2,V_a1_2,V_a2_2) % 154.70/154.52 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) % 154.70/154.52 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2)) % 154.70/154.52 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.52 & ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 154.70/154.52 => ? [B_xa] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 154.70/154.52 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_max__ext_Ointros,axiom, % 154.70/154.52 ! [V_R_2,V_Y_2,V_X_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) % 154.70/154.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Y_2)) % 154.70/154.52 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.52 => ( ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_X_2)) % 154.70/154.52 => ? [B_xa] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_Y_2)) % 154.70/154.52 & 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)) ) ) % 154.70/154.52 => 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))) ) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_rel__compI,axiom, % 154.70/154.52 ! [V_s_2,V_c_2,T_c,V_r_2,V_b_2,V_a_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_b_2),V_c_2)),V_s_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_rel__comp__UNION__distrib,axiom, % 154.70/154.52 ! [V_r_2,V_I_2,T_d,V_s_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_d),hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_s_2)),V_r_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_rel__comp__UNION__distrib2,axiom, % 154.70/154.52 ! [V_s_2,V_r_2,V_I_2,T_d,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_d),c_Relation_Orel__comp(T_a,T_c,T_b)),V_r_2)),V_s_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_rel__comp__empty2,axiom, % 154.70/154.52 ! [V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_rel__comp__empty1,axiom, % 154.70/154.52 ! [V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_rel__comp__distrib2,axiom, % 154.70/154.52 ! [V_R_2,V_T_2,V_S_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),V_S_2),V_T_2)),V_R_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_T_2),V_R_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_rel__comp__distrib,axiom, % 154.70/154.52 ! [V_T_2,V_S_2,V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),V_T_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_rel__comp__mono,axiom, % 154.70/154.52 ! [V_s_2,V_s_H_2,T_c,V_r_2,V_r_H_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_s_H_2),V_s_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_O__assoc,axiom, % 154.70/154.52 ! [V_T_2,V_S_2,V_R_2,T_d,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_d,T_c),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_d,T_b),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_d,T_c,T_b),V_S_2),V_T_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_union__comp__emptyR,axiom, % 154.70/154.52 ! [V_C_2,V_B_2,V_A_2,T_a] : % 154.70/154.52 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 154.70/154.52 => ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 154.70/154.52 => hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_union__comp__emptyL,axiom, % 154.70/154.52 ! [V_B_2,V_C_2,V_A_2,T_a] : % 154.70/154.52 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 154.70/154.52 => ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_B_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 154.70/154.52 => hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_max__ext__compat,axiom, % 154.70/154.52 ! [V_S_2,V_R_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_a,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_a,V_S_2)),hAPP(hAPP(c_Set_Oinsert(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)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_min__ext__compat,axiom, % 154.70/154.52 ! [V_S_2,V_R_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_a,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_a,V_S_2)),hAPP(hAPP(c_Set_Oinsert(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)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_a,V_R_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_pred__comp__rel__comp__eq,axiom, % 154.70/154.52 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_c,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,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(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(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),hAPP(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_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_s_2)),V_x_2),V_y_2)) % 154.70/154.52 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_reduction__pairI,axiom, % 154.70/154.52 ! [V_S_2,V_R_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_R_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2)) % 154.70/154.52 => c_FunDef_Oreduction__pair(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Nitpick_Ozero__frac__def,axiom, % 154.70/154.52 ! [T_a] : c_Nitpick_Ozero__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__less__than,axiom, % 154.70/154.52 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 154.70/154.52 % 154.70/154.52 fof(fact_pred__comp_Ointros,axiom, % 154.70/154.52 ! [T_c,T_b,T_a,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2),V_a_2),V_c_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__empty,axiom, % 154.70/154.52 ! [T_a] : c_Wellfounded_Owf(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__inv__image,axiom, % 154.70/154.52 ! [V_f_2,T_b,V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_r_2) % 154.70/154.52 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Oinv__image(T_a,T_b),V_r_2),V_f_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__lex__prod,axiom, % 154.70/154.52 ! [V_rb_2,T_b,V_ra_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_ra_2) % 154.70/154.52 => ( c_Wellfounded_Owf(T_b,V_rb_2) % 154.70/154.52 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_ra_2,V_rb_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__measure,axiom, % 154.70/154.52 ! [V_f_2,T_a] : c_Wellfounded_Owf(T_a,hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__comp__self,axiom, % 154.70/154.52 ! [V_R_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_R_2) % 154.70/154.52 <=> c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__not__refl,axiom, % 154.70/154.52 ! [V_a_2,V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_r_2) % 154.70/154.52 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__not__sym,axiom, % 154.70/154.52 ! [V_x_2,V_a_2,V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_r_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_x_2)),V_r_2)) % 154.70/154.52 => ~ 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_a_2)),V_r_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__asym,axiom, % 154.70/154.52 ! [V_x_2,V_a_2,V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_r_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_x_2)),V_r_2)) % 154.70/154.52 => ~ 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_a_2)),V_r_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__irrefl,axiom, % 154.70/154.52 ! [V_a_2,V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_r_2) % 154.70/154.52 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_max__ext__wf,axiom, % 154.70/154.52 ! [V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_r_2) % 154.70/154.52 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_r_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__pair__less,axiom, % 154.70/154.52 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 154.70/154.52 % 154.70/154.52 fof(fact_pred__comp_Oequations,axiom, % 154.70/154.52 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_c,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2),V_a1_2),V_a3_2)) % 154.70/154.52 <=> ? [B_b] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) % 154.70/154.52 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__subset,axiom, % 154.70/154.52 ! [V_p_2,V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_r_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_p_2),V_r_2)) % 154.70/154.52 => c_Wellfounded_Owf(T_a,V_p_2) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__Int1,axiom, % 154.70/154.52 ! [V_r_H_2,V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_r_2) % 154.70/154.52 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_r_H_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__Int2,axiom, % 154.70/154.52 ! [V_r_H_2,V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_r_2) % 154.70/154.52 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_H_2),V_r_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__finite__psubset,axiom, % 154.70/154.52 ! [T_a] : c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_a)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__mlex,axiom, % 154.70/154.52 ! [V_f_2,V_R_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_R_2) % 154.70/154.52 => c_Wellfounded_Owf(T_a,c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_min__ext__wf,axiom, % 154.70/154.52 ! [V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_r_2) % 154.70/154.52 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_r_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__less,axiom, % 154.70/154.52 c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__int__ge__less__than,axiom, % 154.70/154.52 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__int__ge__less__than2,axiom, % 154.70/154.52 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_acc__wfD,axiom, % 154.70/154.52 ! [V_x_2,V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_r_2) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__acc__iff,axiom, % 154.70/154.52 ! [V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_r_2) % 154.70/154.52 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__no__loop,axiom, % 154.70/154.52 ! [V_R_2,T_a] : % 154.70/154.52 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 154.70/154.52 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__union__merge,axiom, % 154.70/154.52 ! [V_S_2,V_R_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) % 154.70/154.52 <=> c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_S_2),V_R_2))),V_S_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__iff__no__infinite__down__chain,axiom, % 154.70/154.52 ! [V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_r_2) % 154.70/154.52 <=> ~ ? [B_f] : % 154.70/154.52 ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wfE__pf,axiom, % 154.70/154.52 ! [V_A_2,V_R_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_R_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_a,T_a,V_R_2),V_A_2))) % 154.70/154.52 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__union__compatible,axiom, % 154.70/154.52 ! [V_S_2,V_R_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_R_2) % 154.70/154.52 => ( c_Wellfounded_Owf(T_a,V_S_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2)) % 154.70/154.52 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf,axiom, % 154.70/154.52 ! [T_a] : % 154.70/154.52 ( class_Orderings_Owellorder(T_a) % 154.70/154.52 => c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_a)))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_reduction__pair__def,axiom, % 154.70/154.52 ! [V_P_2,T_a] : % 154.70/154.52 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 154.70/154.52 <=> ( c_Wellfounded_Owf(T_a,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)) % 154.70/154.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_reduction__pair__lemma,axiom, % 154.70/154.52 ! [V_S_2,V_R_2,V_P_2,T_a] : % 154.70/154.52 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))) % 154.70/154.52 => ( c_Wellfounded_Owf(T_a,V_S_2) % 154.70/154.52 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Nitpick_Oone__frac__def,axiom, % 154.70/154.52 ! [T_a] : c_Nitpick_Oone__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Nitpick_Onumber__of__frac__def,axiom, % 154.70/154.52 ! [V_n,T_a] : c_Nitpick_Onumber__of__frac(T_a,V_n) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_n),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Nitpick_Ofrac__def,axiom, % 154.70/154.52 ! [V_b,V_a,T_a] : hAPP(hAPP(c_Nitpick_Ofrac(T_a),V_a),V_b) = c_Nitpick_OAbs__Frac(T_a,c_Nitpick_Onorm__frac(V_a,V_b)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_pred__nat__def,axiom, % 154.70/154.52 c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__lenlex,axiom, % 154.70/154.52 ! [V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_r_2) % 154.70/154.52 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olenlex(T_a,V_r_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__same__fst,axiom, % 154.70/154.52 ! [T_a,V_R_2,T_b,V_P_2] : % 154.70/154.52 ( ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(V_P_2,B_x)) % 154.70/154.52 => c_Wellfounded_Owf(T_b,hAPP(V_R_2,B_x)) ) % 154.70/154.52 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__pred__nat,axiom, % 154.70/154.52 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__lex,axiom, % 154.70/154.52 ! [V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_r_2) % 154.70/154.52 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olex(T_a,V_r_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__lexn,axiom, % 154.70/154.52 ! [V_n_2,V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_r_2) % 154.70/154.52 => c_Wellfounded_Owf(tc_List_Olist(T_a),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__if__measure,axiom, % 154.70/154.52 ! [T_a,V_g_2,V_f_2,V_P_2] : % 154.70/154.52 ( ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(V_P_2,B_x)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,hAPP(V_g_2,B_x))),hAPP(V_f_2,B_x))) ) % 154.70/154.52 => c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),V_g_2))))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_lex__def,axiom, % 154.70/154.52 ! [V_r_2,T_a] : c_List_Olex(T_a,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_a,V_r_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_lexn_Osimps_I1_J,axiom, % 154.70/154.52 ! [V_r_2,T_a] : hAPP(c_List_Olexn(T_a,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Range__Collect__split,axiom, % 154.70/154.52 ! [V_P_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(c_Set_OCollect(tc_prod(T_b,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),V_P_2))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_image__split__eq__Sigma,axiom, % 154.70/154.52 ! [V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] : hAPP(c_Set_Oimage(T_c,tc_prod(T_a,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Set_Oimage(T_c,T_a,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_Oimage(T_c,T_b,V_g_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_a),c_Set_Ovimage(T_c,T_a,V_f_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_A_2))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wfP__def,axiom, % 154.70/154.52 ! [V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_OwfP(T_a,V_r_2) % 154.70/154.52 <=> c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wfP__empty,axiom, % 154.70/154.52 ! [T_a] : c_Wellfounded_OwfP(T_a,hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBK(tc_HOL_Obool,T_a),c_fFalse))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_SigmaI,axiom, % 154.70/154.52 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_RangeI,axiom, % 154.70/154.52 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Times__eq__cancel2,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) % 154.70/154.52 => ( hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_B_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2)) % 154.70/154.52 <=> V_A_2 = V_B_2 ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wfP__accp__iff,axiom, % 154.70/154.52 ! [V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_OwfP(T_a,V_r_2) % 154.70/154.52 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x1)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_accp__wfPD,axiom, % 154.70/154.52 ! [V_x_2,V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_OwfP(T_a,V_r_2) % 154.70/154.52 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_x_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Sigma__Diff__distrib1,axiom, % 154.70/154.52 ! [V_C_2,V_J_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_J_2),V_C_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Times__Diff__distrib1,axiom, % 154.70/154.52 ! [V_C_2,V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Sigma__Diff__distrib2,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_B_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Range__Id__on,axiom, % 154.70/154.52 ! [V_A_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = V_A_2 ). % 154.70/154.52 % 154.70/154.52 fof(fact_Sigma__Union,axiom, % 154.70/154.52 ! [V_B_2,V_X_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),c_Product__Type_OSigma(T_a,T_b)),V_B_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Sigma__empty1,axiom, % 154.70/154.52 ! [V_B_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_card__cartesian__product,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Finite__Set_Ocard(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_setsum__cartesian__product,axiom, % 154.70/154.52 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 154.70/154.52 ( class_Groups_Ocomm__monoid__add(T_a) % 154.70/154.52 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_b,T_c),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Times__empty,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,T_b,T_a] : % 154.70/154.52 ( hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) % 154.70/154.52 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.52 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Sigma__empty2,axiom, % 154.70/154.52 ! [V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Compl__Times__UNIV1,axiom, % 154.70/154.52 ! [V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Compl__Times__UNIV2,axiom, % 154.70/154.52 ! [V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(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))))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),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)))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_setprod__cartesian__product,axiom, % 154.70/154.52 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 154.70/154.52 ( class_Groups_Ocomm__monoid__mult(T_a) % 154.70/154.52 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_a)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_b,T_c),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wfP__subset,axiom, % 154.70/154.52 ! [V_p_2,V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_OwfP(T_a,V_r_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),V_p_2),V_r_2)) % 154.70/154.52 => c_Wellfounded_OwfP(T_a,V_p_2) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Sigma__Un__distrib1,axiom, % 154.70/154.52 ! [V_C_2,V_J_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_J_2),V_C_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Times__Un__distrib1,axiom, % 154.70/154.52 ! [V_C_2,V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Sigma__Un__distrib2,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_B_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_rel__comp__subset__Sigma,axiom, % 154.70/154.52 ! [V_C_2,V_s_2,T_c,V_B_2,V_A_2,V_r_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_s_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)))) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_C_2)))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_swap__product,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_a),tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_prod(T_a,T_b)),hAPP(c_COMBC(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_A_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_finite__cartesian__product,axiom, % 154.70/154.52 ! [V_B_2,T_b,V_A_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 154.70/154.52 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_equiv__type,axiom, % 154.70/154.52 ! [V_r_2,V_A_2,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Sigma__Int__distrib2,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_B_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Times__Int__distrib1,axiom, % 154.70/154.52 ! [V_C_2,V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Sigma__Int__distrib1,axiom, % 154.70/154.52 ! [V_C_2,V_J_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_J_2),V_C_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Id__on__subset__Times,axiom, % 154.70/154.52 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Relation_OId__on(T_a,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Range__Diff__subset,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2))),hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_UNIV__Times__UNIV,axiom, % 154.70/154.52 ! [T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),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_prod(T_a,T_b),tc_HOL_Obool)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_mem__Sigma__iff,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) % 154.70/154.52 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.70/154.52 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_SigmaD1,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_SigmaD2,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_SigmaE2,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) % 154.70/154.52 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.70/154.52 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Range__Union,axiom, % 154.70/154.52 ! [V_S_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_b,T_a)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Range__empty__iff,axiom, % 154.70/154.52 ! [V_r_2,T_a,T_b] : % 154.70/154.52 ( hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.52 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Range__empty,axiom, % 154.70/154.52 ! [T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Range__Un__eq,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_finite__Range,axiom, % 154.70/154.52 ! [V_r_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2)) % 154.70/154.52 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_snd__eq__Range,axiom, % 154.70/154.52 ! [V_R_2,T_a,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_a,c_Product__Type_Osnd(T_b,T_a)),V_R_2) = hAPP(c_Relation_ORange(T_b,T_a),V_R_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_card__cartesian__product__singleton,axiom, % 154.70/154.52 ! [V_A_2,V_x_2,T_b,T_a] : hAPP(c_Finite__Set_Ocard(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Times__subset__cancel2,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_B_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2)))) % 154.70/154.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Image__subset,axiom, % 154.70/154.52 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_C_2)),V_B_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_finite__cartesian__productD2,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) % 154.70/154.52 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.52 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_finite__cartesian__productD1,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) % 154.70/154.52 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 154.70/154.52 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Collect__split,axiom, % 154.70/154.52 ! [V_Q_2,V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_OCollect(T_b),V_Q_2))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_SetCompr__Sigma__eq,axiom, % 154.70/154.52 ! [V_Q_2,V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),V_Q_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_fst__image__times,axiom, % 154.70/154.52 ! [V_A_2,T_b,T_a,V_B_2] : % 154.70/154.52 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.52 => hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 154.70/154.52 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.52 => hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2))) = V_A_2 ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_snd__image__times,axiom, % 154.70/154.52 ! [V_B_2,T_b,T_a,V_A_2] : % 154.70/154.52 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.52 => hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 154.70/154.52 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.52 => hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) = V_B_2 ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Range__iff,axiom, % 154.70/154.52 ! [V_r_2,T_b,V_a_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2))) % 154.70/154.52 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_y),V_a_2)),V_r_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Range__insert,axiom, % 154.70/154.52 ! [V_r_2,V_b_2,V_a_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Range__Int__subset,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2)))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_insert__times__insert,axiom, % 154.70/154.52 ! [V_B_2,V_b_2,V_A_2,V_a_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_finite__equiv__class,axiom, % 154.70/154.52 ! [V_X_2,V_r_2,V_A_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 154.70/154.52 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_vimage__Times,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,tc_prod(T_b,T_c),V_f_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,hAPP(c_Fun_Ocomp(tc_prod(T_b,T_c),T_b,T_a,c_Product__Type_Ofst(T_b,T_c)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_b,T_c),T_c,T_a,c_Product__Type_Osnd(T_b,T_c)),V_f_2)),V_B_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_UN__Times__distrib,axiom, % 154.70/154.52 ! [V_F_2,V_E_2,V_B_2,V_A_2,T_b,T_a,T_d,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_c,T_d),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),tc_fun(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),tc_fun(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_c),c_Product__Type_OSigma(T_a,T_b)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),T_d),c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_F_2))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Sigma__def,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),hAPP(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_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_finite__quotient,axiom, % 154.70/154.52 ! [V_r_2,V_A_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 154.70/154.52 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__in__rel,axiom, % 154.70/154.52 ! [V_R_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_R_2) % 154.70/154.52 => c_Wellfounded_OwfP(T_a,c_FunDef_Oin__rel(T_a,T_a,V_R_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wfP__wf__eq,axiom, % 154.70/154.52 ! [V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_OwfP(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(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(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),hAPP(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)) % 154.70/154.52 <=> c_Wellfounded_Owf(T_a,V_r_2) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_setsum__mult__setsum__if__inj,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] : % 154.70/154.52 ( class_Rings_Osemiring__0(T_c) % 154.70/154.52 => ( c_Fun_Oinj__on(tc_prod(T_a,T_b),T_c,hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,T_c),tc_fun(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_c),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),T_a),c_COMBB(T_c,T_c,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_a),c_Groups_Otimes__class_Otimes(T_c)),V_f_2))),V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) % 154.70/154.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_c),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_c),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_a,tc_fun(T_b,T_c)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_b,T_c)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_b)),c_fequal))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,T_c),tc_fun(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_c),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),T_a),c_COMBB(T_c,T_c,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_a),c_Groups_Otimes__class_Otimes(T_c)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_RangeP__Range__eq,axiom, % 154.70/154.52 ! [V_x_2,V_r_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,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(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(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),hAPP(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)),V_x_2)) % 154.70/154.52 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Ex__inj__on__UNION__Sigma,axiom, % 154.70/154.52 ! [V_A_2,V_I_2,T_b,T_a] : % 154.70/154.52 ? [B_f] : % 154.70/154.52 ( c_Fun_Oinj__on(T_a,tc_prod(T_b,T_a),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)) % 154.70/154.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,tc_prod(T_b,T_a),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_I_2),V_A_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_RangeP_Ointros,axiom, % 154.70/154.52 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 154.70/154.52 => hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_b_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_image__id,axiom, % 154.70/154.52 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),V_Y_2) = V_Y_2 ). % 154.70/154.52 % 154.70/154.52 fof(fact_apfst__id,axiom, % 154.70/154.52 ! [T_b,T_a] : c_Product__Type_Oapfst(T_a,T_a,T_b,c_Fun_Oid(T_a)) = c_Fun_Oid(tc_prod(T_a,T_b)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_apsnd__id,axiom, % 154.70/154.52 ! [T_a,T_b] : c_Product__Type_Oapsnd(T_b,T_b,T_a,c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_vimage__id,axiom, % 154.70/154.52 ! [V_A_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_Fun_Oid(T_a)),V_A_2) = V_A_2 ). % 154.70/154.52 % 154.70/154.52 fof(fact_id__def,axiom, % 154.70/154.52 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ). % 154.70/154.52 % 154.70/154.52 fof(fact_id__apply,axiom, % 154.70/154.52 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ). % 154.70/154.52 % 154.70/154.52 fof(fact_RangeP_Oequations,axiom, % 154.70/154.52 ! [V_a2_2,V_r_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_a2_2)) % 154.70/154.52 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_inj__on__id,axiom, % 154.70/154.52 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_Fun_Oid(T_a),V_A_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_id__o,axiom, % 154.70/154.52 ! [V_g_2,T_a,T_b] : hAPP(c_Fun_Ocomp(T_b,T_b,T_a,c_Fun_Oid(T_b)),V_g_2) = V_g_2 ). % 154.70/154.52 % 154.70/154.52 fof(fact_o__id,axiom, % 154.70/154.52 ! [V_f_2,T_b,T_a] : hAPP(c_Fun_Ocomp(T_a,T_b,T_a,V_f_2),c_Fun_Oid(T_a)) = V_f_2 ). % 154.70/154.52 % 154.70/154.52 fof(fact_o__eq__id__dest,axiom, % 154.70/154.52 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_a,T_b,T_c] : % 154.70/154.52 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_a,c_Fun_Oid(T_b)),V_c_2) % 154.70/154.52 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_of__int__eq__id,axiom, % 154.70/154.52 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ). % 154.70/154.52 % 154.70/154.52 fof(fact_surj__id,axiom, % 154.70/154.52 ! [T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_folding_Oempty,axiom, % 154.70/154.52 ! [V_F_2,V_f_2,T_b,T_a] : % 154.70/154.52 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 154.70/154.52 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Fun_Oid(T_b) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_split__Pair,axiom, % 154.70/154.52 ! [T_b,T_a] : hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_setsum__reindex__id,axiom, % 154.70/154.52 ! [V_B_2,V_f_2,T_a,T_b] : % 154.70/154.52 ( class_Groups_Ocomm__monoid__add(T_b) % 154.70/154.52 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 154.70/154.52 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_b),c_Fun_Oid(T_b)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_setprod__reindex__id,axiom, % 154.70/154.52 ! [V_B_2,V_f_2,T_a,T_b] : % 154.70/154.52 ( class_Groups_Ocomm__monoid__mult(T_b) % 154.70/154.52 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 154.70/154.52 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_b),c_Fun_Oid(T_b)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_setprod__Sigma,axiom, % 154.70/154.52 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 154.70/154.52 ( class_Groups_Ocomm__monoid__mult(T_c) % 154.70/154.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.52 => ( ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.52 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 154.70/154.52 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_a,T_b),T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_setsum__Sigma,axiom, % 154.70/154.52 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 154.70/154.52 ( class_Groups_Ocomm__monoid__add(T_c) % 154.70/154.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.52 => ( ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.52 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 154.70/154.52 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_a,T_b),T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_fold__image__Sigma,axiom, % 154.70/154.52 ! [V_g_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 154.70/154.52 ( class_Groups_Ocomm__monoid__mult(T_c) % 154.70/154.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.52 => ( ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.52 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 154.70/154.52 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_a,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBC(T_a,T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c)),T_a),c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c))),V_g_2)),c_Groups_Oone__class_Oone(T_c))),V_B_2)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,tc_prod(T_a,T_b),c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_g_2)),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_card__SigmaI,axiom, % 154.70/154.52 ! [V_B_2,T_b,V_A_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.52 => ( ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.52 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 154.70/154.52 => hAPP(c_Finite__Set_Ocard(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat,T_a),c_Finite__Set_Ocard(T_b)),V_B_2)),V_A_2) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_finite__SigmaI,axiom, % 154.70/154.52 ! [V_B_2,T_b,V_A_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.52 => ( ! [B_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 154.70/154.52 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) ) % 154.70/154.52 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_RangeE,axiom, % 154.70/154.52 ! [V_r_2,T_b,V_b_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2))) % 154.70/154.52 => ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_SigmaE,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,V_c_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) % 154.70/154.52 => ~ ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.52 => ! [B_y] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(V_B_2,B_x))) % 154.70/154.52 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wfP__acyclicP,axiom, % 154.70/154.52 ! [V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_OwfP(T_a,V_r_2) % 154.70/154.52 => c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__Un,axiom, % 154.70/154.52 ! [V_s_2,V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_r_2) % 154.70/154.52 => ( c_Wellfounded_Owf(T_a,V_s_2) % 154.70/154.52 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_a),V_r_2)),hAPP(c_Relation_ORange(T_a,T_a),V_s_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.52 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_DomainI,axiom, % 154.70/154.52 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Domain__Id__on,axiom, % 154.70/154.52 ! [V_A_2,T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = V_A_2 ). % 154.70/154.52 % 154.70/154.52 fof(fact_acyclic__subset,axiom, % 154.70/154.52 ! [V_r_2,V_s_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Oacyclic(T_a,V_s_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 154.70/154.52 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__acyclic,axiom, % 154.70/154.52 ! [V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_r_2) % 154.70/154.52 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Domain__empty__iff,axiom, % 154.70/154.52 ! [V_r_2,T_b,T_a] : % 154.70/154.52 ( hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.52 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Domain__empty,axiom, % 154.70/154.52 ! [T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Domain__mono,axiom, % 154.70/154.52 ! [V_s_2,V_r_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_s_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Domain__Un__eq,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_A_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_B_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_finite__Domain,axiom, % 154.70/154.52 ! [V_r_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2)) % 154.70/154.52 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_fst__eq__Domain,axiom, % 154.70/154.52 ! [V_R_2,T_b,T_a] : hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),V_R_2) = hAPP(c_Relation_ODomain(T_a,T_b),V_R_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Domain__iff,axiom, % 154.70/154.52 ! [V_r_2,T_b,V_a_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) % 154.70/154.52 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),B_y)),V_r_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Domain__insert,axiom, % 154.70/154.52 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_finite__acyclic__wf,axiom, % 154.70/154.52 ! [V_r_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 154.70/154.52 => ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 154.70/154.52 => c_Wellfounded_Owf(T_a,V_r_2) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__iff__acyclic__if__finite,axiom, % 154.70/154.52 ! [V_r_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 154.70/154.52 => ( c_Wellfounded_Owf(T_a,V_r_2) % 154.70/154.52 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Domain__Int__subset,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_A_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_B_2)))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Domain__Diff__subset,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_A_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_B_2))),hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Field__def,axiom, % 154.70/154.52 ! [V_r_2,T_a] : hAPP(c_Relation_OField(T_a),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_a),V_r_2)),hAPP(c_Relation_ORange(T_a,T_a),V_r_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Domain__Union,axiom, % 154.70/154.52 ! [V_S_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_a,T_b)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Domain__Collect__split,axiom, % 154.70/154.52 ! [V_P_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),V_P_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_DomainP__Domain__eq,axiom, % 154.70/154.52 ! [V_x_2,V_r_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,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(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(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),hAPP(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)),V_x_2)) % 154.70/154.52 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Nitpick_Owf_H__def,axiom, % 154.70/154.52 ! [V_r_2,T_a] : % 154.70/154.52 ( c_Nitpick_Owf_H(T_a,V_r_2) % 154.70/154.52 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 154.70/154.52 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 154.70/154.52 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_DomainE,axiom, % 154.70/154.52 ! [V_r_2,T_b,V_a_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) % 154.70/154.52 => ~ ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),B_y)),V_r_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_DomainP_Ointros,axiom, % 154.70/154.52 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 154.70/154.52 => hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_DomainP_Oequations,axiom, % 154.70/154.52 ! [V_a1_2,V_r_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a1_2)) % 154.70/154.52 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_map__pair__surj,axiom, % 154.70/154.52 ! [V_g_2,T_c,T_d,V_f_2,T_a,T_b] : % 154.70/154.52 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.52 => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) % 154.70/154.52 => hAPP(c_Set_Oimage(tc_prod(T_b,T_d),tc_prod(T_a,T_c),c_Product__Type_Omap__pair(T_b,T_a,T_d,T_c,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_map__pair__inj__on,axiom, % 154.70/154.52 ! [V_B_2,V_g_2,T_d,T_c,V_A_2,V_f_2,T_b,T_a] : % 154.70/154.52 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.52 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,V_B_2) % 154.70/154.52 => c_Fun_Oinj__on(tc_prod(T_a,T_c),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_a,T_b,T_c,T_d,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_B_2))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_map__pair__imageI,axiom, % 154.70/154.52 ! [V_g_2,V_f_2,T_d,T_c,V_R_2,V_b_2,V_a_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_R_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_a,T_b),tc_prod(T_c,T_d),c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,V_f_2,V_g_2)),V_R_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_map__pair_Ocompositionality,axiom, % 154.70/154.52 ! [V_prod_2,V_i_2,V_h_2,T_f,T_e,V_g_2,V_f_2,T_b,T_d,T_a,T_c] : hAPP(c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_e,T_a,T_f,T_b,hAPP(c_Fun_Ocomp(T_c,T_a,T_e,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_d,T_b,T_f,V_g_2),V_i_2)),V_prod_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_map__pair__compose,axiom, % 154.70/154.52 ! [V_g2_2,V_g1_2,T_f,V_f2_2,V_f1_2,T_e,T_d,T_b,T_c,T_a] : c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,hAPP(c_Fun_Ocomp(T_e,T_c,T_a,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_e,T_f),tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_a,T_e,T_b,T_f,V_f2_2,V_g2_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_map__pair_Ocomp,axiom, % 154.70/154.52 ! [V_i_2,V_h_2,V_g_2,V_f_2,T_b,T_a,T_d,T_c,T_f,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_f),tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_a,T_e,T_b,T_f,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,hAPP(c_Fun_Ocomp(T_e,T_c,T_a,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_g_2),V_i_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_snd__comp__map__pair,axiom, % 154.70/154.52 ! [V_g_2,V_f_2,T_b,T_a,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_prod(T_d,T_c),T_c,tc_prod(T_a,T_b),c_Product__Type_Osnd(T_d,T_c)),c_Product__Type_Omap__pair(T_a,T_d,T_b,T_c,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_c,tc_prod(T_a,T_b),V_g_2),c_Product__Type_Osnd(T_a,T_b)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_fst__comp__map__pair,axiom, % 154.70/154.52 ! [V_g_2,V_f_2,T_b,T_a,T_d,T_c] : hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,tc_prod(T_a,T_b),c_Product__Type_Ofst(T_c,T_d)),c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_a,T_c,tc_prod(T_a,T_b),V_f_2),c_Product__Type_Ofst(T_a,T_b)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_fst__map__pair,axiom, % 154.70/154.52 ! [V_x_2,V_g_2,V_f_2,T_d,T_c,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_snd__prod__fun,axiom, % 154.70/154.52 ! [V_x_2,V_g_2,V_f_2,T_d,T_c,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(c_Product__Type_Omap__pair(T_c,T_b,T_d,T_a,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_map__pair__simp,axiom, % 154.70/154.52 ! [V_b_2,V_a_2,V_g_2,V_f_2,T_b,T_d,T_a,T_c] : hAPP(c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_map__pair__ident,axiom, % 154.70/154.52 ! [V_z_2,T_b,T_a] : hAPP(c_Product__Type_Omap__pair(T_a,T_a,T_b,T_b,c_COMBI(T_a),c_COMBI(T_b)),V_z_2) = V_z_2 ). % 154.70/154.52 % 154.70/154.52 fof(fact_map__pair_Oidentity,axiom, % 154.70/154.52 ! [T_b,T_a] : c_Product__Type_Omap__pair(T_a,T_a,T_b,T_b,c_COMBI(T_a),c_COMBI(T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_apsnd__def,axiom, % 154.70/154.52 ! [V_f_2,T_a,T_c,T_b] : c_Product__Type_Oapsnd(T_b,T_c,T_a,V_f_2) = c_Product__Type_Omap__pair(T_a,T_a,T_b,T_c,c_Fun_Oid(T_a),V_f_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_apfst__def,axiom, % 154.70/154.52 ! [V_f_2,T_b,T_c,T_a] : c_Product__Type_Oapfst(T_a,T_c,T_b,V_f_2) = c_Product__Type_Omap__pair(T_a,T_c,T_b,T_b,V_f_2,c_Fun_Oid(T_b)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_map__pair_Oid,axiom, % 154.70/154.52 ! [T_b,T_a] : c_Product__Type_Omap__pair(T_a,T_a,T_b,T_b,c_Fun_Oid(T_a),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_map__pair__def,axiom, % 154.70/154.52 ! [V_g_2,V_f_2,T_d,T_b,T_c,T_a] : c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,T_d),tc_fun(T_b,tc_prod(T_c,T_d))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_b,T_d),tc_fun(T_b,tc_prod(T_c,T_d))),T_a),c_COMBB(T_d,tc_prod(T_c,T_d),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_a),c_Product__Type_OPair(T_c,T_d)),V_f_2))),V_g_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_map__pair__surj__on,axiom, % 154.70/154.52 ! [V_B_H_2,V_B_2,V_g_2,T_c,T_d,V_A_H_2,V_A_2,V_f_2,T_a,T_b] : % 154.70/154.52 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_A_H_2 % 154.70/154.52 => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_B_2) = V_B_H_2 % 154.70/154.52 => hAPP(c_Set_Oimage(tc_prod(T_b,T_d),tc_prod(T_a,T_c),c_Product__Type_Omap__pair(T_b,T_a,T_d,T_c,V_f_2,V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_H_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_B_H_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__map__pair__image,axiom, % 154.70/154.52 ! [V_f_2,T_b,V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_r_2) % 154.70/154.52 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 154.70/154.52 => c_Wellfounded_Owf(T_b,hAPP(c_Set_Oimage(tc_prod(T_a,T_a),tc_prod(T_b,T_b),c_Product__Type_Omap__pair(T_a,T_b,T_a,T_b,V_f_2,V_f_2)),V_r_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_prod__fun__imageE,axiom, % 154.70/154.52 ! [V_R_2,V_g_2,V_f_2,T_d,T_c,V_c_2,T_b,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_c_2),hAPP(c_Set_Oimage(tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2)),V_R_2))) % 154.70/154.52 => ~ ! [B_x,B_y] : % 154.70/154.52 ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y)) % 154.70/154.52 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)),V_R_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_refl__on__def,axiom, % 154.70/154.52 ! [V_r_2,V_A_2,T_a] : % 154.70/154.52 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 154.70/154.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 154.70/154.52 & ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_refl__on__Id__on,axiom, % 154.70/154.52 ! [V_A_2,T_a] : c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_refl__on__empty,axiom, % 154.70/154.52 ! [T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_refl__on__Un,axiom, % 154.70/154.52 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] : % 154.70/154.52 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 154.70/154.52 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2) % 154.70/154.52 => c_Relation_Orefl__on(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_refl__on__Int,axiom, % 154.70/154.52 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] : % 154.70/154.52 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 154.70/154.52 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2) % 154.70/154.52 => c_Relation_Orefl__on(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_refl__onD2,axiom, % 154.70/154.52 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 154.70/154.52 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 154.70/154.52 => ( 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)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_refl__onD1,axiom, % 154.70/154.52 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 154.70/154.52 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 154.70/154.52 => ( 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)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_refl__onD,axiom, % 154.70/154.52 ! [V_a_2,V_r_2,V_A_2,T_a] : % 154.70/154.52 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_reflp__def,axiom, % 154.70/154.52 ! [V_r_2,T_a] : % 154.70/154.52 ( c_Predicate_Oreflp(T_a,V_r_2) % 154.70/154.52 <=> c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_refl__onI,axiom, % 154.70/154.52 ! [V_A_2,V_r_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 154.70/154.52 => ( ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) % 154.70/154.52 => c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_reflpE,axiom, % 154.70/154.52 ! [V_x_2,V_r_2,T_a] : % 154.70/154.52 ( c_Predicate_Oreflp(T_a,V_r_2) % 154.70/154.52 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Rep__Integ__induct,axiom, % 154.70/154.52 ! [V_P_2,V_y_2] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 154.70/154.52 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x))) % 154.70/154.52 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Rep__Integ__cases,axiom, % 154.70/154.52 ! [V_y_2] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 154.70/154.52 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_refl__on__def_H,axiom, % 154.70/154.52 ! [V_r_2,V_A_2,T_a] : % 154.70/154.52 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 154.70/154.52 <=> ( ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),B_x)) ) % 154.70/154.52 & ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Abs__Integ__induct,axiom, % 154.70/154.52 ! [V_x_2,V_P_2] : % 154.70/154.52 ( ! [B_y] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) % 154.70/154.52 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) ) % 154.70/154.52 => hBOOL(hAPP(V_P_2,V_x_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_ball__UNIV,axiom, % 154.70/154.52 ! [V_P_2,T_a] : % 154.70/154.52 ( ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 154.70/154.52 => hBOOL(hAPP(V_P_2,B_x)) ) % 154.70/154.52 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_INFI__bool__eq,axiom, % 154.70/154.52 ! [T_a] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_HOL_Obool) = c_Set_OBall(T_a) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Powp__def,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Predicate_OPowp(T_a,V_A_2),V_B_2)) % 154.70/154.52 <=> ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 154.70/154.52 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_ball__empty,axiom, % 154.70/154.52 ! [V_P_2,T_a,B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 154.70/154.52 => hBOOL(hAPP(V_P_2,B_x)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Collect__ball__eq,axiom, % 154.70/154.52 ! [V_P_2,V_A_2,T_b,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),V_P_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_P_2))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_congruent__def,axiom, % 154.70/154.52 ! [V_f_2,V_r_2,T_b,T_a] : % 154.70/154.52 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) % 154.70/154.52 <=> ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2))),V_f_2)),B_x)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_INTER__def,axiom, % 154.70/154.52 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b)),c_member(T_a))),V_B_2)))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Sup__Inf,axiom, % 154.70/154.52 ! [V_A_2,T_a] : % 154.70/154.52 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.70/154.52 => c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a)))))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Inf__Sup,axiom, % 154.70/154.52 ! [V_A_2,T_a] : % 154.70/154.52 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.70/154.52 => c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),c_Orderings_Oord__class_Oless__eq(T_a))))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Abs__Integ__cases,axiom, % 154.70/154.52 ! [V_x_2] : % 154.70/154.52 ~ ! [B_y] : % 154.70/154.52 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y) % 154.70/154.52 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wfP__SUP,axiom, % 154.70/154.52 ! [T_a,V_r_2,T_b] : % 154.70/154.52 ( ! [B_i] : c_Wellfounded_OwfP(T_b,hAPP(V_r_2,B_i)) % 154.70/154.52 => ( ! [B_i,B_j] : % 154.70/154.52 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) % 154.70/154.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Predicate_ODomainP(T_b,T_b,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_b,T_b,hAPP(V_r_2,B_j))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 154.70/154.52 => c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_triples__valid__Suc,axiom, % 154.70/154.52 ! [V_n_2,V_ts_2,T_a] : % 154.70/154.52 ( ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 154.70/154.52 => c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),B_x) ) % 154.70/154.52 => ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 154.70/154.52 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,B_x) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_hoare__valids__def,axiom, % 154.70/154.52 ! [V_ts_2,V_Ga_2,T_a] : % 154.70/154.52 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,V_ts_2) % 154.70/154.52 <=> ! [B_n] : % 154.70/154.52 ( ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_Ga_2)) % 154.70/154.52 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) % 154.70/154.52 => ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 154.70/154.52 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Inter__eq,axiom, % 154.70/154.52 ! [V_A_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_a),hAPP(c_COMBS(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_a,tc_HOL_Obool))),V_A_2)))),c_member(T_a)))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_mem__splitI2,axiom, % 154.70/154.52 ! [V_c_2,V_z_2,T_c,T_b,T_a,V_p_2] : % 154.70/154.52 ( ! [B_a,B_b] : % 154.70/154.52 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) ) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_c,tc_HOL_Obool)),V_c_2),V_p_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_mem__splitE,axiom, % 154.70/154.52 ! [V_p_2,V_c_2,T_c,T_b,V_z_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_a,tc_HOL_Obool)),V_c_2),V_p_2))) % 154.70/154.52 => ~ ! [B_x,B_y] : % 154.70/154.52 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) % 154.70/154.52 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Eps__split,axiom, % 154.70/154.52 ! [V_P_2,T_b,T_a] : c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2)) = c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(hAPP(c_COMBS(tc_prod(T_a,T_b),T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),tc_prod(T_a,T_b)),V_P_2),c_Product__Type_Ofst(T_a,T_b))),c_Product__Type_Osnd(T_a,T_b))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wfI__pf,axiom, % 154.70/154.52 ! [V_R_2,T_a] : % 154.70/154.52 ( ! [B_A] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_a,T_a,V_R_2),B_A))) % 154.70/154.52 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) % 154.70/154.52 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_exE__some,axiom, % 154.70/154.52 ! [T_a,V_c_2,V_P_2] : % 154.70/154.52 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 154.70/154.52 => ( V_c_2 = c_Hilbert__Choice_OEps(T_a,V_P_2) % 154.70/154.52 => hBOOL(hAPP(V_P_2,V_c_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_someI,axiom, % 154.70/154.52 ! [T_a,V_x_2,V_P_2] : % 154.70/154.52 ( hBOOL(hAPP(V_P_2,V_x_2)) % 154.70/154.52 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_tfl__some,axiom, % 154.70/154.52 ! [T_a,B_P] : % 154.70/154.52 ( ? [B_x] : hBOOL(hAPP(B_P,B_x)) % 154.70/154.52 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_a,B_P))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_someI__ex,axiom, % 154.70/154.52 ! [T_a,V_P_2] : % 154.70/154.52 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 154.70/154.52 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_some__eq__ex,axiom, % 154.70/154.52 ! [T_a,V_P_2] : % 154.70/154.52 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) % 154.70/154.52 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_some__eq__trivial,axiom, % 154.70/154.52 ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2 ). % 154.70/154.52 % 154.70/154.52 fof(fact_some__sym__eq__trivial,axiom, % 154.70/154.52 ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 154.70/154.52 % 154.70/154.52 fof(fact_Eps__split__eq,axiom, % 154.70/154.52 ! [V_y_2,V_x_2,T_b,T_a] : c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_split__paired__Eps,axiom, % 154.70/154.52 ! [V_P_2,T_b,T_a] : c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),V_P_2) = c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b)))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_LeastM__def,axiom, % 154.70/154.52 ! [V_P_2,V_m_2,T_a,T_b] : % 154.70/154.52 ( class_Orderings_Oord(T_b) % 154.70/154.52 => c_Hilbert__Choice_OLeastM(T_a,T_b,V_m_2,V_P_2) = c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_m_2))),V_m_2))))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_GreatestM__def,axiom, % 154.70/154.52 ! [V_P_2,V_m_2,T_a,T_b] : % 154.70/154.52 ( class_Orderings_Oord(T_b) % 154.70/154.52 => hAPP(c_Hilbert__Choice_OGreatestM(T_a,T_b,V_m_2),V_P_2) = c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2))),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_m_2))),V_m_2))))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_LeastM__nat__lemma,axiom, % 154.70/154.52 ! [V_m_2,T_a,V_k_2,V_P_2] : % 154.70/154.52 ( hBOOL(hAPP(V_P_2,V_k_2)) % 154.70/154.52 => ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) % 154.70/154.52 & ! [B_y] : % 154.70/154.52 ( hBOOL(hAPP(V_P_2,B_y)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_m_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))),hAPP(V_m_2,B_y))) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_LeastM__nat__le,axiom, % 154.70/154.52 ! [T_a,V_m_2,V_x_2,V_P_2] : % 154.70/154.52 ( hBOOL(hAPP(V_P_2,V_x_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_m_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))),hAPP(V_m_2,V_x_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Greatest__def,axiom, % 154.70/154.52 ! [T_a] : % 154.70/154.52 ( class_Orderings_Oord(T_a) % 154.70/154.52 => c_Hilbert__Choice_OGreatest(T_a) = c_Hilbert__Choice_OGreatestM(T_a,T_a,c_COMBI(T_a)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Sigma__mono,axiom, % 154.70/154.52 ! [V_D_2,V_B_2,T_b,V_C_2,V_A_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 154.70/154.52 => ( ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,B_x)),hAPP(V_D_2,B_x))) ) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_C_2),V_D_2))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_LeastM__natI,axiom, % 154.70/154.52 ! [V_m_2,T_a,V_k_2,V_P_2] : % 154.70/154.52 ( hBOOL(hAPP(V_P_2,V_k_2)) % 154.70/154.52 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_acc_OaccI,axiom, % 154.70/154.52 ! [V_r_2,V_x_2,T_a] : % 154.70/154.52 ( ! [B_y] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_x_2)),V_r_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(T_a),B_y),c_Wellfounded_Oacc(T_a,V_r_2))) ) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_not__acc__down,axiom, % 154.70/154.52 ! [V_R_2,V_x_2,T_a] : % 154.70/154.52 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_R_2))) % 154.70/154.52 => ~ ! [B_z] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_x_2)),V_R_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(T_a),B_z),c_Wellfounded_Oacc(T_a,V_R_2))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_max__ext_Osimps,axiom, % 154.70/154.52 ! [V_R_2,V_a2_2,V_a1_2,T_a] : % 154.70/154.52 ( 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))) % 154.70/154.52 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) % 154.70/154.52 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2)) % 154.70/154.52 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.52 & ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 154.70/154.52 => ? [B_xa] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 154.70/154.52 & 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)) ) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__no__infinite__down__chainE,axiom, % 154.70/154.52 ! [V_f_2,V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_r_2) % 154.70/154.52 => ~ ! [B_k] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_k))),hAPP(V_f_2,B_k))),V_r_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_com_Osize_I3_J,axiom, % 154.70/154.52 ! [V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_com_Osize_I11_J,axiom, % 154.70/154.52 ! [V_com_2,V_fun_2,V_loc_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_WTs__elim__cases_I3_J,axiom, % 154.70/154.52 ! [V_c_2,V_a_2,V_Y_2] : % 154.70/154.52 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2))) % 154.70/154.52 => hBOOL(hAPP(c_Com_OWT,V_c_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_com_Osimps_I39_J,axiom, % 154.70/154.52 ! [V_com_2,V_fun_2,V_loc_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_com_Osimps_I38_J,axiom, % 154.70/154.52 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_com_Osimps_I2_J,axiom, % 154.70/154.52 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] : % 154.70/154.52 ( c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) = c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) % 154.70/154.52 <=> ( V_loc_2 = V_loc_H_2 % 154.70/154.52 & V_fun_2 = V_fun_H_2 % 154.70/154.52 & V_com_2 = V_com_H_2 ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_com_Osimps_I40_J,axiom, % 154.70/154.52 ! [V_pname_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_com_Osimps_I41_J,axiom, % 154.70/154.52 ! [V_com_2,V_fun_2,V_loc_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_WT_OLocal,axiom, % 154.70/154.52 ! [V_a_2,V_Y_2,V_c_2] : % 154.70/154.52 ( hBOOL(hAPP(c_Com_OWT,V_c_2)) % 154.70/154.52 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_WT_Oequations_I3_J,axiom, % 154.70/154.52 ! [V_a1_2,V_a3_2,V_a2_2] : % 154.70/154.52 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2))) % 154.70/154.52 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_com_Osimps_I10_J,axiom, % 154.70/154.52 ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_com_Osimps_I11_J,axiom, % 154.70/154.52 ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ). % 154.70/154.52 % 154.70/154.52 fof(fact_com_Osimps_I35_J,axiom, % 154.70/154.52 ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_com_Osimps_I34_J,axiom, % 154.70/154.52 ! [V_com2_H_2,V_com1_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_com_Osimps_I36_J,axiom, % 154.70/154.52 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_com_Osimps_I37_J,axiom, % 154.70/154.52 ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_setsum__reindex__cong,axiom, % 154.70/154.52 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 154.70/154.52 ( class_Groups_Ocomm__monoid__add(T_c) % 154.70/154.52 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 154.70/154.52 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 154.70/154.52 => ( ! [B_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 154.70/154.52 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) ) % 154.70/154.52 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),V_g_2),V_A_2) ) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_scomp__unfold,axiom, % 154.70/154.52 ! [V_x_2,V_g_2,V_f_2,T_a,T_d,T_c,T_b] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,T_a),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),hAPP(V_f_2,V_x_2))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_scomp__scomp,axiom, % 154.70/154.52 ! [V_h_2,V_g_2,V_f_2,T_f,T_e,T_b,T_d,T_c,T_a] : hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_c,T_d,T_b),hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_e,T_f,tc_prod(T_c,T_d)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_e,T_f,T_b),V_f_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_c,tc_fun(T_d,T_b)),tc_fun(T_f,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_c,tc_fun(T_d,T_b)),tc_fun(T_f,T_b)),T_e),c_Product__Type_Oscomp(T_f,T_c,T_d,T_b)),V_g_2)),V_h_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Pair__scomp,axiom, % 154.70/154.52 ! [V_f_2,V_x_2,T_b,T_c,T_a] : hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_c,T_a,T_b),hAPP(c_Product__Type_OPair(T_c,T_a),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_scomp__Pair,axiom, % 154.70/154.52 ! [V_x_2,T_c,T_b,T_a] : hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_b,T_c,tc_prod(T_b,T_c)),V_x_2),c_Product__Type_OPair(T_b,T_c)) = V_x_2 ). % 154.70/154.52 % 154.70/154.52 fof(fact_scomp__apply,axiom, % 154.70/154.52 ! [V_x_2,V_g_2,V_f_2,T_a,T_d,T_c,T_b] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,T_a),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_a),V_g_2),hAPP(V_f_2,V_x_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_scomp__def,axiom, % 154.70/154.52 ! [V_x_2,V_g_2,V_f_2,T_a,T_d,T_c,T_b] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,T_a),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_a),V_g_2),hAPP(V_f_2,V_x_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_iterate_Osimps,axiom, % 154.70/154.52 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] : % 154.70/154.52 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 154.70/154.52 => hAPP(c_Random_Oiterate(T_b,T_a,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2) ) % 154.70/154.52 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 154.70/154.52 => hAPP(c_Random_Oiterate(T_b,T_a,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_b,T_a,tc_prod(T_b,T_a)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_b,T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_f_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_setsum__ivl__cong,axiom, % 154.70/154.52 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_a,T_b] : % 154.70/154.52 ( ( class_Groups_Ocomm__monoid__add(T_b) % 154.70/154.52 & class_Orderings_Oord(T_a) ) % 154.70/154.52 => ( V_a_2 = V_c_2 % 154.70/154.52 => ( V_b_2 = V_d_2 % 154.70/154.52 => ( ! [B_x] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),B_x)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_d_2)) % 154.70/154.52 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) % 154.70/154.52 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2)) ) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_log_Osimps,axiom, % 154.70/154.52 ! [V_i,V_b] : % 154.70/154.52 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) % 154.70/154.52 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 154.70/154.52 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 154.70/154.52 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) % 154.70/154.52 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 154.70/154.52 => c_Random_Olog(V_b,V_i) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(V_b,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_i),V_b))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_minus__shift__def,axiom, % 154.70/154.52 ! [V_r,V_l,V_k] : % 154.70/154.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 154.70/154.52 => c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_r),V_k)),V_l) ) % 154.70/154.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 154.70/154.52 => c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k),V_l) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_inc__shift__def,axiom, % 154.70/154.52 ! [V_k,V_v] : % 154.70/154.52 ( ( V_v = V_k % 154.70/154.52 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 154.70/154.52 & ( V_v != V_k % 154.70/154.52 => c_Random_Oinc__shift(V_v,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_k),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_range,axiom, % 154.70/154.52 ! [V_s,V_k] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_k)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(V_k),V_s))),V_k)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_less__eq,axiom, % 154.70/154.52 ! [V_n_2,V_m_2] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) % 154.70/154.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_nat__intermed__int__val,axiom, % 154.70/154.52 ! [V_k_2,V_f_2,V_n_2,V_m_2] : % 154.70/154.52 ( ! [B_i] : % 154.70/154.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 154.70/154.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 154.70/154.52 => ? [B_i] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 154.70/154.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 154.70/154.52 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_wf__trancl,axiom, % 154.70/154.52 ! [V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Owf(T_a,V_r_2) % 154.70/154.52 => c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_less__than__def,axiom, % 154.70/154.52 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 154.70/154.52 % 154.70/154.52 fof(fact_acyclic__def,axiom, % 154.70/154.52 ! [V_r_2,T_a] : % 154.70/154.52 ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 154.70/154.52 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_trancl_Or__into__trancl,axiom, % 154.70/154.52 ! [V_r_2,V_b_2,V_a_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_trancl__subset__Field2,axiom, % 154.70/154.52 ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_Relation_OField(T_a),V_r_2))))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_r__into__trancl_H,axiom, % 154.70/154.52 ! [V_r_2,V_p_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_trancl__empty,axiom, % 154.70/154.52 ! [T_a] : c_Transitive__Closure_Otrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_trancl__domain,axiom, % 154.70/154.52 ! [V_r_2,T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)) = hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_trancl__range,axiom, % 154.70/154.52 ! [V_r_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)) = hAPP(c_Relation_ORange(T_a,T_a),V_r_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_finite__trancl,axiom, % 154.70/154.52 ! [V_r_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 154.70/154.52 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_trancl__trans,axiom, % 154.70/154.52 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom, % 154.70/154.52 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),V_r_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_trancl__into__trancl2,axiom, % 154.70/154.52 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_r__r__into__trancl,axiom, % 154.70/154.52 ! [V_c_2,V_R_2,V_b_2,V_a_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_R_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),V_R_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_trancl__mono,axiom, % 154.70/154.52 ! [V_s_2,V_r_2,V_p_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_s_2))) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_trancl__unfold,axiom, % 154.70/154.52 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)),V_r_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_trancl__subset__Sigma,axiom, % 154.70/154.52 ! [V_A_2,V_r_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_trancl__Int__subset,axiom, % 154.70/154.52 ! [V_s_2,V_r_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),V_s_2)),V_r_2)),V_s_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),V_s_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_trancl__insert,axiom, % 154.70/154.52 ! [V_r_2,V_x_2,V_y_2,T_a] : c_Transitive__Closure_Otrancl(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(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))),hAPP(hAPP(c_COMBC(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),V_y_2))),c_Transitive__Closure_Ortrancl(T_a,V_r_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(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))),hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2))),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_reflcl__set__eq,axiom, % 154.70/154.52 ! [V_y_2,V_x_2,V_r_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),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(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(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),hAPP(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)),c_fequal),V_x_2),V_y_2)) % 154.70/154.52 <=> 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)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a)))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_r__into__rtrancl,axiom, % 154.70/154.52 ! [V_r_2,V_p_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_rtrancl_Ortrancl__refl,axiom, % 154.70/154.52 ! [V_r_2,V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_IdI,axiom, % 154.70/154.52 ! [V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),c_Relation_OId(T_a))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_trancl__into__rtrancl,axiom, % 154.70/154.52 ! [V_r_2,V_b_2,V_a_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_trancl__unfold__left,axiom, % 154.70/154.52 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_trancl__unfold__right,axiom, % 154.70/154.52 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_r_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_reflcl__trancl,axiom, % 154.70/154.52 ! [V_r_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),c_Relation_OId(T_a)) = c_Transitive__Closure_Ortrancl(T_a,V_r_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_trancl__reflcl,axiom, % 154.70/154.52 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_r_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_rtrancl__trancl__absorb,axiom, % 154.70/154.52 ! [V_R_2,T_a] : c_Transitive__Closure_Otrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_trancl__rtrancl__absorb,axiom, % 154.70/154.52 ! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Otrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_rtrancl__Int__subset,axiom, % 154.70/154.52 ! [V_r_2,V_s_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Relation_OId(T_a)),V_s_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_s_2)),V_r_2)),V_s_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_s_2)) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_rtrancl__subset__rtrancl,axiom, % 154.70/154.52 ! [V_s_2,V_r_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_s_2))) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(T_a,V_s_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_rtrancl__subset,axiom, % 154.70/154.52 ! [V_S_2,V_R_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 154.70/154.52 => c_Transitive__Closure_Ortrancl(T_a,V_S_2) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_rtrancl__mono,axiom, % 154.70/154.52 ! [V_s_2,V_r_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 154.70/154.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(T_a,V_s_2))) ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_rtrancl__Un__subset,axiom, % 154.70/154.52 ! [V_S_2,V_R_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_S_2))),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)))) ). % 154.70/154.52 % 154.70/154.52 fof(fact_Image__closed__trancl,axiom, % 154.70/154.52 ! [V_X_2,V_r_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),V_X_2)),V_X_2)) % 154.70/154.52 => hAPP(c_Relation_OImage(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_X_2) = V_X_2 ) ). % 154.70/154.52 % 154.70/154.52 fof(fact_refl__rtrancl,axiom, % 154.70/154.52 ! [V_r_2,T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) ). % 154.70/154.52 % 154.70/154.52 fof(fact_rtrancl__r__diff__Id,axiom, % 154.70/154.52 ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_r_2) ). % 154.70/154.52 % 154.70/154.52 fof(fact_rtrancl__trans,axiom, % 154.70/154.52 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 154.70/154.52 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 154.70/154.52 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom, % 154.70/154.53 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),V_r_2)) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_converse__rtrancl__into__rtrancl,axiom, % 154.70/154.53 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtrancl__idemp,axiom, % 154.70/154.53 ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Transitive__Closure_Ortrancl(T_a,V_r_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtrancl__reflcl,axiom, % 154.70/154.53 ! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtrancl__Un__rtrancl,axiom, % 154.70/154.53 ! [V_S_2,V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) = c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtrancl__reflcl__absorb,axiom, % 154.70/154.53 ! [V_R_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Relation_OId(T_a)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_in__rtrancl__UnI,axiom, % 154.70/154.53 ! [V_S_2,V_R_2,V_x_2,T_a] : % 154.70/154.53 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 154.70/154.53 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) ) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtrancl__idemp__self__comp,axiom, % 154.70/154.53 ! [V_R_2,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_r__comp__rtrancl__eq,axiom, % 154.70/154.53 ! [V_r_2,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_r_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtrancl__unfold,axiom, % 154.70/154.53 ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Relation_OId(T_a)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_r_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtrancl__empty,axiom, % 154.70/154.53 ! [T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Relation_OId(T_a) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Range__rtrancl,axiom, % 154.70/154.53 ! [V_R_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Domain__rtrancl,axiom, % 154.70/154.53 ! [V_R_2,T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_R__O__Id,axiom, % 154.70/154.53 ! [V_R_2,T_b,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_b),V_R_2),c_Relation_OId(T_b)) = V_R_2 ). % 154.70/154.53 % 154.70/154.53 fof(fact_Id__O__R,axiom, % 154.70/154.53 ! [V_R_2,T_b,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_b),c_Relation_OId(T_a)),V_R_2) = V_R_2 ). % 154.70/154.53 % 154.70/154.53 fof(fact_Image__Id,axiom, % 154.70/154.53 ! [V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId(T_a)),V_A_2) = V_A_2 ). % 154.70/154.53 % 154.70/154.53 fof(fact_pair__in__Id__conv,axiom, % 154.70/154.53 ! [V_b_2,V_a_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Relation_OId(T_a))) % 154.70/154.53 <=> V_a_2 = V_b_2 ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtrancl__trancl__trancl,axiom, % 154.70/154.53 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_trancl__rtrancl__trancl,axiom, % 154.70/154.53 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtrancl__into__trancl1,axiom, % 154.70/154.53 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),V_r_2)) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtranclD,axiom, % 154.70/154.53 ! [V_R_2,V_b_2,V_a_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 154.70/154.53 => ( V_a_2 = V_b_2 % 154.70/154.53 | ( V_a_2 != V_b_2 % 154.70/154.53 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtrancl__into__trancl2,axiom, % 154.70/154.53 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtrancl__eq__or__trancl,axiom, % 154.70/154.53 ! [V_R_2,V_y_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 154.70/154.53 <=> ( V_x_2 = V_y_2 % 154.70/154.53 | ( V_x_2 != V_y_2 % 154.70/154.53 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Domain__Id,axiom, % 154.70/154.53 ! [T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Relation_OId(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Range__Id,axiom, % 154.70/154.53 ! [T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Relation_OId(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_refl__Id,axiom, % 154.70/154.53 ! [T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Relation_OId(T_a)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_pair__leq__def,axiom, % 154.70/154.53 c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Not__Domain__rtrancl,axiom, % 154.70/154.53 ! [V_y_2,V_R_2,V_x_2,T_a] : % 154.70/154.53 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_a),V_R_2))) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 154.70/154.53 <=> V_x_2 = V_y_2 ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_acc__downwards,axiom, % 154.70/154.53 ! [V_b_2,V_r_2,V_a_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_acc__downwards__aux,axiom, % 154.70/154.53 ! [V_r_2,V_a_2,V_b_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_wf__insert,axiom, % 154.70/154.53 ! [V_r_2,V_x_2,V_y_2,T_a] : % 154.70/154.53 ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2)) % 154.70/154.53 <=> ( c_Wellfounded_Owf(T_a,V_r_2) % 154.70/154.53 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_acyclic__insert,axiom, % 154.70/154.53 ! [V_r_2,V_x_2,V_y_2,T_a] : % 154.70/154.53 ( c_Wellfounded_Oacyclic(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2)) % 154.70/154.53 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 154.70/154.53 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_refl__reflcl,axiom, % 154.70/154.53 ! [V_r_2,T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Id__def,axiom, % 154.70/154.53 ! [T_a] : c_Relation_OId(T_a) = hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_a,T_a)),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(tc_prod(T_a,T_a),tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_HOL_Obool)),tc_prod(T_a,T_a)),c_COMBB(tc_prod(T_a,T_a),tc_HOL_Obool,T_a)),c_fequal)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a))))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_irrefl__diff__Id,axiom, % 154.70/154.53 ! [V_r_2,T_a] : c_Relation_Oirrefl(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_pred__nat__trancl__eq__le,axiom, % 154.70/154.53 ! [V_n_2,V_m_2] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) % 154.70/154.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_trancl__subset__Sigma__aux,axiom, % 154.70/154.53 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 154.70/154.53 => ( V_a_2 = V_b_2 % 154.70/154.53 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_irrefl__tranclI,axiom, % 154.70/154.53 ! [V_x_2,V_r_2,T_a] : % 154.70/154.53 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 154.70/154.53 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_sequence__trans,axiom, % 154.70/154.53 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_a] : % 154.70/154.53 ( ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))),hAPP(V_f_2,V_i_2))),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtrancl__converse,axiom, % 154.70/154.53 ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_converse__Id,axiom, % 154.70/154.53 ! [T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId(T_a)) = c_Relation_OId(T_a) ). % 154.70/154.53 % 154.70/154.53 fof(fact_converse__INTER,axiom, % 154.70/154.53 ! [V_r_2,V_S_2,T_c,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_c),c_Relation_Oconverse(T_b,T_a)),V_r_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_refl__on__converse,axiom, % 154.70/154.53 ! [V_r_2,V_A_2,T_a] : % 154.70/154.53 ( c_Relation_Orefl__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 154.70/154.53 <=> c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_converse__UNION,axiom, % 154.70/154.53 ! [V_r_2,V_S_2,T_c,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_c),c_Relation_Oconverse(T_b,T_a)),V_r_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_converse__iff,axiom, % 154.70/154.53 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) % 154.70/154.53 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_b_2),V_a_2)),V_r_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_converseI,axiom, % 154.70/154.53 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_converseD,axiom, % 154.70/154.53 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_b_2),V_a_2)),V_r_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_converse__inv__image,axiom, % 154.70/154.53 ! [V_f_2,V_R_2,T_b,T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),hAPP(c_Relation_Oconverse(T_b,T_b),V_R_2)),V_f_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Field__converse,axiom, % 154.70/154.53 ! [V_r_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_OField(T_a),V_r_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_finite__converse,axiom, % 154.70/154.53 ! [V_r_2,T_b,T_a] : % 154.70/154.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) % 154.70/154.53 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_a)),V_r_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_converse__converse,axiom, % 154.70/154.53 ! [V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2)) = V_r_2 ). % 154.70/154.53 % 154.70/154.53 fof(fact_converse__Int,axiom, % 154.70/154.53 ! [V_s_2,V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_s_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_converse__Id__on,axiom, % 154.70/154.53 ! [V_A_2,T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = c_Relation_OId__on(T_a,V_A_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_converse__Un,axiom, % 154.70/154.53 ! [V_s_2,V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_s_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_converse__rel__comp,axiom, % 154.70/154.53 ! [V_s_2,V_r_2,T_c,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_a),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(c_Relation_Oconverse(T_c,T_a),V_s_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_acyclic__converse,axiom, % 154.70/154.53 ! [V_r_2,T_a] : % 154.70/154.53 ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 154.70/154.53 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_trancl__converse,axiom, % 154.70/154.53 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_wf__converse__trancl,axiom, % 154.70/154.53 ! [V_r_2,T_a] : % 154.70/154.53 ( c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 154.70/154.53 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_equiv__comp__eq,axiom, % 154.70/154.53 ! [V_r_2,V_A_2,T_a] : % 154.70/154.53 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 154.70/154.53 => hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2) = V_r_2 ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Range__def,axiom, % 154.70/154.53 ! [V_r_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Domain__converse,axiom, % 154.70/154.53 ! [V_r_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) = hAPP(c_Relation_ORange(T_b,T_a),V_r_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Range__converse,axiom, % 154.70/154.53 ! [V_r_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2)) = hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtrancl__converseI,axiom, % 154.70/154.53 ! [V_r_2,V_x_2,V_y_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtrancl__converseD,axiom, % 154.70/154.53 ! [V_r_2,V_y_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_trancl__converseI,axiom, % 154.70/154.53 ! [V_r_2,V_y_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_trancl__converseD,axiom, % 154.70/154.53 ! [V_r_2,V_y_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Image__subset__eq,axiom, % 154.70/154.53 ! [V_B_2,V_A_2,V_r_2,T_b,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2)),V_B_2)) % 154.70/154.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2))))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_refl__on__comp__subset,axiom, % 154.70/154.53 ! [V_r_2,V_A_2,T_a] : % 154.70/154.53 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_comp__equivI,axiom, % 154.70/154.53 ! [V_A_2,V_r_2,T_a] : % 154.70/154.53 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2) = V_r_2 % 154.70/154.53 => ( hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) = V_A_2 % 154.70/154.53 => c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_finite__acyclic__wf__converse,axiom, % 154.70/154.53 ! [V_r_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 154.70/154.53 => ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 154.70/154.53 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_converse__def,axiom, % 154.70/154.53 ! [V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_a)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_a)))),hAPP(c_COMBC(T_b,T_a,tc_prod(T_b,T_a)),c_Product__Type_OPair(T_b,T_a))))),V_r_2))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Image__INT__eq,axiom, % 154.70/154.53 ! [V_B_2,T_c,V_A_2,V_r_2,T_b,T_a] : % 154.70/154.53 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) % 154.70/154.53 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 154.70/154.53 => hAPP(c_Relation_OImage(T_b,T_a,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Relation_OImage(T_b,T_a,V_r_2)),V_B_2)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_total__on__diff__Id,axiom, % 154.70/154.53 ! [V_r_2,V_A_2,T_a] : % 154.70/154.53 ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) % 154.70/154.53 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_single__valued__Id,axiom, % 154.70/154.53 ! [T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_single__valued__Id__on,axiom, % 154.70/154.53 ! [V_A_2,T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_single__valued__rel__comp,axiom, % 154.70/154.53 ! [V_s_2,T_c,V_r_2,T_b,T_a] : % 154.70/154.53 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 154.70/154.53 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2) % 154.70/154.53 => c_Relation_Osingle__valued(T_a,T_c,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_single__valued__subset,axiom, % 154.70/154.53 ! [V_s_2,V_r_2,T_b,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 154.70/154.53 => ( c_Relation_Osingle__valued(T_a,T_b,V_s_2) % 154.70/154.53 => c_Relation_Osingle__valued(T_a,T_b,V_r_2) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_total__on__empty,axiom, % 154.70/154.53 ! [V_r_2,T_a] : c_Relation_Ototal__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_r_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_total__on__converse,axiom, % 154.70/154.53 ! [V_r_2,V_A_2,T_a] : % 154.70/154.53 ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 154.70/154.53 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_single__valuedD,axiom, % 154.70/154.53 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b,T_a] : % 154.70/154.53 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 154.70/154.53 => ( 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)) % 154.70/154.53 => ( 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_z_2)),V_r_2)) % 154.70/154.53 => V_y_2 = V_z_2 ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_single__valued__def,axiom, % 154.70/154.53 ! [V_r_2,T_b,T_a] : % 154.70/154.53 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 154.70/154.53 <=> ! [B_x,B_y] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y)),V_r_2)) % 154.70/154.53 => ! [B_z] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z)),V_r_2)) % 154.70/154.53 => B_y = B_z ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_total__on__def,axiom, % 154.70/154.53 ! [V_r_2,V_A_2,T_a] : % 154.70/154.53 ( c_Relation_Ototal__on(T_a,V_A_2,V_r_2) % 154.70/154.53 <=> ! [B_x] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.53 => ! [B_xa] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 154.70/154.53 => ( B_x != B_xa % 154.70/154.53 => ( 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)) % 154.70/154.53 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_xa),B_x)),V_r_2)) ) ) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_single__valued__confluent,axiom, % 154.70/154.53 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] : % 154.70/154.53 ( c_Relation_Osingle__valued(T_a,T_a,V_r_2) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 154.70/154.53 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Image__Int__eq,axiom, % 154.70/154.53 ! [V_B_2,V_A_2,V_R_2,T_b,T_a] : % 154.70/154.53 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_R_2)) % 154.70/154.53 => hAPP(c_Relation_OImage(T_b,T_a,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_B_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtrancl__imp__UN__rel__pow,axiom, % 154.70/154.53 ! [V_R_2,V_p_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2)))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_acyclicI,axiom, % 154.70/154.53 ! [V_r_2,T_a] : % 154.70/154.53 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 154.70/154.53 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_single__valued__rel__pow,axiom, % 154.70/154.53 ! [V_n_2,V_R_2,T_a] : % 154.70/154.53 ( c_Relation_Osingle__valued(T_a,T_a,V_R_2) % 154.70/154.53 => c_Relation_Osingle__valued(T_a,T_a,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_comp__funpow,axiom, % 154.70/154.53 ! [V_f_2,V_n_2,T_b,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_a,T_b),tc_fun(T_a,T_b)),V_n_2),c_Fun_Ocomp(T_b,T_b,T_a,V_f_2)) = c_Fun_Ocomp(T_b,T_b,T_a,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_funpow__swap1,axiom, % 154.70/154.53 ! [V_x_2,V_n_2,T_a,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2),hAPP(V_f_2,V_x_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_funpow__mult,axiom, % 154.70/154.53 ! [V_f_2,V_m_2,V_n_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_wf__exp,axiom, % 154.70/154.53 ! [V_R_2,V_n_2,T_a] : % 154.70/154.53 ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) % 154.70/154.53 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rel__pow__commute,axiom, % 154.70/154.53 ! [V_n_2,V_R_2,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rel__pow__1,axiom, % 154.70/154.53 ! [V_R_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_R_2) = V_R_2 ). % 154.70/154.53 % 154.70/154.53 fof(fact_rel__pow__imp__rtrancl,axiom, % 154.70/154.53 ! [V_R_2,V_n_2,V_p_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtrancl__power,axiom, % 154.70/154.53 ! [V_R_2,V_p_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 154.70/154.53 <=> ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_n),V_R_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_relpow_Osimps_I2_J,axiom, % 154.70/154.53 ! [V_R_2,V_n_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rel__pow__add,axiom, % 154.70/154.53 ! [V_R_2,V_n_2,V_m_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_relpow_Osimps_I1_J,axiom, % 154.70/154.53 ! [V_R_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_a) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rel__pow__0__E,axiom, % 154.70/154.53 ! [V_R_2,V_y_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) % 154.70/154.53 => V_x_2 = V_y_2 ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rel__pow__0__I,axiom, % 154.70/154.53 ! [V_R_2,V_x_2,T_a] : 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_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rel__pow__Suc__I2,axiom, % 154.70/154.53 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_R_2)) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rel__pow__Suc__I,axiom, % 154.70/154.53 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),V_R_2)) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_funpow_Osimps_I2_J,axiom, % 154.70/154.53 ! [V_f_2,V_n_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_a,T_a,T_a,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_funpow__add,axiom, % 154.70/154.53 ! [V_f_2,V_n_2,V_m_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_a,T_a,T_a,hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_funpow_Osimps_I1_J,axiom, % 154.70/154.53 ! [V_f_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_a) ). % 154.70/154.53 % 154.70/154.53 fof(fact_trancl__power,axiom, % 154.70/154.53 ! [V_R_2,V_p_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_R_2))) % 154.70/154.53 <=> ? [B_n] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 154.70/154.53 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_n),V_R_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtrancl__is__UN__rel__pow,axiom, % 154.70/154.53 ! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_funpow__code__def,axiom, % 154.70/154.53 ! [T_a] : c_Nat_Ofunpow(T_a) = c_Nat_Ocompow(T_a,T_a) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rel__pow__E,axiom, % 154.70/154.53 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) % 154.70/154.53 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.53 => V_x_2 != V_z_2 ) % 154.70/154.53 => ~ ! [B_y,B_m] : % 154.70/154.53 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_m),V_R_2))) % 154.70/154.53 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),V_R_2)) ) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rel__pow__E2,axiom, % 154.70/154.53 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) % 154.70/154.53 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.53 => V_x_2 != V_z_2 ) % 154.70/154.53 => ~ ! [B_y,B_m] : % 154.70/154.53 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2)) % 154.70/154.53 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_m),V_R_2))) ) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtrancl__Un__separatorE,axiom, % 154.70/154.53 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2),V_Q_2)))) % 154.70/154.53 => ( ! [B_x] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) % 154.70/154.53 => ! [B_y] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_Q_2)) % 154.70/154.53 => B_x = B_y ) ) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtrancl__Un__separator__converseE,axiom, % 154.70/154.53 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2),V_Q_2)))) % 154.70/154.53 => ( ! [B_x] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) % 154.70/154.53 => ! [B_y] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_x)),V_Q_2)) % 154.70/154.53 => B_y = B_x ) ) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rel__pow__Suc__E,axiom, % 154.70/154.53 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) % 154.70/154.53 => ~ ! [B_y] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) % 154.70/154.53 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),V_R_2)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rel__pow__Suc__D2,axiom, % 154.70/154.53 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) % 154.70/154.53 => ? [B_y] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2)) % 154.70/154.53 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rel__pow__Suc__E2,axiom, % 154.70/154.53 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) % 154.70/154.53 => ~ ! [B_y] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2)) % 154.70/154.53 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_tranclD2,axiom, % 154.70/154.53 ! [V_R_2,V_y_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) % 154.70/154.53 => ? [B_z] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 154.70/154.53 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_y_2)),V_R_2)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_tranclD,axiom, % 154.70/154.53 ! [V_R_2,V_y_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) % 154.70/154.53 => ? [B_z] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_z)),V_R_2)) % 154.70/154.53 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_IdE,axiom, % 154.70/154.53 ! [V_p_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Relation_OId(T_a))) % 154.70/154.53 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_mod__div__decomp,axiom, % 154.70/154.53 ! [V_b,V_a,T_a] : % 154.70/154.53 ( class_Divides_Osemiring__div(T_a) % 154.70/154.53 => V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_wf__eq__minimal,axiom, % 154.70/154.53 ! [V_r_2,T_a] : % 154.70/154.53 ( c_Wellfounded_Owf(T_a,V_r_2) % 154.70/154.53 <=> ! [B_Q] : % 154.70/154.53 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) % 154.70/154.53 => ? [B_x] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) % 154.70/154.53 & ! [B_y] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_x)),V_r_2)) % 154.70/154.53 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_y),B_Q)) ) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_transfer__nat__int__set__cong,axiom, % 154.70/154.53 ! [V_P_H_2,V_P_2] : % 154.70/154.53 ( ! [B_x] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 154.70/154.53 => ( hBOOL(hAPP(V_P_2,B_x)) % 154.70/154.53 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) ) % 154.70/154.53 => hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Int__Collect__mono,axiom, % 154.70/154.53 ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.70/154.53 => ( ! [B_x] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.53 => ( hBOOL(hAPP(V_P_2,B_x)) % 154.70/154.53 => hBOOL(hAPP(V_Q_2,B_x)) ) ) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_a),V_Q_2)))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rel__compE,axiom, % 154.70/154.53 ! [V_s_2,V_r_2,T_c,V_xz_2,T_b,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_r_2),V_s_2))) % 154.70/154.53 => ~ ! [B_x,B_y,B_z] : % 154.70/154.53 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),B_x),B_y)),V_r_2)) % 154.70/154.53 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),B_z)),V_s_2)) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_converseE,axiom, % 154.70/154.53 ! [V_r_2,V_yx_2,T_b,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_yx_2),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) % 154.70/154.53 => ~ ! [B_x,B_y] : % 154.70/154.53 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_y),B_x) % 154.70/154.53 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),B_y)),V_r_2)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Nitpick_Oplus__frac__def,axiom, % 154.70/154.53 ! [V_r_2,V_q_2,T_a] : c_Nitpick_Oplus__frac(T_a,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_a),V_q_2),hAPP(c_Nitpick_Odenom(T_a),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_a),tc_Int_Oint),c_Nitpick_Ofrac(T_a)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_a),V_q_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_r_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_a),V_r_2)))))),c_COMBI(tc_Int_Oint))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Nitpick_Otimes__frac__def,axiom, % 154.70/154.53 ! [V_r,V_q,T_a] : c_Nitpick_Otimes__frac(T_a,V_q,V_r) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Odenom(T_a),V_r))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Nitpick_Oof__frac__def,axiom, % 154.70/154.53 ! [V_q,T_a,T_b] : % 154.70/154.53 ( ( class_Rings_Oinverse(T_b) % 154.70/154.53 & class_Rings_Oring__1(T_b) ) % 154.70/154.53 => c_Nitpick_Oof__frac(T_a,T_b,V_q) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Odenom(T_a),V_q))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Nitpick_Oinverse__frac__def,axiom, % 154.70/154.53 ! [V_q,T_a] : c_Nitpick_Oinverse__frac(T_a,V_q) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_q)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Nitpick_Ouminus__frac__def,axiom, % 154.70/154.53 ! [V_q,T_a] : c_Nitpick_Ouminus__frac(T_a,V_q) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Nitpick_Odenom(T_a),V_q))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Nitpick_Oless__frac__def,axiom, % 154.70/154.53 ! [V_r_2,V_q_2,T_a] : % 154.70/154.53 ( c_Nitpick_Oless__frac(T_a,V_q_2,V_r_2) % 154.70/154.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),c_Nitpick_Oplus__frac(T_a,V_q_2,c_Nitpick_Ouminus__frac(T_a,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Nitpick_Oless__eq__frac__def,axiom, % 154.70/154.53 ! [V_r_2,V_q_2,T_a] : % 154.70/154.53 ( c_Nitpick_Oless__eq__frac(T_a,V_q_2,V_r_2) % 154.70/154.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),c_Nitpick_Oplus__frac(T_a,V_q_2,c_Nitpick_Ouminus__frac(T_a,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Nitpick_Odenom__def,axiom, % 154.70/154.53 ! [T_a] : c_Nitpick_Odenom(T_a) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_a,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_a)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Nitpick_Onum__def,axiom, % 154.70/154.53 ! [T_a] : c_Nitpick_Onum(T_a) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_a,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_a)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_setprod__pos,axiom, % 154.70/154.53 ! [V_f_2,V_A_2,T_a,T_b] : % 154.70/154.53 ( class_Rings_Olinordered__semidom(T_b) % 154.70/154.53 => ( ! [B_x] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_internal__split__def,axiom, % 154.70/154.53 ! [T_c,T_b,T_a] : c_Product__Type_Ointernal__split(T_a,T_b,T_c) = c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c) ). % 154.70/154.53 % 154.70/154.53 fof(fact_internal__split__conv,axiom, % 154.70/154.53 ! [V_b_2,V_a_2,V_c_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_b,T_c,T_a),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_c_2,V_a_2),V_b_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_setprod__nonneg,axiom, % 154.70/154.53 ! [V_f_2,V_A_2,T_a,T_b] : % 154.70/154.53 ( class_Rings_Olinordered__semidom(T_b) % 154.70/154.53 => ( ! [B_x] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_bool_Osize_I1_J,axiom, % 154.70/154.53 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.70/154.53 % 154.70/154.53 fof(fact_bool_Osize_I2_J,axiom, % 154.70/154.53 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.70/154.53 % 154.70/154.53 fof(fact_finite__less__ub,axiom, % 154.70/154.53 ! [V_u_2,V_f_2] : % 154.70/154.53 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n))) % 154.70/154.53 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_f_2)),V_u_2)))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_lenlex__def,axiom, % 154.70/154.53 ! [V_r_2,T_a] : c_List_Olenlex(T_a,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_a)),tc_List_Olist(T_a)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_a),c_Wellfounded_Oless__than,c_List_Olex(T_a,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_prod(tc_Nat_Onat,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_a),tc_prod(tc_Nat_Onat,tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_a))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_COMBI(tc_List_Olist(T_a)))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_lexn__length,axiom, % 154.70/154.53 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2))) % 154.70/154.53 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = V_n_2 % 154.70/154.53 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_neq__if__length__neq,axiom, % 154.70/154.53 ! [V_ys,V_xs,T_a] : % 154.70/154.53 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys) % 154.70/154.53 => V_xs != V_ys ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_lenlex__conv,axiom, % 154.70/154.53 ! [V_r_2,T_a] : c_List_Olenlex(T_a,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBC(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))))),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a))))),c_List_Olex(T_a,V_r_2)))))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_length__sublist,axiom, % 154.70/154.53 ! [V_I_2,V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osublist(T_a,V_xs_2,V_I_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2)))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_lexn_Osimps_I2_J,axiom, % 154.70/154.53 ! [V_n_2,V_r_2,T_a] : hAPP(c_List_Olexn(T_a,V_r_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_a,tc_List_Olist(T_a)),tc_prod(T_a,tc_List_Olist(T_a))),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_Product__Type_Omap__pair(tc_prod(T_a,tc_List_Olist(T_a)),tc_List_Olist(T_a),tc_prod(T_a,tc_List_Olist(T_a)),tc_List_Olist(T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)))),c_Wellfounded_Olex__prod(T_a,tc_List_Olist(T_a),V_r_2,hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),hAPP(c_Nat_OSuc,V_n_2)))))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_impossible__Cons,axiom, % 154.70/154.53 ! [V_x,V_ys,V_xs,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys))) % 154.70/154.53 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list_Oinject,axiom, % 154.70/154.53 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_a] : % 154.70/154.53 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H_2),V_list_H_2) % 154.70/154.53 <=> ( V_a_2 = V_a_H_2 % 154.70/154.53 & V_list_2 = V_list_H_2 ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_not__Cons__self2,axiom, % 154.70/154.53 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ). % 154.70/154.53 % 154.70/154.53 fof(fact_not__Cons__self,axiom, % 154.70/154.53 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list_Osize_I4_J,axiom, % 154.70/154.53 ! [V_list,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),V_list)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_list)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Cons__in__lex,axiom, % 154.70/154.53 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olex(T_a,V_r_2))) % 154.70/154.53 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 154.70/154.53 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) ) % 154.70/154.53 | ( V_x_2 = V_y_2 % 154.70/154.53 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olex(T_a,V_r_2))) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__Cons__def,axiom, % 154.70/154.53 ! [V_XS_2,V_A_2,T_a] : c_List_Oset__Cons(T_a,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_a)),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),c_COMBS(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),T_a),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),c_COMBB(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_List_Olist(T_a),tc_HOL_Obool,tc_List_Olist(T_a))),c_fequal))),c_List_Olist_OCons(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),V_XS_2)))))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_pick_Osimps,axiom, % 154.70/154.53 ! [V_xs,V_x,T_a,V_i] : % 154.70/154.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) % 154.70/154.53 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a),V_x) ) % 154.70/154.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) % 154.70/154.53 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Random_Opick(T_a,V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_select__weight__cons__zero,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,T_a] : c_Random_Oselect__weight(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_a,V_xs_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_lexord__cons__cons,axiom, % 154.70/154.53 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_b_2),V_y_2))),c_List_Olexord(T_a,V_r_2))) % 154.70/154.53 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 154.70/154.53 | ( V_a_2 = V_b_2 % 154.70/154.53 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_lexord__lex,axiom, % 154.70/154.53 ! [V_r_2,V_y_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olex(T_a,V_r_2))) % 154.70/154.53 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) % 154.70/154.53 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtrancl__listrel1__ConsI2,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list_Osize_I2_J,axiom, % 154.70/154.53 ! [V_list_2,V_a_2,V_fa_2,T_a] : c_List_Olist_Olist__size(T_a,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_list_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),c_List_Olist_Olist__size(T_a,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Cons__acc__listrel1I,axiom, % 154.70/154.53 ! [V_xs_2,V_r_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel1__mono,axiom, % 154.70/154.53 ! [V_s_2,V_r_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel1(T_a,V_r_2)),c_List_Olistrel1(T_a,V_s_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel1__converse,axiom, % 154.70/154.53 ! [V_r_2,T_a] : c_List_Olistrel1(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel1(T_a,V_r_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom, % 154.70/154.53 ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel1(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtrancl__listrel1__ConsI1,axiom, % 154.70/154.53 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel1I2,axiom, % 154.70/154.53 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_ys_2))),c_List_Olistrel1(T_a,V_r_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtrancl__listrel1__eq__len,axiom, % 154.70/154.53 ! [V_r_2,V_y_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) % 154.70/154.53 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel1__eq__len,axiom, % 154.70/154.53 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 154.70/154.53 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_in__listrel1__converse,axiom, % 154.70/154.53 ! [V_r_2,V_y_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olistrel1(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) % 154.70/154.53 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel1(T_a,V_r_2)))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel1I1,axiom, % 154.70/154.53 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_xs_2))),c_List_Olistrel1(T_a,V_r_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Cons__listrel1__Cons,axiom, % 154.70/154.53 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel1(T_a,V_r_2))) % 154.70/154.53 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 154.70/154.53 & V_xs_2 = V_ys_2 ) % 154.70/154.53 | ( V_x_2 = V_y_2 % 154.70/154.53 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel__Cons,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,V_r_2,T_a] : hAPP(c_Relation_OImage(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) = c_List_Oset__Cons(T_a,hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_lexord__irreflexive,axiom, % 154.70/154.53 ! [V_y_2,V_r_2,T_a] : % 154.70/154.53 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) % 154.70/154.53 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_y_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel__rtrancl__refl,axiom, % 154.70/154.53 ! [V_r_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_xs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel__mono,axiom, % 154.70/154.53 ! [V_s_2,V_r_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel(T_a,V_r_2)),c_List_Olistrel(T_a,V_s_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel__subset__rtrancl__listrel1,axiom, % 154.70/154.53 ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel__eq__len,axiom, % 154.70/154.53 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) % 154.70/154.53 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel__rtrancl__trans,axiom, % 154.70/154.53 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_ys_2),V_zs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_zs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom, % 154.70/154.53 ! [V_r_2,T_a] : c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel__reflcl__if__listrel1,axiom, % 154.70/154.53 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel1__subset__listrel,axiom, % 154.70/154.53 ! [V_r_H_2,V_r_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_r_H_2)) % 154.70/154.53 => ( c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_r_H_2) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel1(T_a,V_r_2)),c_List_Olistrel(T_a,V_r_H_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rtrancl__listrel1__if__listrel,axiom, % 154.70/154.53 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel_OCons,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel(T_a,V_r_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrelp__listrel__eq,axiom, % 154.70/154.53 ! [V_xa_2,V_x_2,V_r_2,T_a] : % 154.70/154.53 ( c_List_Olistrelp(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(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(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),hAPP(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) % 154.70/154.53 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_xa_2)),c_List_Olistrel(T_a,V_r_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel__Cons2,axiom, % 154.70/154.53 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel(T_a,V_r_2))) % 154.70/154.53 => ~ ! [B_x,B_xs] : % 154.70/154.53 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_y_2)),V_r_2)) % 154.70/154.53 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),B_xs),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrelp_Oequations_I2_J,axiom, % 154.70/154.53 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_a] : % 154.70/154.53 ( c_List_Olistrelp(T_a,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a4_2)) % 154.70/154.53 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) % 154.70/154.53 & c_List_Olistrelp(T_a,V_r_2,V_a3_2,V_a4_2) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrelp_OCons,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,T_a,V_y_2,V_x_2,V_r_2] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 154.70/154.53 => ( c_List_Olistrelp(T_a,V_r_2,V_xs_2,V_ys_2) % 154.70/154.53 => c_List_Olistrelp(T_a,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel__Cons1,axiom, % 154.70/154.53 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_a,V_r_2))) % 154.70/154.53 => ~ ! [B_y,B_ys] : % 154.70/154.53 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_ys) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),B_y)),V_r_2)) % 154.70/154.53 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_ys_2),B_ys)),c_List_Olistrel(T_a,V_r_2))) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel__subset,axiom, % 154.70/154.53 ! [V_A_2,V_r_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olists(T_a,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_List_Olist(T_a)),c_List_Olists(T_a,V_A_2))))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_lists__UNIV,axiom, % 154.70/154.53 ! [T_a] : c_List_Olists(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_lists__mono,axiom, % 154.70/154.53 ! [V_B_2,V_A_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),c_List_Olists(T_a,V_A_2)),c_List_Olists(T_a,V_B_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_equiv__listrel,axiom, % 154.70/154.53 ! [V_r_2,V_A_2,T_a] : % 154.70/154.53 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 154.70/154.53 => c_Equiv__Relations_Oequiv(tc_List_Olist(T_a),c_List_Olists(T_a,V_A_2),c_List_Olistrel(T_a,V_r_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel__refl__on,axiom, % 154.70/154.53 ! [V_r_2,V_A_2,T_a] : % 154.70/154.53 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 154.70/154.53 => c_Relation_Orefl__on(tc_List_Olist(T_a),c_List_Olists(T_a,V_A_2),c_List_Olistrel(T_a,V_r_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Cons__in__lists__iff,axiom, % 154.70/154.53 ! [V_A_2,V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_List_Olists(T_a,V_A_2))) % 154.70/154.53 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.53 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_lists__accI,axiom, % 154.70/154.53 ! [V_r_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,c_Wellfounded_Oacc(T_a,V_r_2)))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_lists__accD,axiom, % 154.70/154.53 ! [V_r_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,c_Wellfounded_Oacc(T_a,V_r_2)))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel__iff__nth,axiom, % 154.70/154.53 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) % 154.70/154.53 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) % 154.70/154.53 & ! [B_n] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_n))),V_r_2)) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_lexord__linear,axiom, % 154.70/154.53 ! [V_y_2,V_x_2,V_r_2,T_a] : % 154.70/154.53 ( ! [B_a,B_b] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_a),B_b)),V_r_2)) % 154.70/154.53 | B_a = B_b % 154.70/154.53 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_b),B_a)),V_r_2)) ) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) % 154.70/154.53 | V_x_2 = V_y_2 % 154.70/154.53 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_y_2),V_x_2)),c_List_Olexord(T_a,V_r_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_infinite__UNIV__listI,axiom, % 154.70/154.53 ! [T_a] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list__eq__iff__nth__eq,axiom, % 154.70/154.53 ! [T_a,V_ys_2,V_xs_2] : % 154.70/154.53 ( V_xs_2 = V_ys_2 % 154.70/154.53 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) % 154.70/154.53 & ! [B_i] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.53 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_i) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_nth__Cons__Suc,axiom, % 154.70/154.53 ! [V_n,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ). % 154.70/154.53 % 154.70/154.53 fof(fact_nth__Cons__0,axiom, % 154.70/154.53 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_x ). % 154.70/154.53 % 154.70/154.53 fof(fact_nth_Osimps,axiom, % 154.70/154.53 ! [V_n_2,V_xs_2,V_x_2,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_a,V_x_2,hAPP(c_List_Onth(T_a),V_xs_2),V_n_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_nth__Cons_H,axiom, % 154.70/154.53 ! [V_xs,V_x,T_a,V_n] : % 154.70/154.53 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.53 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x ) % 154.70/154.53 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.53 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_nth__Cons__number__of,axiom, % 154.70/154.53 ! [V_xs,V_x,T_a,V_v] : % 154.70/154.53 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.53 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = V_x ) % 154.70/154.53 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.53 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_lexord__take__index__conv,axiom, % 154.70/154.53 ! [V_r_2,V_y_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) % 154.70/154.53 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2))) % 154.70/154.53 & hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2)),V_y_2) = V_x_2 ) % 154.70/154.53 | ? [B_i] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2)))) % 154.70/154.53 & hAPP(hAPP(c_List_Otake(T_a),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_a),B_i),V_y_2) % 154.70/154.53 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_y_2),B_i))),V_r_2)) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__sublist,axiom, % 154.70/154.53 ! [V_I_2,V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_a),V_xs_2))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2))))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_finite__set,axiom, % 154.70/154.53 ! [V_xs_2,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__subset__Cons,axiom, % 154.70/154.53 ! [V_x_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_take__all,axiom, % 154.70/154.53 ! [V_n,V_xs,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) % 154.70/154.53 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__take__subset__set__take,axiom, % 154.70/154.53 ! [V_xs_2,T_a,V_n_2,V_m_2] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2)))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__take__subset,axiom, % 154.70/154.53 ! [V_xs_2,V_n_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__sublist__subset,axiom, % 154.70/154.53 ! [V_I_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_nth__take,axiom, % 154.70/154.53 ! [V_xs,T_a,V_n,V_i] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 154.70/154.53 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_take__Suc__Cons,axiom, % 154.70/154.53 ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__ConsD,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,V_y_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)))) % 154.70/154.53 => ( V_y_2 = V_x_2 % 154.70/154.53 | hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_in__set__sublistD,axiom, % 154.70/154.53 ! [V_I_2,V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2)))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_in__set__takeD,axiom, % 154.70/154.53 ! [V_xs_2,V_n_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2)))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_notin__set__sublistI,axiom, % 154.70/154.53 ! [V_I_2,V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.53 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2)))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_length__take,axiom, % 154.70/154.53 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n) ). % 154.70/154.53 % 154.70/154.53 fof(fact_take__take,axiom, % 154.70/154.53 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),V_m)),V_xs) ). % 154.70/154.53 % 154.70/154.53 fof(fact_sublist__upt__eq__take,axiom, % 154.70/154.53 ! [V_n_2,V_l_2,T_a] : c_List_Osublist(T_a,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_l_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_List_Oset_Osimps_I2_J,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_card__length,axiom, % 154.70/154.53 ! [V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_all__set__conv__all__nth,axiom, % 154.70/154.53 ! [V_P_2,V_xs_2,T_a] : % 154.70/154.53 ( ! [B_x] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.53 => hBOOL(hAPP(V_P_2,B_x)) ) % 154.70/154.53 <=> ! [B_i] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.53 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list__size__estimation,axiom, % 154.70/154.53 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_a,V_f_2,V_xs_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list__size__estimation_H,axiom, % 154.70/154.53 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_a,V_f_2,V_xs_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_in__lists__conv__set,axiom, % 154.70/154.53 ! [V_A_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) % 154.70/154.53 <=> ! [B_x] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_length__pos__if__in__set,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_nth__mem,axiom, % 154.70/154.53 ! [V_xs_2,T_a,V_n_2] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_in__set__conv__nth,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.53 <=> ? [B_i] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.53 & hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = V_x_2 ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_lists__eq__set,axiom, % 154.70/154.53 ! [V_A_2,T_a] : c_List_Olists(T_a,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__conv__nth,axiom, % 154.70/154.53 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_a),V_xs_2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_finite__lists__length__eq,axiom, % 154.70/154.53 ! [V_n_2,V_A_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.53 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_finite__lists__length__le,axiom, % 154.70/154.53 ! [V_n_2,V_A_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.53 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_WT__bodies__def,axiom, % 154.70/154.53 ( c_Com_OWT__bodies % 154.70/154.53 <=> ! [B_x] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),B_x),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),B_x)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel__iff__zip,axiom, % 154.70/154.53 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) % 154.70/154.53 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) % 154.70/154.53 & ! [B_x] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_ys_2)))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),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(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(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),hAPP(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)),B_x)) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_take__zip,axiom, % 154.70/154.53 ! [V_ys,V_xs,V_n,T_b,T_a] : hAPP(hAPP(c_List_Otake(tc_prod(T_a,T_b)),V_n),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_b),V_n),V_ys)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_length__zip,axiom, % 154.70/154.53 ! [V_ys,V_xs,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(T_a,T_b))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_zip__Cons__Cons,axiom, % 154.70/154.53 ! [V_ys,V_y,V_xs,V_x,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list__eq__iff__zip__eq,axiom, % 154.70/154.53 ! [T_a,V_ys_2,V_xs_2] : % 154.70/154.53 ( V_xs_2 = V_ys_2 % 154.70/154.53 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) % 154.70/154.53 & ! [B_x] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_ys_2)))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_zip__same,axiom, % 154.70/154.53 ! [V_xs_2,V_b_2,V_a_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_xs_2)))) % 154.70/154.53 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.53 & V_a_2 = V_b_2 ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__zip__leftD,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 154.70/154.53 ( 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)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__zip__rightD,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 154.70/154.53 ( 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)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_in__set__zipE,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 154.70/154.53 ( 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)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) % 154.70/154.53 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.53 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_nth__zip,axiom, % 154.70/154.53 ! [V_ys,T_b,V_xs,T_a,V_i] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys))) % 154.70/154.53 => hAPP(hAPP(c_List_Onth(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_b),V_ys),V_i)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__zip,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_a,T_b)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_a,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_a,T_b)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(T_a,T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(T_a,T_b),tc_fun(tc_Nat_Onat,tc_prod(T_a,T_b)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_a,T_b)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_a,T_b)),c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),tc_Nat_Onat),c_Product__Type_OPair(T_a,T_b)),hAPP(c_List_Onth(T_a),V_xs_2))),hAPP(c_List_Onth(T_b),V_ys_2)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)))))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_greaterThanLessThan__upto,axiom, % 154.70/154.53 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listsum__setsum__nth,axiom, % 154.70/154.53 ! [V_xs_2,T_a] : % 154.70/154.53 ( class_Groups_Ocomm__monoid__add(T_a) % 154.70/154.53 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(c_List_Onth(T_a),V_xs_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listsum__eq__0__nat__iff__nat,axiom, % 154.70/154.53 ! [V_ns_2] : % 154.70/154.53 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.53 <=> ! [B_x] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 154.70/154.53 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__upto,axiom, % 154.70/154.53 ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_atLeastAtMost__upto,axiom, % 154.70/154.53 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_elem__le__listsum__nat,axiom, % 154.70/154.53 ! [V_ns,V_k] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listsum__simps_I2_J,axiom, % 154.70/154.53 ! [V_xs,V_x,T_a] : % 154.70/154.53 ( class_Groups_Omonoid__add(T_a) % 154.70/154.53 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_atLeastLessThan__upto,axiom, % 154.70/154.53 ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_greaterThanAtMost__upto,axiom, % 154.70/154.53 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_nat__list__def,axiom, % 154.70/154.53 ! [V_l_2] : % 154.70/154.53 ( c_List_Onat__list(V_l_2) % 154.70/154.53 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list__size__pointwise,axiom, % 154.70/154.53 ! [V_g_2,V_f_2,V_xs_2,T_a] : % 154.70/154.53 ( ! [B_x] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(T_a,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_a,V_g_2,V_xs_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listsum__update__nat,axiom, % 154.70/154.53 ! [V_n,V_ns,V_k] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns))) % 154.70/154.53 => hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,V_ns),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns)),V_n)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_butlast__take,axiom, % 154.70/154.53 ! [V_xs,T_a,V_n] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.53 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list__update__beyond,axiom, % 154.70/154.53 ! [V_x,V_i,V_xs,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)) % 154.70/154.53 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list__update__id,axiom, % 154.70/154.53 ! [V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)) = V_xs ). % 154.70/154.53 % 154.70/154.53 fof(fact_nth__list__update__neq,axiom, % 154.70/154.53 ! [V_x,V_xs,T_a,V_j,V_i] : % 154.70/154.53 ( V_i != V_j % 154.70/154.53 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_butlast__list__update,axiom, % 154.70/154.53 ! [V_x,V_xs,T_a,V_k] : % 154.70/154.53 ( ( V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) % 154.70/154.53 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Obutlast(T_a,V_xs) ) % 154.70/154.53 & ( V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) % 154.70/154.53 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = hAPP(hAPP(c_List_Olist__update(T_a,c_List_Obutlast(T_a,V_xs)),V_k),V_x) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_length__list__update,axiom, % 154.70/154.53 ! [V_x,V_i,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ). % 154.70/154.53 % 154.70/154.53 fof(fact_zip__update,axiom, % 154.70/154.53 ! [V_y,V_ys,V_x,V_i,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),V_y)) = hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_update__zip,axiom, % 154.70/154.53 ! [V_xy,V_i,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),V_xy) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(c_Product__Type_Ofst(T_a,T_b),V_xy))),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),hAPP(c_Product__Type_Osnd(T_a,T_b),V_xy))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list__update__swap,axiom, % 154.70/154.53 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] : % 154.70/154.53 ( V_i != V_i_H % 154.70/154.53 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i_H),V_x_H) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i_H),V_x_H)),V_i),V_x) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list__update__overwrite,axiom, % 154.70/154.53 ! [V_y,V_x,V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i),V_y) = hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list__update__code_I3_J,axiom, % 154.70/154.53 ! [V_y,V_i,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_i)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list__update_Osimps_I2_J,axiom, % 154.70/154.53 ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_a),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_a,tc_List_Olist(T_a)),c_List_Olist__update(T_a,V_xs_2)),V_v_2)),V_i_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list__update__code_I2_J,axiom, % 154.70/154.53 ! [V_y,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs) ). % 154.70/154.53 % 154.70/154.53 fof(fact_in__set__butlastD,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__update__subsetI,axiom, % 154.70/154.53 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),V_A_2)) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2))),V_A_2)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__update__subset__insert,axiom, % 154.70/154.53 ! [V_x_2,V_i_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_nth__list__update__eq,axiom, % 154.70/154.53 ! [V_x,V_xs,T_a,V_i] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.53 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i) = V_x ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list__update__same__conv,axiom, % 154.70/154.53 ! [V_x_2,V_xs_2,T_a,V_i_2] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.53 => ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2) = V_xs_2 % 154.70/154.53 <=> hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = V_x_2 ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_nth__list__update,axiom, % 154.70/154.53 ! [V_x,V_j,V_xs,T_a,V_i] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.53 => ( ( V_i = V_j % 154.70/154.53 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = V_x ) % 154.70/154.53 & ( V_i != V_j % 154.70/154.53 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_take__butlast,axiom, % 154.70/154.53 ! [V_xs,T_a,V_n] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.53 => hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_length__butlast,axiom, % 154.70/154.53 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__update__memI,axiom, % 154.70/154.53 ! [V_x_2,V_xs_2,T_a,V_n_2] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_n_2),V_x_2)))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_butlast__conv__take,axiom, % 154.70/154.53 ! [V_xs,T_a] : c_List_Obutlast(T_a,V_xs) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel1__iff__update,axiom, % 154.70/154.53 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 154.70/154.53 <=> ? [B_y,B_n] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n)),B_y)),V_r_2)) % 154.70/154.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.53 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),B_n),B_y) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_distinct__list__update,axiom, % 154.70/154.53 ! [V_i_2,V_a_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 154.70/154.53 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 154.70/154.53 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_a_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_distinct__upto,axiom, % 154.70/154.53 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_distinct__take,axiom, % 154.70/154.53 ! [V_i,V_xs,T_a] : % 154.70/154.53 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 154.70/154.53 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_distinct__sublistI,axiom, % 154.70/154.53 ! [V_I_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 154.70/154.53 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_distinct__zipI2,axiom, % 154.70/154.53 ! [V_xs,T_b,V_ys,T_a] : % 154.70/154.53 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys)) % 154.70/154.53 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_distinct__zipI1,axiom, % 154.70/154.53 ! [V_ys,T_b,V_xs,T_a] : % 154.70/154.53 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 154.70/154.53 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_distinct_Osimps_I2_J,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) % 154.70/154.53 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.53 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_card__distinct,axiom, % 154.70/154.53 ! [V_xs_2,T_a] : % 154.70/154.53 ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) % 154.70/154.53 => hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_distinct__card,axiom, % 154.70/154.53 ! [V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 154.70/154.53 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_nth__eq__iff__index__eq,axiom, % 154.70/154.53 ! [V_j_2,V_i_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.53 => ( hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_j_2) % 154.70/154.53 <=> V_i_2 = V_j_2 ) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_distinct__conv__nth,axiom, % 154.70/154.53 ! [V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 154.70/154.53 <=> ! [B_i] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.53 => ! [B_j] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.53 => ( B_i != B_j % 154.70/154.53 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j) ) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_distinct__listsum__conv__Setsum,axiom, % 154.70/154.53 ! [V_xs_2,T_a] : % 154.70/154.53 ( class_Groups_Ocomm__monoid__add(T_a) % 154.70/154.53 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 154.70/154.53 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_a),c_COMBI(T_a)),hAPP(c_List_Oset(T_a),V_xs_2)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Nitpick_Ocard_H__def,axiom, % 154.70/154.53 ! [V_A_2,T_a] : % 154.70/154.53 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.53 => c_Nitpick_Ocard_H(T_a,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Hilbert__Choice_OEps(tc_List_Olist(T_a),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_List_Oset(T_a))),V_A_2))),c_List_Odistinct(T_a)))) ) % 154.70/154.53 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.53 => c_Nitpick_Ocard_H(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_dom__map__upds,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)),V_xs_2))),c_Map_Odom(T_a,T_b,V_m_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__upds__apply__nontin,axiom, % 154.70/154.53 ! [V_ys_2,V_f_2,T_b,V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.53 => hAPP(c_Map_Omap__upds(T_a,T_b,V_f_2,V_xs_2,V_ys_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__upds__list__update2__drop,axiom, % 154.70/154.53 ! [V_y_2,V_m_2,V_ys_2,T_b,V_i_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_i_2)) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))) % 154.70/154.53 => c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,hAPP(hAPP(c_List_Olist__update(T_b,V_ys_2),V_i_2),V_y_2)) = c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_nth__take__lemma,axiom, % 154.70/154.53 ! [V_ys,V_xs,T_a,V_k] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys))) % 154.70/154.53 => ( ! [B_i] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k)) % 154.70/154.53 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) ) % 154.70/154.53 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_restrict__map__upds,axiom, % 154.70/154.53 ! [V_m_2,V_D_2,V_ys_2,T_b,V_xs_2,T_a] : % 154.70/154.53 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),V_D_2)) % 154.70/154.53 => c_Map_Orestrict__map(T_a,T_b,c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2),V_D_2) = c_Map_Omap__upds(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(c_List_Oset(T_a),V_xs_2))),V_xs_2,V_ys_2) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_restrict__map__insert,axiom, % 154.70/154.53 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_f_2,V_A_2)),V_a_2),hAPP(V_f_2,V_a_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_restrict__restrict,axiom, % 154.70/154.53 ! [V_B_2,V_A_2,V_m_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_B_2) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_restrict__in,axiom, % 154.70/154.53 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.53 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_dom__restrict,axiom, % 154.70/154.53 ! [V_A_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_m_2)),V_A_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_fun__upd__restrict,axiom, % 154.70/154.53 ! [V_y_2,V_x_2,V_D_2,V_m_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_fun__upd__restrict__conv,axiom, % 154.70/154.53 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 154.70/154.53 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_restrict__fun__upd,axiom, % 154.70/154.53 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] : % 154.70/154.53 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 154.70/154.53 => c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),V_y_2),V_D_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ) % 154.70/154.53 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 154.70/154.53 => c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),V_y_2),V_D_2) = c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__remove1__eq,axiom, % 154.70/154.53 ! [V_x_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 154.70/154.53 => hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_take__Cons__number__of,axiom, % 154.70/154.53 ! [V_xs,V_x,T_a,V_v] : % 154.70/154.53 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.53 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 154.70/154.53 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.53 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_lists_ONil,axiom, % 154.70/154.53 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olists(T_a,V_A_2))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel__Nil2,axiom, % 154.70/154.53 ! [V_r_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olistrel(T_a,V_r_2))) % 154.70/154.53 => V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel__Nil1,axiom, % 154.70/154.53 ! [V_r_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xs_2)),c_List_Olistrel(T_a,V_r_2))) % 154.70/154.53 => V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list__update__code_I1_J,axiom, % 154.70/154.53 ! [V_y,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_y) = c_List_Olist_ONil(T_a) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list__update_Osimps_I1_J,axiom, % 154.70/154.53 ! [V_v,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_v) = c_List_Olist_ONil(T_a) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list__update__nonempty,axiom, % 154.70/154.53 ! [V_x_2,V_k_2,V_xs_2,T_a] : % 154.70/154.53 ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_a) % 154.70/154.53 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_List_Oset_Osimps_I1_J,axiom, % 154.70/154.53 ! [T_a] : hAPP(c_List_Oset(T_a),c_List_Olist_ONil(T_a)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__empty2,axiom, % 154.70/154.53 ! [V_xs_2,T_a] : % 154.70/154.53 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),V_xs_2) % 154.70/154.53 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__empty,axiom, % 154.70/154.53 ! [V_xs_2,T_a] : % 154.70/154.53 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.53 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_length__0__conv,axiom, % 154.70/154.53 ! [V_xs_2,T_a] : % 154.70/154.53 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.53 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list_Osize_I3_J,axiom, % 154.70/154.53 ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listsum__simps_I1_J,axiom, % 154.70/154.53 ! [T_a] : % 154.70/154.53 ( class_Groups_Omonoid__add(T_a) % 154.70/154.53 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_zip__Nil,axiom, % 154.70/154.53 ! [V_ys,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Olist_ONil(T_a)),V_ys) = c_List_Olist_ONil(tc_prod(T_a,T_b)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_zip_Osimps_I1_J,axiom, % 154.70/154.53 ! [V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(tc_prod(T_a,T_b)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrelp_Oequations_I1_J,axiom, % 154.70/154.53 ! [V_r_2,T_a] : c_List_Olistrelp(T_a,V_r_2,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrelp_ONil,axiom, % 154.70/154.53 ! [V_r_2,T_a] : c_List_Olistrelp(T_a,V_r_2,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list_Osize_I1_J,axiom, % 154.70/154.53 ! [V_fa_2,T_a] : c_List_Olist_Olist__size(T_a,V_fa_2,c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.70/154.53 % 154.70/154.53 fof(fact_remove1__commute,axiom, % 154.70/154.53 ! [V_zs,V_y,V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Oremove1(T_a,V_y,V_zs)) = c_List_Oremove1(T_a,V_y,c_List_Oremove1(T_a,V_x,V_zs)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_remove1_Osimps_I1_J,axiom, % 154.70/154.53 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 154.70/154.53 % 154.70/154.53 fof(fact_sublist__nil,axiom, % 154.70/154.53 ! [V_A_2,T_a] : c_List_Osublist(T_a,c_List_Olist_ONil(T_a),V_A_2) = c_List_Olist_ONil(T_a) ). % 154.70/154.53 % 154.70/154.53 fof(fact_take__eq__Nil,axiom, % 154.70/154.53 ! [V_xs_2,V_n_2,T_a] : % 154.70/154.53 ( hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 154.70/154.53 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.53 | V_xs_2 = c_List_Olist_ONil(T_a) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_take__0,axiom, % 154.70/154.53 ! [V_xs,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = c_List_Olist_ONil(T_a) ). % 154.70/154.53 % 154.70/154.53 fof(fact_take__Nil,axiom, % 154.70/154.53 ! [V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 154.70/154.53 % 154.70/154.53 fof(fact_upto__empty,axiom, % 154.70/154.53 ! [V_i,V_j] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i)) % 154.70/154.53 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list_Osimps_I2_J,axiom, % 154.70/154.53 ! [V_list_H,V_a_H,T_a] : c_List_Olist_ONil(T_a) != hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list_Osimps_I3_J,axiom, % 154.70/154.53 ! [V_list_H,V_a_H,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H) != c_List_Olist_ONil(T_a) ). % 154.70/154.53 % 154.70/154.53 fof(fact_remove1_Osimps_I2_J,axiom, % 154.70/154.53 ! [V_xs,T_a,V_y,V_x] : % 154.70/154.53 ( ( V_x = V_y % 154.70/154.53 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) % 154.70/154.53 & ( V_x != V_y % 154.70/154.53 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Oremove1(T_a,V_x,V_xs)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_butlast_Osimps_I2_J,axiom, % 154.70/154.53 ! [V_x,T_a,V_xs] : % 154.70/154.53 ( ( V_xs = c_List_Olist_ONil(T_a) % 154.70/154.53 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 154.70/154.53 & ( V_xs != c_List_Olist_ONil(T_a) % 154.70/154.53 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Obutlast(T_a,V_xs)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_butlast_Osimps_I1_J,axiom, % 154.70/154.53 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 154.70/154.53 % 154.70/154.53 fof(fact_in__set__remove1,axiom, % 154.70/154.53 ! [V_xs_2,T_a,V_b_2,V_a_2] : % 154.70/154.53 ( V_a_2 != V_b_2 % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_b_2,V_xs_2)))) % 154.70/154.53 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_notin__set__remove1,axiom, % 154.70/154.53 ! [V_y_2,V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.53 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_y_2,V_xs_2)))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_remove1__idem,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.53 => c_List_Oremove1(T_a,V_x_2,V_xs_2) = V_xs_2 ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__upds__Nil1,axiom, % 154.70/154.53 ! [V_bs_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,c_List_Olist_ONil(T_a),V_bs_2) = V_m_2 ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__upds__Nil2,axiom, % 154.70/154.53 ! [V_as_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_as_2,c_List_Olist_ONil(T_b)) = V_m_2 ). % 154.70/154.53 % 154.70/154.53 fof(fact_distinct__remove1,axiom, % 154.70/154.53 ! [V_x,V_xs,T_a] : % 154.70/154.53 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 154.70/154.53 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_distinct_Osimps_I1_J,axiom, % 154.70/154.53 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_distinct__butlast,axiom, % 154.70/154.53 ! [T_a,V_xs] : % 154.70/154.53 ( V_xs != c_List_Olist_ONil(T_a) % 154.70/154.53 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 154.70/154.53 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_sublist__empty,axiom, % 154.70/154.53 ! [V_xs_2,T_a] : c_List_Osublist(T_a,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_a) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__remove1__subset,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_length__greater__0__conv,axiom, % 154.70/154.53 ! [V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.53 <=> V_xs_2 != c_List_Olist_ONil(T_a) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_take__1__Cons,axiom, % 154.70/154.53 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_not__listrel1__Nil,axiom, % 154.70/154.53 ! [V_r_2,V_xs_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olistrel1(T_a,V_r_2))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_not__Nil__listrel1,axiom, % 154.70/154.53 ! [V_r_2,V_xs_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xs_2)),c_List_Olistrel1(T_a,V_r_2))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel_ONil,axiom, % 154.70/154.53 ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(T_a))),c_List_Olistrel(T_a,V_r_2))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_lexord__Nil__right,axiom, % 154.70/154.53 ! [V_r_2,V_x_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),c_List_Olist_ONil(T_a))),c_List_Olexord(T_a,V_r_2))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Nil2__notin__lex,axiom, % 154.70/154.53 ! [V_r_2,V_xs_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olex(T_a,V_r_2))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Nil__notin__lex,axiom, % 154.70/154.53 ! [V_r_2,V_ys_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_ys_2)),c_List_Olex(T_a,V_r_2))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_take__Cons,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,V_n_2,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_a),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Otake(T_a)),V_xs_2)),V_n_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_upto_Osimps,axiom, % 154.70/154.53 ! [V_j,V_i] : % 154.70/154.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 154.70/154.53 => c_List_Oupto(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j)) ) % 154.70/154.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 154.70/154.53 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_sublist__singleton,axiom, % 154.70/154.53 ! [V_x_2,T_a,V_A_2] : % 154.70/154.53 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 154.70/154.53 => c_List_Osublist(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) % 154.70/154.53 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 154.70/154.53 => c_List_Osublist(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)),V_A_2) = c_List_Olist_ONil(T_a) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_lists__empty,axiom, % 154.70/154.53 ! [T_a] : c_List_Olists(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_take__Cons_H,axiom, % 154.70/154.53 ! [V_xs,V_x,T_a,V_n] : % 154.70/154.53 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.53 => hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 154.70/154.53 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.53 => hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_upto__rec__number__of,axiom, % 154.70/154.53 ! [V_n,V_m] : % 154.70/154.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) % 154.70/154.53 => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) ) % 154.70/154.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) % 154.70/154.53 => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = c_List_Olist_ONil(tc_Int_Oint) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel__Nil,axiom, % 154.70/154.53 ! [V_r_2,T_a] : hAPP(c_Relation_OImage(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__Cons__sing__Nil,axiom, % 154.70/154.53 ! [V_A_2,T_a] : c_List_Oset__Cons(T_a,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_a,tc_List_Olist(T_a),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))),V_A_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_length__remove1,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.53 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) % 154.70/154.53 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.53 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_upto_Opsimps,axiom, % 154.70/154.53 ! [V_j_2,V_i_2] : % 154.70/154.53 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_i_2),V_j_2))) % 154.70/154.53 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 154.70/154.53 => c_List_Oupto(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i_2),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ) % 154.70/154.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 154.70/154.53 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_select,axiom, % 154.70/154.53 ! [V_s_2,T_a,V_xs_2] : % 154.70/154.53 ( V_xs_2 != c_List_Olist_ONil(T_a) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Product__Type_Ofst(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_a,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listset_Osimps_I1_J,axiom, % 154.70/154.53 ! [T_a] : c_List_Olistset(T_a,c_List_Olist_ONil(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_zip__Cons,axiom, % 154.70/154.53 ! [V_ys_2,V_y_2,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_a,T_b)),T_a,c_List_Olist_ONil(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b)))),T_a),c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),T_a),c_List_Olist_OCons(tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b))),c_List_Ozip(T_a,T_b)),V_ys_2))),V_xs_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list_Osimps_I5_J,axiom, % 154.70/154.53 ! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_List_Olist_Olist__case(T_a,T_b,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_list_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list_Osimps_I4_J,axiom, % 154.70/154.53 ! [V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_List_Olist_Olist__case(T_a,T_b,V_f1_2,V_f2_2),c_List_Olist_ONil(T_b)) = V_f1_2 ). % 154.70/154.53 % 154.70/154.53 fof(fact_listset_Osimps_I2_J,axiom, % 154.70/154.53 ! [V_As_2,V_A_2,T_a] : c_List_Olistset(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_a,V_A_2,c_List_Olistset(T_a,V_As_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_zip__Cons1,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,V_x_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_a,T_b)),T_b,c_List_Olist_ONil(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b)))),T_b),c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),T_b),c_List_Olist_OCons(tc_prod(T_a,T_b))),hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2)))),hAPP(c_List_Ozip(T_a,T_b),V_xs_2))),V_ys_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_sorted__list__of__set__remove,axiom, % 154.70/154.53 ! [V_x_2,V_A_2,T_a] : % 154.70/154.53 ( class_Orderings_Olinorder(T_a) % 154.70/154.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.53 => c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = c_List_Oremove1(T_a,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_upto_Opinduct,axiom, % 154.70/154.53 ! [V_P_2,V_a1_2,V_a0_2] : % 154.70/154.53 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) % 154.70/154.53 => ( ! [B_i,B_j] : % 154.70/154.53 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_i),B_j))) % 154.70/154.53 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) % 154.70/154.53 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j)) ) % 154.70/154.53 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) % 154.70/154.53 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_sorted__list__of__set__empty,axiom, % 154.70/154.53 ! [T_a] : % 154.70/154.53 ( class_Orderings_Olinorder(T_a) % 154.70/154.53 => c_List_Olinorder__class_Osorted__list__of__set(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_List_Olist_ONil(T_a) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_anamorph_Osimps,axiom, % 154.70/154.53 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] : % 154.70/154.53 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 154.70/154.53 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,V_f_2),V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),T_b),c_List_Olist_ONil(T_a)),V_x_2) ) % 154.70/154.53 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 154.70/154.53 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,V_f_2),V_k_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),T_b),c_List_Olist_ONil(T_a)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(tc_List_Olist(T_a),T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),T_a),c_COMBB(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),tc_fun(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b)),T_a),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),T_b,tc_prod(tc_List_Olist(T_a),T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),T_a),hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_List_Olist(T_a),T_b))),c_List_Olist_OCons(T_a))))),hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(V_f_2,V_x_2)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_sublist__Cons,axiom, % 154.70/154.53 ! [V_A_2,V_l_2,V_x_2,T_a] : c_List_Osublist(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_a)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))),c_List_Olist_ONil(T_a))),c_List_Osublist(T_a,V_l_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_A_2)))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_append__eq__Cons__conv,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_a] : % 154.70/154.53 ( hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) % 154.70/154.53 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a) % 154.70/154.53 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) % 154.70/154.53 | ? [B_ys_H] : % 154.70/154.53 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) % 154.70/154.53 & hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Cons__eq__append__conv,axiom, % 154.70/154.53 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2) % 154.70/154.53 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a) % 154.70/154.53 & hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = V_zs_2 ) % 154.70/154.53 | ? [B_ys_H] : % 154.70/154.53 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) = V_ys_2 % 154.70/154.53 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_append1__eq__conv,axiom, % 154.70/154.53 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] : % 154.70/154.53 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))) % 154.70/154.53 <=> ( V_xs_2 = V_ys_2 % 154.70/154.53 & V_x_2 = V_y_2 ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_append__Cons,axiom, % 154.70/154.53 ! [V_ys,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_ys) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Cons__eq__appendI,axiom, % 154.70/154.53 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] : % 154.70/154.53 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys % 154.70/154.53 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs) % 154.70/154.53 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__append,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_zip__append,axiom, % 154.70/154.53 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] : % 154.70/154.53 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_us) % 154.70/154.53 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_vs) % 154.70/154.53 => hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_List_Oappend(T_b),V_us),V_vs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_us)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),V_vs)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_length__append,axiom, % 154.70/154.53 ! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listsum__append,axiom, % 154.70/154.53 ! [V_ys,V_xs,T_a] : % 154.70/154.53 ( class_Groups_Omonoid__add(T_a) % 154.70/154.53 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_ys)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_append__eq__appendI,axiom, % 154.70/154.53 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] : % 154.70/154.53 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs % 154.70/154.53 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us) % 154.70/154.53 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_append__same__eq,axiom, % 154.70/154.53 ! [V_zs_2,V_xs_2,V_ys_2,T_a] : % 154.70/154.53 ( hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_xs_2) % 154.70/154.53 <=> V_ys_2 = V_zs_2 ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_same__append__eq,axiom, % 154.70/154.53 ! [V_zs_2,V_ys_2,V_xs_2,T_a] : % 154.70/154.53 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_zs_2) % 154.70/154.53 <=> V_ys_2 = V_zs_2 ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_append__eq__append__conv2,axiom, % 154.70/154.53 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a] : % 154.70/154.53 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_ts_2) % 154.70/154.53 <=> ? [B_us] : % 154.70/154.53 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),B_us) % 154.70/154.53 & hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ys_2) = V_ts_2 ) % 154.70/154.53 | ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),B_us) = V_zs_2 % 154.70/154.53 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ts_2) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_append__assoc,axiom, % 154.70/154.53 ! [V_zs,V_ys,V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_append__in__lists__conv,axiom, % 154.70/154.53 ! [V_A_2,V_ys_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)),c_List_Olists(T_a,V_A_2))) % 154.70/154.53 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) % 154.70/154.53 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),c_List_Olists(T_a,V_A_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_fun__upds__append2__drop,axiom, % 154.70/154.53 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 154.70/154.53 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 154.70/154.53 => c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2)) = c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_fun__upds__append__drop,axiom, % 154.70/154.53 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 154.70/154.53 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 154.70/154.53 => c_Map_Omap__upds(T_a,T_b,V_m_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_zs_2),V_ys_2) = c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_butlast__append,axiom, % 154.70/154.53 ! [V_xs,T_a,V_ys] : % 154.70/154.53 ( ( V_ys = c_List_Olist_ONil(T_a) % 154.70/154.53 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) % 154.70/154.53 & ( V_ys != c_List_Olist_ONil(T_a) % 154.70/154.53 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Obutlast(T_a,V_ys)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_append__Nil,axiom, % 154.70/154.53 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ). % 154.70/154.53 % 154.70/154.53 fof(fact_Nil__is__append__conv,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,T_a] : % 154.70/154.53 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 154.70/154.53 <=> ( V_xs_2 = c_List_Olist_ONil(T_a) % 154.70/154.53 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_append__Nil2,axiom, % 154.70/154.53 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ). % 154.70/154.53 % 154.70/154.53 fof(fact_self__append__conv,axiom, % 154.70/154.53 ! [V_ys_2,T_a,V_xs_2] : % 154.70/154.53 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 154.70/154.53 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_self__append__conv2,axiom, % 154.70/154.53 ! [V_xs_2,T_a,V_ys_2] : % 154.70/154.53 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 154.70/154.53 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_append__is__Nil__conv,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,T_a] : % 154.70/154.53 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_a) % 154.70/154.53 <=> ( V_xs_2 = c_List_Olist_ONil(T_a) % 154.70/154.53 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_append__self__conv,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,T_a] : % 154.70/154.53 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_xs_2 % 154.70/154.53 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_append__self__conv2,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,T_a] : % 154.70/154.53 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_ys_2 % 154.70/154.53 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_eq__Nil__appendI,axiom, % 154.70/154.53 ! [T_a,V_ys,V_xs] : % 154.70/154.53 ( V_xs = V_ys % 154.70/154.53 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_nth__append__length,axiom, % 154.70/154.53 ! [V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = V_x ). % 154.70/154.53 % 154.70/154.53 fof(fact_nth__append__length__plus,axiom, % 154.70/154.53 ! [V_n,V_ys,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_ys),V_n) ). % 154.70/154.53 % 154.70/154.53 fof(fact_take__append,axiom, % 154.70/154.53 ! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list__update__append1,axiom, % 154.70/154.53 ! [V_x,V_ys,V_xs,T_a,V_i] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.53 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_i),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_ys) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list__update__length,axiom, % 154.70/154.53 ! [V_y,V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_y) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_remove1__append,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.53 => c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2)),V_ys_2) ) % 154.70/154.53 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.53 => c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_Oremove1(T_a,V_x_2,V_ys_2)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_in__set__butlast__appendI,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) % 154.70/154.53 | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_ys_2)))) ) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_butlast__snoc,axiom, % 154.70/154.53 ! [V_x,V_xs,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_xs ). % 154.70/154.53 % 154.70/154.53 fof(fact_append__listrel1I,axiom, % 154.70/154.53 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 154.70/154.53 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 154.70/154.53 & V_us_2 = V_vs_2 ) % 154.70/154.53 | ( V_xs_2 = V_ys_2 % 154.70/154.53 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_us_2),V_vs_2)),c_List_Olistrel1(T_a,V_r_2))) ) ) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_vs_2))),c_List_Olistrel1(T_a,V_r_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_lexord__append__leftI,axiom, % 154.70/154.53 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_u_2),V_v_2)),c_List_Olexord(T_a,V_r_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_v_2))),c_List_Olexord(T_a,V_r_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_distinct__append,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) % 154.70/154.53 <=> ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 154.70/154.53 & hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2)) % 154.70/154.53 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_nth__append,axiom, % 154.70/154.53 ! [V_ys,V_xs,T_a,V_n] : % 154.70/154.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.53 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ) % 154.70/154.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.53 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list__update__append,axiom, % 154.70/154.53 ! [V_x,V_ys,V_xs,T_a,V_n] : % 154.70/154.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.53 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_n),V_x)),V_ys) ) % 154.70/154.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.53 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist__update(T_a,V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_x)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_sublist__append,axiom, % 154.70/154.53 ! [V_A_2,V_l_H_2,V_l_2,T_a] : c_List_Osublist(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Osublist(T_a,V_l_2,V_A_2)),c_List_Osublist(T_a,V_l_H_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_l_2)))),V_A_2)))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel1I,axiom, % 154.70/154.53 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 154.70/154.53 => ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_vs_2)) % 154.70/154.53 => ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_vs_2)) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_lexord__append__left__rightI,axiom, % 154.70/154.53 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_a),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_b_2),V_y_2)))),c_List_Olexord(T_a,V_r_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_take__Suc__conv__app__nth,axiom, % 154.70/154.53 ! [V_xs,T_a,V_i] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.53 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),c_List_Olist_ONil(T_a))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_snoc__listrel1__snoc__iff,axiom, % 154.70/154.53 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)))),hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))))),c_List_Olistrel1(T_a,V_r_2))) % 154.70/154.53 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 154.70/154.53 & V_x_2 = V_y_2 ) % 154.70/154.53 | ( V_xs_2 = V_ys_2 % 154.70/154.53 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listrel1E,axiom, % 154.70/154.53 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 154.70/154.53 => ~ ! [B_x,B_y] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2)) % 154.70/154.53 => ! [B_us,B_vs] : % 154.70/154.53 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_vs)) % 154.70/154.53 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_vs)) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_lexord__append__leftD,axiom, % 154.70/154.53 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_v_2))),c_List_Olexord(T_a,V_r_2))) % 154.70/154.53 => ( ! [B_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_a),B_a)),V_r_2)) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_u_2),V_v_2)),c_List_Olexord(T_a,V_r_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rotate1__def,axiom, % 154.70/154.53 ! [V_xs_2,T_a] : hAPP(c_List_Orotate1(T_a),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Oappend(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a)))),V_xs_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__upds__append1,axiom, % 154.70/154.53 ! [V_x_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))) % 154.70/154.53 => c_Map_Omap__upds(T_a,T_b,V_m_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))),V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_image__map__upd,axiom, % 154.70/154.53 ! [V_y_2,V_m_2,T_b,V_A_2,V_x_2,T_a] : % 154.70/154.53 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.53 => hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))),V_A_2) = hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_b),V_m_2),V_A_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__rotate1,axiom, % 154.70/154.53 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_length__rotate1,axiom, % 154.70/154.53 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate1(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ). % 154.70/154.53 % 154.70/154.53 fof(fact_dom__const,axiom, % 154.70/154.53 ! [V_f_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_a),c_Option_Ooption_OSome(T_b)),V_f_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_domI,axiom, % 154.70/154.53 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] : % 154.70/154.53 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_a,V_m_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_insert__dom,axiom, % 154.70/154.53 ! [T_b,V_y_2,T_a,V_x_2,V_f_2] : % 154.70/154.53 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 154.70/154.53 => hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Map_Odom(T_b,T_a,V_f_2)) = c_Map_Odom(T_b,T_a,V_f_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_distinct1__rotate,axiom, % 154.70/154.53 ! [V_xs_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2))) % 154.70/154.53 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__upd__eqD1,axiom, % 154.70/154.53 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_b,T_a] : % 154.70/154.53 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_n_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) % 154.70/154.53 => V_x_2 = V_y_2 ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__upd__triv,axiom, % 154.70/154.53 ! [T_b,V_x_2,T_a,V_k_2,V_t_2] : % 154.70/154.53 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 154.70/154.53 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_a),V_x_2)) = V_t_2 ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__upd__Some__unfold,axiom, % 154.70/154.53 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_a,T_b] : % 154.70/154.53 ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 154.70/154.53 <=> ( ( V_x_2 = V_a_2 % 154.70/154.53 & V_b_2 = V_y_2 ) % 154.70/154.53 | ( V_x_2 != V_a_2 % 154.70/154.53 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rotate1__is__Nil__conv,axiom, % 154.70/154.53 ! [V_xs_2,T_a] : % 154.70/154.53 ( hAPP(c_List_Orotate1(T_a),V_xs_2) = c_List_Olist_ONil(T_a) % 154.70/154.53 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__upds__Cons,axiom, % 154.70/154.53 ! [V_bs_2,V_b_2,V_as_2,V_a_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_as_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_bs_2)) = c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_as_2,V_bs_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_WT_Oequations_I7_J,axiom, % 154.70/154.53 ! [V_a_2] : % 154.70/154.53 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2))) % 154.70/154.53 <=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_finite__range__updI,axiom, % 154.70/154.53 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] : % 154.70/154.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) % 154.70/154.53 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_WT__bodiesD,axiom, % 154.70/154.53 ! [V_b,V_pn] : % 154.70/154.53 ( c_Com_OWT__bodies % 154.70/154.53 => ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) % 154.70/154.53 => hBOOL(hAPP(c_Com_OWT,V_b)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__upds__twist,axiom, % 154.70/154.53 ! [V_bs_2,V_b_2,V_m_2,T_b,V_as_2,V_a_2,T_a] : % 154.70/154.53 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_as_2))) % 154.70/154.53 => c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_as_2,V_bs_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__upds(T_a,T_b,V_m_2,V_as_2,V_bs_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_restrict__upd__same,axiom, % 154.70/154.53 ! [V_y_2,V_x_2,V_m_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rotate__simps,axiom, % 154.70/154.53 ! [V_xs,V_x,T_b,T_a] : % 154.70/154.53 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) % 154.70/154.53 & hAPP(c_List_Orotate1(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),c_List_Olist_ONil(T_b))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rotate1__length01,axiom, % 154.70/154.53 ! [V_xs,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) % 154.70/154.53 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__upd__upds__conv__if,axiom, % 154.70/154.53 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_b,V_x_2,T_a] : % 154.70/154.53 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)),V_xs_2)))) % 154.70/154.53 => c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),V_xs_2,V_ys_2) = c_Map_Omap__upds(T_a,T_b,V_f_2,V_xs_2,V_ys_2) ) % 154.70/154.53 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)),V_xs_2)))) % 154.70/154.53 => c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),V_xs_2,V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__upds(T_a,T_b,V_f_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_option_Osize_I2_J,axiom, % 154.70/154.53 ! [V_a_2,V_fa_2,T_a] : c_Option_Ooption_Ooption__size(T_a,V_fa_2,hAPP(c_Option_Ooption_OSome(T_a),V_a_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_option_Osimps_I5_J,axiom, % 154.70/154.53 ! [V_a_2,V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_Option_Ooption_Ooption__case(T_a,T_b,V_f1_2,V_f2_2),hAPP(c_Option_Ooption_OSome(T_b),V_a_2)) = hAPP(V_f2_2,V_a_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_inj__Some,axiom, % 154.70/154.53 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_a),c_Option_Ooption_OSome(T_a),V_A_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_option_Oinject,axiom, % 154.70/154.53 ! [V_a_H_2,V_a_2,T_a] : % 154.70/154.53 ( hAPP(c_Option_Ooption_OSome(T_a),V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_a_H_2) % 154.70/154.53 <=> V_a_2 = V_a_H_2 ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_the_Osimps,axiom, % 154.70/154.53 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ). % 154.70/154.53 % 154.70/154.53 fof(fact_WTs__elim__cases_I7_J,axiom, % 154.70/154.53 ! [V_P] : % 154.70/154.53 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P))) % 154.70/154.53 => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Option_Oset_Osimps_I2_J,axiom, % 154.70/154.53 ! [V_x_2,T_a] : c_Option_Oset(T_a,hAPP(c_Option_Ooption_OSome(T_a),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_elem__set,axiom, % 154.70/154.53 ! [V_xo_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Option_Oset(T_a,V_xo_2))) % 154.70/154.53 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_upd__conv__take__nth__drop,axiom, % 154.70/154.53 ! [V_a,V_xs,T_a,V_i] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.53 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_a) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_id__take__nth__drop,axiom, % 154.70/154.53 ! [V_xs,T_a,V_i] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.53 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_drop__Nil,axiom, % 154.70/154.53 ! [V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 154.70/154.53 % 154.70/154.53 fof(fact_distinct__drop,axiom, % 154.70/154.53 ! [V_i,V_xs,T_a] : % 154.70/154.53 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 154.70/154.53 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_drop__butlast,axiom, % 154.70/154.53 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_butlast__drop,axiom, % 154.70/154.53 ! [V_xs,V_n,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_take__drop,axiom, % 154.70/154.53 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_m),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_drop__take,axiom, % 154.70/154.53 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_drop__drop,axiom, % 154.70/154.53 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs) ). % 154.70/154.53 % 154.70/154.53 fof(fact_drop__0,axiom, % 154.70/154.53 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ). % 154.70/154.53 % 154.70/154.53 fof(fact_drop__zip,axiom, % 154.70/154.53 ! [V_ys,V_xs,V_n,T_b,T_a] : hAPP(hAPP(c_List_Odrop(tc_prod(T_a,T_b)),V_n),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_b),V_n),V_ys)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_length__drop,axiom, % 154.70/154.53 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n) ). % 154.70/154.53 % 154.70/154.53 fof(fact_in__set__dropD,axiom, % 154.70/154.53 ! [V_xs_2,V_n_2,V_x_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2)))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__drop__subset,axiom, % 154.70/154.53 ! [V_xs_2,V_n_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_drop__Suc__Cons,axiom, % 154.70/154.53 ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) ). % 154.70/154.53 % 154.70/154.53 fof(fact_drop__1__Cons,axiom, % 154.70/154.53 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs ). % 154.70/154.53 % 154.70/154.53 fof(fact_nth__via__drop,axiom, % 154.70/154.53 ! [V_ys,V_y,V_xs,V_n,T_a] : % 154.70/154.53 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys) % 154.70/154.53 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_append__take__drop__id,axiom, % 154.70/154.53 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = V_xs ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__drop__subset__set__drop,axiom, % 154.70/154.53 ! [V_xs_2,T_a,V_m_2,V_n_2] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2)))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_drop__eq__Nil,axiom, % 154.70/154.53 ! [V_xs_2,V_n_2,T_a] : % 154.70/154.53 ( hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 154.70/154.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_n_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_drop__all,axiom, % 154.70/154.53 ! [V_n,V_xs,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) % 154.70/154.53 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_drop__append,axiom, % 154.70/154.53 ! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_append__eq__conv__conj,axiom, % 154.70/154.53 ! [V_zs_2,V_ys_2,V_xs_2,T_a] : % 154.70/154.53 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_zs_2 % 154.70/154.53 <=> ( V_xs_2 = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_zs_2) % 154.70/154.53 & V_ys_2 = hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_zs_2) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_drop__Cons,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,V_n_2,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Odrop(T_a)),V_xs_2),V_n_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_drop__Cons_H,axiom, % 154.70/154.53 ! [V_xs,V_x,T_a,V_n] : % 154.70/154.53 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.53 => hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ) % 154.70/154.53 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.53 => hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_nth__drop,axiom, % 154.70/154.53 ! [V_xs,T_a,V_i,V_n] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.53 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_append__eq__append__conv__if,axiom, % 154.70/154.53 ! [V_ys_092_060_094isub_0622_2,V_ys_092_060_094isub_0621_2,V_xs_092_060_094isub_0622_2,V_xs_092_060_094isub_0621_2,T_a] : % 154.70/154.53 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2) % 154.70/154.53 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2))) % 154.70/154.53 => ( V_xs_092_060_094isub_0621_2 = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2) % 154.70/154.53 & V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2) ) ) % 154.70/154.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2))) % 154.70/154.53 => ( hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) = V_ys_092_060_094isub_0621_2 % 154.70/154.53 & hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2)),V_xs_092_060_094isub_0622_2) = V_ys_092_060_094isub_0622_2 ) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_nth__drop_H,axiom, % 154.70/154.53 ! [V_xs,T_a,V_i] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.53 => hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_drop__Cons__number__of,axiom, % 154.70/154.53 ! [V_xs,V_x,T_a,V_v] : % 154.70/154.53 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.53 => hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ) % 154.70/154.53 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.53 => hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_take__add,axiom, % 154.70/154.53 ! [V_xs,T_a,V_j,V_i] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.53 => hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_j),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_zip__append2,axiom, % 154.70/154.53 ! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Oappend(T_b),V_ys),V_zs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_ys)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_zs)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_zip__append1,axiom, % 154.70/154.53 ! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_take__hd__drop,axiom, % 154.70/154.53 ! [V_xs,T_a,V_n] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.53 => hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_hd__drop__conv__nth,axiom, % 154.70/154.53 ! [V_n,T_a,V_xs] : % 154.70/154.53 ( V_xs != c_List_Olist_ONil(T_a) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.53 => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_hd_Osimps,axiom, % 154.70/154.53 ! [V_xs,V_x,T_a] : hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ). % 154.70/154.53 % 154.70/154.53 fof(fact_hd__append,axiom, % 154.70/154.53 ! [V_ys,T_a,V_xs] : % 154.70/154.53 ( ( V_xs = c_List_Olist_ONil(T_a) % 154.70/154.53 => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_ys) ) % 154.70/154.53 & ( V_xs != c_List_Olist_ONil(T_a) % 154.70/154.53 => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_hd__append2,axiom, % 154.70/154.53 ! [V_ys,T_a,V_xs] : % 154.70/154.53 ( V_xs != c_List_Olist_ONil(T_a) % 154.70/154.53 => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_hd__in__set,axiom, % 154.70/154.53 ! [T_a,V_xs_2] : % 154.70/154.53 ( V_xs_2 != c_List_Olist_ONil(T_a) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_List_Ohd(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_hd__conv__nth,axiom, % 154.70/154.53 ! [T_a,V_xs] : % 154.70/154.53 ( V_xs != c_List_Olist_ONil(T_a) % 154.70/154.53 => hAPP(c_List_Ohd(T_a),V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rotate1__hd__tl,axiom, % 154.70/154.53 ! [T_a,V_xs] : % 154.70/154.53 ( V_xs != c_List_Olist_ONil(T_a) % 154.70/154.53 => hAPP(c_List_Orotate1(T_a),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),c_List_Olist_ONil(T_a))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_option_Osize_I4_J,axiom, % 154.70/154.53 ! [V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(T_a)),hAPP(c_Option_Ooption_OSome(T_a),V_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.70/154.53 % 154.70/154.53 fof(fact_tl__drop,axiom, % 154.70/154.53 ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_drop__tl,axiom, % 154.70/154.53 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_tl_Osimps_I1_J,axiom, % 154.70/154.53 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 154.70/154.53 % 154.70/154.53 fof(fact_distinct__tl,axiom, % 154.70/154.53 ! [V_xs,T_a] : % 154.70/154.53 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 154.70/154.53 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_tl_Osimps_I2_J,axiom, % 154.70/154.53 ! [V_xs,V_x,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs ). % 154.70/154.53 % 154.70/154.53 fof(fact_tl__append2,axiom, % 154.70/154.53 ! [V_ys,T_a,V_xs] : % 154.70/154.53 ( V_xs != c_List_Olist_ONil(T_a) % 154.70/154.53 => hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),V_ys) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_take__tl,axiom, % 154.70/154.53 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_drop__Suc,axiom, % 154.70/154.53 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_tl__append,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,hAPP(c_List_Otl(T_a),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Oappend(T_a)),V_ys_2))),V_xs_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_length__tl,axiom, % 154.70/154.53 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_tl__take,axiom, % 154.70/154.53 ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(T_a),V_xs)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_take__Suc,axiom, % 154.70/154.53 ! [V_n,T_a,V_xs] : % 154.70/154.53 ( V_xs != c_List_Olist_ONil(T_a) % 154.70/154.53 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_fold1__set,axiom, % 154.70/154.53 ! [V_xs_2,T_a] : % 154.70/154.53 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 154.70/154.53 => ( V_xs_2 != c_List_Olist_ONil(T_a) % 154.70/154.53 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),hAPP(c_List_Ohd(T_a),V_xs_2)),hAPP(c_List_Otl(T_a),V_xs_2)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_hd__rotate__conv__nth,axiom, % 154.70/154.53 ! [V_n,T_a,V_xs] : % 154.70/154.53 ( V_xs != c_List_Olist_ONil(T_a) % 154.70/154.53 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_length__rotate,axiom, % 154.70/154.53 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ). % 154.70/154.53 % 154.70/154.53 fof(fact_foldl__append,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),V_xs_2)),V_ys_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_foldl__Cons,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_x_2)),V_xs_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__rotate,axiom, % 154.70/154.53 ! [V_xs_2,V_n_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_start__le__sum,axiom, % 154.70/154.53 ! [V_ns_2,V_n_2,V_m_2] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_ns_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rotate0,axiom, % 154.70/154.53 ! [T_a] : c_List_Orotate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_foldl__absorb0,axiom, % 154.70/154.53 ! [V_zs_2,V_x_2,T_a] : % 154.70/154.53 ( class_Groups_Omonoid__add(T_a) % 154.70/154.53 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_zs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_zs_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_foldl__assoc,axiom, % 154.70/154.53 ! [V_zs_2,V_y_2,V_x_2,T_a] : % 154.70/154.53 ( class_Groups_Osemigroup__add(T_a) % 154.70/154.53 => hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_y_2),V_zs_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rotate__rotate,axiom, % 154.70/154.53 ! [V_xs,V_n,V_m,T_a] : hAPP(c_List_Orotate(T_a,V_m),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_xs) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rotate__add,axiom, % 154.70/154.53 ! [V_n_2,V_m_2,T_a] : c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Orotate(T_a,V_m_2)),c_List_Orotate(T_a,V_n_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_distinct__rotate,axiom, % 154.70/154.53 ! [V_xs_2,V_n_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2))) % 154.70/154.53 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rotate__is__Nil__conv,axiom, % 154.70/154.53 ! [V_xs_2,V_n_2,T_a] : % 154.70/154.53 ( hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 154.70/154.53 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_foldl__Nil,axiom, % 154.70/154.53 ! [V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),c_List_Olist_ONil(T_b)) = V_a_2 ). % 154.70/154.53 % 154.70/154.53 fof(fact_rotate__def,axiom, % 154.70/154.53 ! [V_n_2,T_a] : c_List_Orotate(T_a,V_n_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_n_2),c_List_Orotate1(T_a)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rotate1__rotate__swap,axiom, % 154.70/154.53 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orotate1(T_a),V_xs)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rotate__conv__mod,axiom, % 154.70/154.53 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(c_List_Orotate(T_a,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rotate__Suc,axiom, % 154.70/154.53 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listsum__foldl,axiom, % 154.70/154.53 ! [T_a] : % 154.70/154.53 ( class_Groups_Omonoid__add(T_a) % 154.70/154.53 => c_List_Omonoid__add__class_Olistsum(T_a) = c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_sum__eq__0__conv,axiom, % 154.70/154.53 ! [V_ns_2,V_m_2] : % 154.70/154.53 ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.53 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.53 & ! [B_x] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 154.70/154.53 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rotate__id,axiom, % 154.70/154.53 ! [V_xs,T_a,V_n] : % 154.70/154.53 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.53 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rotate__length01,axiom, % 154.70/154.53 ! [V_n,V_xs,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) % 154.70/154.53 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_fun__left__comm__idem_Ofold__set,axiom, % 154.70/154.53 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] : % 154.70/154.53 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 154.70/154.53 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),V_f_2),V_y_2),V_xs_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Sup__set__fold,axiom, % 154.70/154.53 ! [V_xs_2,T_a] : % 154.70/154.53 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.70/154.53 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_xs_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Inf__set__fold,axiom, % 154.70/154.53 ! [V_xs_2,T_a] : % 154.70/154.53 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.70/154.53 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_xs_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Sup__fin__set__fold,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( class_Lattices_Olattice(T_a) % 154.70/154.53 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_xs_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Inf__fin__set__fold,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( class_Lattices_Olattice(T_a) % 154.70/154.53 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_xs_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Min__fin__set__fold,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( class_Orderings_Olinorder(T_a) % 154.70/154.53 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omin(T_a),V_x_2),V_xs_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Max__fin__set__fold,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( class_Orderings_Olinorder(T_a) % 154.70/154.53 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_x_2),V_xs_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_min__max_OInf__fin__set__fold,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( class_Orderings_Olinorder(T_a) % 154.70/154.53 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omin(T_a),V_x_2),V_xs_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_min__max_OSup__fin__set__fold,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( class_Orderings_Olinorder(T_a) % 154.70/154.53 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_x_2),V_xs_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_SUPR__set__fold,axiom, % 154.70/154.53 ! [V_f_2,V_xs_2,T_b,T_a] : % 154.70/154.53 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.70/154.53 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),hAPP(c_List_Oset(T_b),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_f_2)),c_Orderings_Obot__class_Obot(T_a)),V_xs_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_INFI__set__fold,axiom, % 154.70/154.53 ! [V_f_2,V_xs_2,T_b,T_a] : % 154.70/154.53 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 154.70/154.53 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),hAPP(c_List_Oset(T_b),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_f_2)),c_Orderings_Otop__class_Otop(T_a)),V_xs_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__upds__fold__map__upd,axiom, % 154.70/154.53 ! [V_vs_2,V_ks_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_ks_2,V_vs_2) = hAPP(c_List_Ofoldl(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_prod(T_a,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(tc_prod(T_a,T_b),tc_fun(T_a,tc_Option_Ooption(T_b))),tc_fun(T_a,tc_Option_Ooption(T_b))),c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_a,tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),tc_fun(T_a,tc_Option_Ooption(T_b))),c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(T_a,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),tc_fun(T_a,tc_Option_Ooption(T_b))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b))),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b)))),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)),T_b))),c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b))))),c_Option_Ooption_OSome(T_b))),V_m_2),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ks_2),V_vs_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_elem__le__sum,axiom, % 154.70/154.53 ! [V_ns_2,V_n_2] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_ns_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rotate__drop__take,axiom, % 154.70/154.53 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)),hAPP(hAPP(c_List_Otake(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_ran__def,axiom, % 154.70/154.53 ! [V_m_2,T_a,T_b] : c_Map_Oran(T_b,T_a,V_m_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_Option_Ooption(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool),T_b),c_fequal),V_m_2))),c_Option_Ooption_OSome(T_a)))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_lexord__append__rightI,axiom, % 154.70/154.53 ! [V_r_2,V_x_2,T_a,V_y_2] : % 154.70/154.53 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_b),B_z) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_y_2))),c_List_Olexord(T_a,V_r_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_ranI,axiom, % 154.70/154.53 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] : % 154.70/154.53 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_sorted__list__of__set__insert,axiom, % 154.70/154.53 ! [V_x_2,V_A_2,T_a] : % 154.70/154.53 ( class_Orderings_Olinorder(T_a) % 154.70/154.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.53 => c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_lexord__Nil__left,axiom, % 154.70/154.53 ! [V_r_2,V_y_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_y_2)),c_List_Olexord(T_a,V_r_2))) % 154.70/154.53 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_x) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_length__insort,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 154.70/154.53 ( class_Orderings_Olinorder(T_b) % 154.70/154.53 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_insort__key_Osimps_I1_J,axiom, % 154.70/154.53 ! [V_x_2,V_f_2,T_a,T_b] : % 154.70/154.53 ( class_Orderings_Olinorder(T_b) % 154.70/154.53 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_insort__key_Osimps_I2_J,axiom, % 154.70/154.53 ! [V_ys_2,T_b,V_y_2,V_x_2,V_f_2,T_a] : % 154.70/154.53 ( class_Orderings_Olinorder(T_a) % 154.70/154.53 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 154.70/154.53 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) % 154.70/154.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 154.70/154.53 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_ys_2)) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__insort,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 154.70/154.53 ( class_Orderings_Olinorder(T_b) % 154.70/154.53 => hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_insort__key__left__comm,axiom, % 154.70/154.53 ! [V_xs_2,T_b,V_y_2,V_x_2,V_f_2,T_a] : % 154.70/154.53 ( class_Orderings_Olinorder(T_a) % 154.70/154.53 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) % 154.70/154.53 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_y_2),V_xs_2)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_insort__left__comm,axiom, % 154.70/154.53 ! [V_xs_2,V_y_2,V_x_2,T_a] : % 154.70/154.53 ( class_Orderings_Olinorder(T_a) % 154.70/154.53 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_fun__left__comm__insort,axiom, % 154.70/154.53 ! [T_a] : % 154.70/154.53 ( class_Orderings_Olinorder(T_a) % 154.70/154.53 => c_Finite__Set_Ofun__left__comm(T_a,tc_List_Olist(T_a),c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_remove1__insort,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( class_Orderings_Olinorder(T_a) % 154.70/154.53 => c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)) = V_xs_2 ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_insort__not__Nil,axiom, % 154.70/154.53 ! [V_xs_2,V_a_2,V_f_2,T_a,T_b] : % 154.70/154.53 ( class_Orderings_Olinorder(T_b) % 154.70/154.53 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_a) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_distinct__insort,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 154.70/154.53 ( class_Orderings_Olinorder(T_b) % 154.70/154.53 => ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2))) % 154.70/154.53 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.53 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_insort__insert__insort__key,axiom, % 154.70/154.53 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] : % 154.70/154.53 ( class_Orderings_Olinorder(T_a) % 154.70/154.53 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)))) % 154.70/154.53 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_insort__insert__insort,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( class_Orderings_Olinorder(T_a) % 154.70/154.53 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.53 => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_distinct__insort__insert,axiom, % 154.70/154.53 ! [V_x_2,V_f_2,V_xs_2,T_a,T_b] : % 154.70/154.53 ( class_Orderings_Olinorder(T_b) % 154.70/154.53 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 154.70/154.53 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Oinsort__insert__key(T_a,T_b,V_f_2,V_x_2,V_xs_2))) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_insort__insert__triv,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( class_Orderings_Olinorder(T_a) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.53 => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = V_xs_2 ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__insort__insert,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.53 ( class_Orderings_Olinorder(T_a) % 154.70/154.53 => hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_insort__insert__key__triv,axiom, % 154.70/154.53 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] : % 154.70/154.53 ( class_Orderings_Olinorder(T_a) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)))) % 154.70/154.53 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_last__list__update,axiom, % 154.70/154.53 ! [V_x,V_k,T_a,V_xs] : % 154.70/154.53 ( V_xs != c_List_Olist_ONil(T_a) % 154.70/154.53 => ( ( V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) % 154.70/154.53 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) % 154.70/154.53 & ( V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) % 154.70/154.53 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Olast(T_a,V_xs) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_last__conv__nth,axiom, % 154.70/154.53 ! [T_a,V_xs] : % 154.70/154.53 ( V_xs != c_List_Olist_ONil(T_a) % 154.70/154.53 => c_List_Olast(T_a,V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_last__appendL,axiom, % 154.70/154.53 ! [V_xs,T_a,V_ys] : % 154.70/154.53 ( V_ys = c_List_Olist_ONil(T_a) % 154.70/154.53 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_last__appendR,axiom, % 154.70/154.53 ! [V_xs,T_a,V_ys] : % 154.70/154.53 ( V_ys != c_List_Olist_ONil(T_a) % 154.70/154.53 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_last__append,axiom, % 154.70/154.53 ! [V_xs,T_a,V_ys] : % 154.70/154.53 ( ( V_ys = c_List_Olist_ONil(T_a) % 154.70/154.53 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) % 154.70/154.53 & ( V_ys != c_List_Olist_ONil(T_a) % 154.70/154.53 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_last__ConsL,axiom, % 154.70/154.53 ! [V_x,T_a,V_xs] : % 154.70/154.53 ( V_xs = c_List_Olist_ONil(T_a) % 154.70/154.53 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_last__ConsR,axiom, % 154.70/154.53 ! [V_x,T_a,V_xs] : % 154.70/154.53 ( V_xs != c_List_Olist_ONil(T_a) % 154.70/154.53 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_last_Osimps,axiom, % 154.70/154.53 ! [V_x,T_a,V_xs] : % 154.70/154.53 ( ( V_xs = c_List_Olist_ONil(T_a) % 154.70/154.53 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) % 154.70/154.53 & ( V_xs != c_List_Olist_ONil(T_a) % 154.70/154.53 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_last__in__set,axiom, % 154.70/154.53 ! [T_a,V_as_2] : % 154.70/154.53 ( V_as_2 != c_List_Olist_ONil(T_a) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(T_a),c_List_Olast(T_a,V_as_2)),hAPP(c_List_Oset(T_a),V_as_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_last__snoc,axiom, % 154.70/154.53 ! [V_x,V_xs,T_a] : c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_x ). % 154.70/154.53 % 154.70/154.53 fof(fact_last__drop,axiom, % 154.70/154.53 ! [V_xs,T_a,V_n] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.53 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_append__butlast__last__id,axiom, % 154.70/154.53 ! [T_a,V_xs] : % 154.70/154.53 ( V_xs != c_List_Olist_ONil(T_a) % 154.70/154.53 => hAPP(hAPP(c_List_Oappend(T_a),c_List_Obutlast(T_a,V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),c_List_Olast(T_a,V_xs)),c_List_Olist_ONil(T_a))) = V_xs ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_snoc__eq__iff__butlast,axiom, % 154.70/154.53 ! [V_ys_2,V_x_2,V_xs_2,T_a] : % 154.70/154.53 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))) = V_ys_2 % 154.70/154.53 <=> ( V_ys_2 != c_List_Olist_ONil(T_a) % 154.70/154.53 & c_List_Obutlast(T_a,V_ys_2) = V_xs_2 % 154.70/154.53 & c_List_Olast(T_a,V_ys_2) = V_x_2 ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_lists_Osimps,axiom, % 154.70/154.53 ! [V_A_2,V_a_2,T_a] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_a_2),c_List_Olists(T_a,V_A_2))) % 154.70/154.53 <=> ( V_a_2 = c_List_Olist_ONil(T_a) % 154.70/154.53 | ? [B_a,B_l] : % 154.70/154.53 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_l) % 154.70/154.53 & hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 154.70/154.53 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_l),c_List_Olists(T_a,V_A_2))) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__of__zip__upd,axiom, % 154.70/154.53 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_b,V_ys_2,T_a] : % 154.70/154.53 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 154.70/154.53 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 154.70/154.53 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 154.70/154.53 => ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_a),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_a),V_z_2)) % 154.70/154.53 => hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2)) = hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2)) ) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_finite__dom__map__of,axiom, % 154.70/154.53 ! [V_l_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_l_2)))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__of__zip__inject,axiom, % 154.70/154.53 ! [V_zs_2,V_xs_2,T_b,V_ys_2,T_a] : % 154.70/154.53 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 154.70/154.53 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 154.70/154.53 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 154.70/154.53 => ( hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2)) = hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2)) % 154.70/154.53 => V_ys_2 = V_zs_2 ) ) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_body__def,axiom, % 154.70/154.53 c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__of__Cons__code_I2_J,axiom, % 154.70/154.53 ! [V_ps,V_v,T_c,T_b,V_k,V_l] : % 154.70/154.53 ( ( V_l = V_k % 154.70/154.53 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_l),V_v)),V_ps)),V_k) = hAPP(c_Option_Ooption_OSome(T_c),V_v) ) % 154.70/154.53 & ( V_l != V_k % 154.70/154.53 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_l),V_v)),V_ps)),V_k) = hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_ps),V_k) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__of__eq__dom,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,T_b,T_a] : % 154.70/154.53 ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) % 154.70/154.53 => hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_ys_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_finite__range__map__of,axiom, % 154.70/154.53 ! [V_xys_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__of__is__SomeD,axiom, % 154.70/154.53 ! [V_y_2,V_x_2,V_xys_2,T_a,T_b] : % 154.70/154.53 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xys_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__of__SomeD,axiom, % 154.70/154.53 ! [V_y_2,V_k_2,V_xs_2,T_a,T_b] : % 154.70/154.53 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_k_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xs_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_dom__map__of__conv__image__fst,axiom, % 154.70/154.53 ! [V_xys_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__of__zip__is__Some,axiom, % 154.70/154.53 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] : % 154.70/154.53 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 154.70/154.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.53 <=> ? [B_y] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_dom__map__of__zip,axiom, % 154.70/154.53 ! [V_ys_2,T_b,V_xs_2,T_a] : % 154.70/154.53 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 154.70/154.53 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 154.70/154.53 => c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) = hAPP(c_List_Oset(T_a),V_xs_2) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__of_Osimps_I2_J,axiom, % 154.70/154.53 ! [V_ps_2,V_p_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),V_p_2),V_ps_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_Map_Omap__of(T_a,T_b),V_ps_2)),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p_2)),hAPP(c_Option_Ooption_OSome(T_b),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p_2))) ). % 154.70/154.53 % 154.70/154.53 fof(fact_ran__distinct,axiom, % 154.70/154.53 ! [V_al_2,T_b,T_a] : % 154.70/154.53 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_al_2))) % 154.70/154.53 => c_Map_Oran(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_al_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_al_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__map__of__compr,axiom, % 154.70/154.53 ! [V_xs_2,T_b,T_a] : % 154.70/154.53 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2))) % 154.70/154.53 => hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_a),c_fequal),hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2)))),c_Option_Ooption_OSome(T_b)))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_inj__mapI,axiom, % 154.70/154.53 ! [V_f_2,T_b,T_a] : % 154.70/154.53 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 154.70/154.53 => c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listsum__abs,axiom, % 154.70/154.53 ! [V_xs_2,T_a] : % 154.70/154.53 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_a,T_a),c_Groups_Oabs__class_Oabs(T_a)),V_xs_2)))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_foldl__map,axiom, % 154.70/154.53 ! [V_xs_2,V_f_2,T_c,V_a_2,V_g_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,T_a)),T_a),c_COMBB(T_b,T_a,T_c)),V_g_2)),V_f_2),V_a_2),V_xs_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_zip__map2,axiom, % 154.70/154.53 ! [V_ys_2,V_f_2,T_c,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_c,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),T_a),c_COMBB(T_b,tc_prod(T_a,T_b),T_c)),c_Product__Type_OPair(T_a,T_b))),V_f_2))),hAPP(hAPP(c_List_Ozip(T_a,T_c),V_xs_2),V_ys_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__zip__map2,axiom, % 154.70/154.53 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_a),V_f_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_c)),tc_fun(T_d,T_a),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_d),V_f_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),T_b),c_COMBB(T_c,tc_prod(T_b,T_c),T_d)),c_Product__Type_OPair(T_b,T_c))),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_b,T_d),V_xs_2),V_ys_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__zip__map,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,V_g_2,T_d,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_a),V_f_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_a),T_d),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_c),V_f_2)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_zip__map1,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_b),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_zip__map__map,axiom, % 154.70/154.53 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,tc_prod(T_a,T_b))),T_c),c_COMBB(T_b,tc_prod(T_a,T_b),T_d)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_List_Omap_Ocomp,axiom, % 154.70/154.53 ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_c),tc_List_Olist(T_b),tc_List_Olist(T_a),hAPP(c_List_Omap(T_c,T_b),V_f_2)),hAPP(c_List_Omap(T_a,T_c),V_g_2)) = hAPP(c_List_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__comp__map,axiom, % 154.70/154.53 ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_c),tc_List_Olist(T_b),tc_List_Olist(T_a),hAPP(c_List_Omap(T_c,T_b),V_f_2)),hAPP(c_List_Omap(T_a,T_c),V_g_2)) = hAPP(c_List_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_List_Omap_Ocompositionality,axiom, % 154.70/154.53 ! [V_list_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_list_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__map,axiom, % 154.70/154.53 ! [V_xs_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_xs_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_List_Omap_Oidentity,axiom, % 154.70/154.53 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_List_Omap_Oid,axiom, % 154.70/154.53 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_list__size__map,axiom, % 154.70/154.53 ! [V_xs_2,V_g_2,T_b,V_f_2,T_a] : c_List_Olist_Olist__size(T_a,V_f_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_b,hAPP(c_Fun_Ocomp(T_a,tc_Nat_Onat,T_b,V_f_2),V_g_2),V_xs_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_nth__map,axiom, % 154.70/154.53 ! [V_f_2,T_b,V_xs_2,T_a,V_n_2] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.53 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__fun__upd,axiom, % 154.70/154.53 ! [V_v_2,V_f_2,T_b,V_xs_2,V_y_2,T_a] : % 154.70/154.53 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.53 => hAPP(hAPP(c_List_Omap(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_y_2),V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__tl,axiom, % 154.70/154.53 ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Otl(T_b),V_xs_2)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_length__map,axiom, % 154.70/154.53 ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__eq__imp__length__eq,axiom, % 154.70/154.53 ! [V_ys_2,V_g_2,T_c,V_xs_2,V_f_2,T_a,T_b] : % 154.70/154.53 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_a),V_g_2),V_ys_2) % 154.70/154.53 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_set__map,axiom, % 154.70/154.53 ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__append,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map_Osimps_I2_J,axiom, % 154.70/154.53 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__update,axiom, % 154.70/154.53 ! [V_y_2,V_k_2,V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__eq__conv,axiom, % 154.70/154.53 ! [V_g_2,V_xs_2,V_f_2,T_a,T_b] : % 154.70/154.53 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2) % 154.70/154.53 <=> ! [B_x] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 154.70/154.53 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listsum__0,axiom, % 154.70/154.53 ! [V_xs_2,T_b,T_a] : % 154.70/154.53 ( class_Groups_Omonoid__add(T_a) % 154.70/154.53 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Ozero__class_Ozero(T_a))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listsum__mult__const,axiom, % 154.70/154.53 ! [V_xs_2,V_c_2,V_f_2,T_b,T_a] : % 154.70/154.53 ( class_Rings_Osemiring__0(T_a) % 154.70/154.53 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_c_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),V_c_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listsum__const__mult,axiom, % 154.70/154.53 ! [V_xs_2,V_f_2,V_c_2,T_b,T_a] : % 154.70/154.53 ( class_Rings_Osemiring__0(T_a) % 154.70/154.53 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listsum__subtractf,axiom, % 154.70/154.53 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 154.70/154.53 ( class_Groups_Oab__group__add(T_a) % 154.70/154.53 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_listsum__addf,axiom, % 154.70/154.53 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 154.70/154.53 ( class_Groups_Ocomm__monoid__add(T_a) % 154.70/154.53 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Oplus__class_Oplus(T_a)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__ident,axiom, % 154.70/154.53 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)),V_xs_2) = V_xs_2 ). % 154.70/154.53 % 154.70/154.53 fof(fact_take__map,axiom, % 154.70/154.53 ! [V_xs_2,V_f_2,T_b,V_n_2,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__butlast,axiom, % 154.70/154.53 ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Obutlast(T_b,V_xs_2)) = c_List_Obutlast(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_Nil__is__map__conv,axiom, % 154.70/154.53 ! [V_xs_2,V_f_2,T_b,T_a] : % 154.70/154.53 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) % 154.70/154.53 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map_Osimps_I1_J,axiom, % 154.70/154.53 ! [V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__is__Nil__conv,axiom, % 154.70/154.53 ! [V_xs_2,V_f_2,T_a,T_b] : % 154.70/154.53 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = c_List_Olist_ONil(T_a) % 154.70/154.53 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_inj__map__eq__map,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] : % 154.70/154.53 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 154.70/154.53 => ( hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2) % 154.70/154.53 <=> V_xs_2 = V_ys_2 ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__injective,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 154.70/154.53 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2) % 154.70/154.53 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 154.70/154.53 => V_xs_2 = V_ys_2 ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_hd__map,axiom, % 154.70/154.53 ! [V_f_2,T_b,T_a,V_xs_2] : % 154.70/154.53 ( V_xs_2 != c_List_Olist_ONil(T_a) % 154.70/154.53 => hAPP(c_List_Ohd(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_a),V_xs_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_drop__map,axiom, % 154.70/154.53 ! [V_xs_2,V_f_2,T_b,V_n_2,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__inj__on,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 154.70/154.53 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2) % 154.70/154.53 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2))) % 154.70/154.53 => V_xs_2 = V_ys_2 ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_inj__on__map__eq__map,axiom, % 154.70/154.53 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] : % 154.70/154.53 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2))) % 154.70/154.53 => ( hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2) % 154.70/154.53 <=> V_xs_2 = V_ys_2 ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_rotate__map,axiom, % 154.70/154.53 ! [V_xs_2,V_f_2,T_b,V_n_2,T_a] : hAPP(c_List_Orotate(T_a,V_n_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)) ). % 154.70/154.53 % 154.70/154.53 fof(fact_distinct__map,axiom, % 154.70/154.53 ! [V_xs_2,V_f_2,T_b,T_a] : % 154.70/154.53 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) % 154.70/154.53 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 154.70/154.53 & c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_last__map,axiom, % 154.70/154.53 ! [V_f_2,T_b,T_a,V_xs_2] : % 154.70/154.53 ( V_xs_2 != c_List_Olist_ONil(T_a) % 154.70/154.53 => c_List_Olast(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_a,V_xs_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_uminus__listsum__map,axiom, % 154.70/154.53 ! [V_xs_2,V_f_2,T_b,T_a] : % 154.70/154.53 ( class_Groups_Oab__group__add(T_a) % 154.70/154.53 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_Fun_Ocomp(T_a,T_a,T_b,c_Groups_Ouminus__class_Ouminus(T_a)),V_f_2)),V_xs_2)) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_inj__on__mapI,axiom, % 154.70/154.53 ! [V_A_2,V_f_2,T_b,T_a] : % 154.70/154.53 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),c_List_Oset(T_a)),V_A_2))) % 154.70/154.53 => c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),V_A_2) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__fst__zip,axiom, % 154.70/154.53 ! [V_ys_2,T_b,V_xs_2,T_a] : % 154.70/154.53 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 154.70/154.53 => hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = V_xs_2 ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_map__snd__zip,axiom, % 154.70/154.53 ! [V_ys_2,T_b,V_xs_2,T_a] : % 154.70/154.53 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 154.70/154.53 => hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = V_ys_2 ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_zip__map__fst__snd,axiom, % 154.70/154.53 ! [V_zs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),V_zs_2)) = V_zs_2 ). % 154.70/154.53 % 154.70/154.53 fof(fact_inj__map,axiom, % 154.70/154.53 ! [V_f_2,T_b,T_a] : % 154.70/154.53 ( c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) % 154.70/154.53 <=> c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_inj__mapD,axiom, % 154.70/154.53 ! [V_f_2,T_b,T_a] : % 154.70/154.53 ( c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) % 154.70/154.53 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 154.70/154.53 % 154.70/154.53 fof(fact_pick__member,axiom, % 154.70/154.53 ! [V_xs_2,T_a,V_i_2] : % 154.70/154.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i_2),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) % 154.70/154.53 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Random_Opick(T_a,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),T_a),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_listsum__distinct__conv__setsum__set,axiom, % 154.70/154.54 ! [V_f_2,V_xs_2,T_a,T_b] : % 154.70/154.54 ( class_Groups_Ocomm__monoid__add(T_b) % 154.70/154.54 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 154.70/154.54 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_List_Oset(T_a),V_xs_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_zip__eq__conv,axiom, % 154.70/154.54 ! [V_zs_2,V_ys_2,T_b,V_xs_2,T_a] : % 154.70/154.54 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 154.70/154.54 => ( hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2) = V_zs_2 % 154.70/154.54 <=> ( hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_zs_2) = V_xs_2 % 154.70/154.54 & hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),V_zs_2) = V_ys_2 ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_listsum__triv,axiom, % 154.70/154.54 ! [V_xs_2,V_r_2,T_b,T_a] : % 154.70/154.54 ( class_Rings_Osemiring__1(T_a) % 154.70/154.54 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_COMBK(T_a,T_b),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),V_r_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__of__inject__set,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,T_b,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2))) % 154.70/154.54 => ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_ys_2))) % 154.70/154.54 => ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) % 154.70/154.54 <=> hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2) = hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_ys_2) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_listsum__map__remove1,axiom, % 154.70/154.54 ! [V_f_2,V_xs_2,V_x_2,T_a,T_b] : % 154.70/154.54 ( class_Groups_Ocomm__monoid__add(T_b) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),c_List_Oremove1(T_a,V_x_2,V_xs_2)))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_select__weight__member,axiom, % 154.70/154.54 ! [V_s_2,V_xs_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) % 154.70/154.54 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Product__Type_Ofst(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_a,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),T_a),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_select__weight__def,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : c_Random_Oselect__weight(T_a,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_a,V_xs_2))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__of__mapk__SomeI,axiom, % 154.70/154.54 ! [V_x_2,V_k_2,V_t_2,T_c,V_f_2,T_b,T_a] : % 154.70/154.54 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 154.70/154.54 => ( hAPP(hAPP(c_Map_Omap__of(T_a,T_c),V_t_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),V_x_2) % 154.70/154.54 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_a),c_Product__Type_OPair(T_b,T_c)),V_f_2))),V_t_2)),hAPP(V_f_2,V_k_2)) = hAPP(c_Option_Ooption_OSome(T_c),V_x_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_Some__eq__map__of__iff,axiom, % 154.70/154.54 ! [V_x_2,V_y_2,V_xys_2,T_b,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2))) % 154.70/154.54 => ( hAPP(c_Option_Ooption_OSome(T_b),V_y_2) = hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2) % 154.70/154.54 <=> 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)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__of__eq__Some__iff,axiom, % 154.70/154.54 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2))) % 154.70/154.54 => ( hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) % 154.70/154.54 <=> 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)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__of__is__SomeI,axiom, % 154.70/154.54 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2))) % 154.70/154.54 => ( 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)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) % 154.70/154.54 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_Nitpick_Osetsum_H__def,axiom, % 154.70/154.54 ! [V_f_2,V_A_2,T_a,T_b] : % 154.70/154.54 ( class_Groups_Ocomm__monoid__add(T_b) % 154.70/154.54 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.54 => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_a),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_List_Oset(T_a))),V_A_2))),c_List_Odistinct(T_a))))) ) % 154.70/154.54 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.54 => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_listsum__mono,axiom, % 154.70/154.54 ! [V_g_2,V_f_2,V_xs_2,T_a,T_b] : % 154.70/154.54 ( ( class_Groups_Omonoid__add(T_b) % 154.70/154.54 & class_Groups_Oordered__ab__semigroup__add(T_b) ) % 154.70/154.54 => ( ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 154.70/154.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_g_2),V_xs_2)))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_zip__same__conv__map,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_a)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a))),V_xs_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__size__conv__listsum,axiom, % 154.70/154.54 ! [V_xs_2,V_f_2,T_a] : c_List_Olist_Olist__size(T_a,V_f_2,V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(T_a,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_interv__listsum__conv__setsum__set__int,axiom, % 154.70/154.54 ! [V_l_2,V_k_2,V_f_2,T_a] : % 154.70/154.54 ( class_Groups_Ocomm__monoid__add(T_a) % 154.70/154.54 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_a),V_f_2),c_List_Oupto(V_k_2,V_l_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_setsum__set__upto__conv__listsum__int,axiom, % 154.70/154.54 ! [V_j_2,V_i_2,V_f_2,T_a] : % 154.70/154.54 ( class_Groups_Ocomm__monoid__add(T_a) % 154.70/154.54 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_a),V_f_2),c_List_Oupto(V_i_2,V_j_2))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__of__map__restrict,axiom, % 154.70/154.54 ! [V_ks_2,V_f_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),V_f_2)),V_ks_2)) = c_Map_Orestrict__map(T_a,T_b,hAPP(c_Fun_Ocomp(T_b,tc_Option_Ooption(T_b),T_a,c_Option_Ooption_OSome(T_b)),V_f_2),hAPP(c_List_Oset(T_a),V_ks_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__of__map__keys,axiom, % 154.70/154.54 ! [V_m_2,T_b,V_xs_2,T_a] : % 154.70/154.54 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Map_Odom(T_a,T_b,V_m_2) % 154.70/154.54 => hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),T_b,T_a),c_Option_Othe(T_b)),V_m_2))),V_xs_2)) = V_m_2 ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_select__weigth__select,axiom, % 154.70/154.54 ! [T_a,V_xs_2] : % 154.70/154.54 ( V_xs_2 != c_List_Olist_ONil(T_a) % 154.70/154.54 => c_Random_Oselect__weight(T_a,hAPP(hAPP(c_List_Omap(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_a,V_xs_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_pick__same,axiom, % 154.70/154.54 ! [V_xs_2,T_a,V_l_2] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_l_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.54 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Omap(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)),hAPP(c_Code__Numeral_Oof__nat,V_l_2)) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_l_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__of__map,axiom, % 154.70/154.54 ! [V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_c,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),T_a),c_COMBB(T_b,tc_prod(T_a,T_b),T_c)),c_Product__Type_OPair(T_a,T_b))),V_f_2))),V_xs_2)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_Map_Omap__of(T_a,T_c),V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_option__map__comp,axiom, % 154.70/154.54 ! [V_opt_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_Option_Omap(T_c,T_b),V_g_2),V_opt_2)) = hAPP(hAPP(c_Option_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_opt_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_Option_Omap_Ocompositionality,axiom, % 154.70/154.54 ! [V_option_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_Option_Omap(T_c,T_b),V_g_2),V_option_2)) = hAPP(hAPP(c_Option_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_option_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_Option_Omap_Ocomp,axiom, % 154.70/154.54 ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),tc_Option_Ooption(T_a),hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_Option_Omap(T_a,T_c),V_g_2)) = hAPP(c_Option_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_option__map__o__map__upd,axiom, % 154.70/154.54 ! [V_b_2,V_a_2,V_m_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),V_m_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_b_2))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_number__of__code__numeral__def,axiom, % 154.70/154.54 c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(fact_Option_Omap_Oidentity,axiom, % 154.70/154.54 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_Option_Omap_Oid,axiom, % 154.70/154.54 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_code__numeral_Oof__nat__inject,axiom, % 154.70/154.54 ! [V_y_2,V_x_2] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 154.70/154.54 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2) % 154.70/154.54 <=> V_x_2 = V_y_2 ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_less__code__numeral__code,axiom, % 154.70/154.54 ! [V_m_2,V_n_2] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2))) % 154.70/154.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_option__map__Some,axiom, % 154.70/154.54 ! [V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(c_Option_Ooption_OSome(T_a),hAPP(V_f_2,V_x_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_option__map__eq__Some,axiom, % 154.70/154.54 ! [V_y_2,V_xo_2,V_f_2,T_a,T_b] : % 154.70/154.54 ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_xo_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 154.70/154.54 <=> ? [B_z] : % 154.70/154.54 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),B_z) % 154.70/154.54 & hAPP(V_f_2,B_z) = V_y_2 ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_dom__option__map,axiom, % 154.70/154.54 ! [V_m_2,V_f_2,T_c,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBS(T_a,tc_Option_Ooption(T_c),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b)),T_a),c_Option_Omap(T_c,T_b)),V_f_2)),V_m_2)) = c_Map_Odom(T_a,T_c,V_m_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_Code__Numeral_Oof__nat__code,axiom, % 154.70/154.54 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(fact_times__code__numeral__code,axiom, % 154.70/154.54 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_Code__Numeral_Oof__nat__inject,axiom, % 154.70/154.54 ! [V_m_2,V_n_2] : % 154.70/154.54 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2) % 154.70/154.54 <=> V_n_2 = V_m_2 ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_zero__code__numeral__def,axiom, % 154.70/154.54 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_one__code__numeral__def,axiom, % 154.70/154.54 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_plus__code__numeral__code,axiom, % 154.70/154.54 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_less__eq__code__numeral__code,axiom, % 154.70/154.54 ! [V_m_2,V_n_2] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2))) % 154.70/154.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_code__numeral__not__eq__zero,axiom, % 154.70/154.54 ! [V_i_2] : % 154.70/154.54 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 154.70/154.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_i_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_select__def,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : c_Random_Oselect(T_a,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_a),V_xs_2)),c_Code__Numeral_Onat__of))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_subtract__code__numeral__code,axiom, % 154.70/154.54 ! [V_m,V_n] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_type__definition__code__numeral,axiom, % 154.70/154.54 c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_times__code__numeral__def,axiom, % 154.70/154.54 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_nat__of__inverse,axiom, % 154.70/154.54 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ). % 154.70/154.54 % 154.70/154.54 fof(fact_of__nat__nat__of,axiom, % 154.70/154.54 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ). % 154.70/154.54 % 154.70/154.54 fof(fact_nat__of__of__nat,axiom, % 154.70/154.54 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ). % 154.70/154.54 % 154.70/154.54 fof(fact_Code__Numeral_Onat__of__inject,axiom, % 154.70/154.54 ! [V_l_2,V_k_2] : % 154.70/154.54 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2) % 154.70/154.54 <=> V_k_2 = V_l_2 ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_code__numeral_Onat__of__inject,axiom, % 154.70/154.54 ! [V_y_2,V_x_2] : % 154.70/154.54 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2) % 154.70/154.54 <=> V_x_2 = V_y_2 ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_less__code__numeral__def,axiom, % 154.70/154.54 ! [V_m_2,V_n_2] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 154.70/154.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_nat__of,axiom, % 154.70/154.54 ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_x_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_nat__of__number,axiom, % 154.70/154.54 ! [V_k] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),V_k)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_k) ). % 154.70/154.54 % 154.70/154.54 fof(fact_int__of__def,axiom, % 154.70/154.54 c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of) ). % 154.70/154.54 % 154.70/154.54 fof(fact_less__eq__code__numeral__def,axiom, % 154.70/154.54 ! [V_m_2,V_n_2] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 154.70/154.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_nat__of__code,axiom, % 154.70/154.54 ! [V_i] : hAPP(c_Code__Numeral_Onat__of,V_i) = c_Code__Numeral_Onat__of__aux(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_nat__of__aux__def,axiom, % 154.70/154.54 ! [V_n,V_i] : c_Code__Numeral_Onat__of__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_i)),V_n) ). % 154.70/154.54 % 154.70/154.54 fof(fact_Suc__code__numeral__def,axiom, % 154.70/154.54 ! [V_k] : c_Code__Numeral_OSuc__code__numeral(V_k) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,V_k))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_minus__code__numeral__def,axiom, % 154.70/154.54 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_of__nat__inverse,axiom, % 154.70/154.54 ! [V_y_2] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 154.70/154.54 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_plus__code__numeral__def,axiom, % 154.70/154.54 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_div__code__numeral__def,axiom, % 154.70/154.54 ! [V_m,V_n] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_subtract__code__numeral__def,axiom, % 154.70/154.54 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(fact_minus__code__numeral__code,axiom, % 154.70/154.54 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,V_n),V_m) ). % 154.70/154.54 % 154.70/154.54 fof(fact_mod__code__numeral__def,axiom, % 154.70/154.54 ! [V_m,V_n] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,V_n),hAPP(c_Code__Numeral_Onat__of,V_m))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_code__numeral__decr,axiom, % 154.70/154.54 ! [V_k] : % 154.70/154.54 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 154.70/154.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_k)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,V_k))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_New__DSequence_Opos__not__seq__def,axiom, % 154.70/154.54 ! [V_i_2,V_xq_2] : hAPP(c_New__DSequence_Opos__not__seq(V_xq_2),V_i_2) = c_Lazy__Sequence_Ohb__not__seq(hAPP(V_xq_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_i_2))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_weak__map__of__SomeI,axiom, % 154.70/154.54 ! [V_l_2,V_x_2,V_k_2,T_b,T_a] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_k_2),V_x_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_l_2))) % 154.70/154.54 => ? [B_x] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_l_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_x) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__of__zip__map,axiom, % 154.70/154.54 ! [V_f_2,T_b,V_xs_2,V_x_2,T_a] : % 154.70/154.54 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_x_2)) ) % 154.70/154.54 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),V_x_2) = c_Option_Ooption_ONone(T_b) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_partition__set,axiom, % 154.70/154.54 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] : % 154.70/154.54 ( c_List_Opartition(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_yes_2),V_no_2) % 154.70/154.54 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_yes_2)),hAPP(c_List_Oset(T_a),V_no_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_option__map__o__empty,axiom, % 154.70/154.54 ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_b),tc_Option_Ooption(T_a),T_c,hAPP(c_Option_Omap(T_b,T_a),V_f_2)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))),V_x_2) = c_Option_Ooption_ONone(T_a) ). % 154.70/154.54 % 154.70/154.54 fof(fact_option__map__is__None,axiom, % 154.70/154.54 ! [V_opt_2,V_f_2,T_a,T_b] : % 154.70/154.54 ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_a) % 154.70/154.54 <=> V_opt_2 = c_Option_Ooption_ONone(T_b) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_option__map__None,axiom, % 154.70/154.54 ! [V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),c_Option_Ooption_ONone(T_b)) = c_Option_Ooption_ONone(T_a) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__of__Cons__code_I1_J,axiom, % 154.70/154.54 ! [V_k,T_a,T_b] : hAPP(hAPP(c_Map_Omap__of(T_b,T_a),c_List_Olist_ONil(tc_prod(T_b,T_a))),V_k) = c_Option_Ooption_ONone(T_a) ). % 154.70/154.54 % 154.70/154.54 fof(fact_set__empty__eq,axiom, % 154.70/154.54 ! [V_xo_2,T_a] : % 154.70/154.54 ( c_Option_Oset(T_a,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.54 <=> V_xo_2 = c_Option_Ooption_ONone(T_a) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_Option_Oset_Osimps_I1_J,axiom, % 154.70/154.54 ! [T_a] : c_Option_Oset(T_a,c_Option_Ooption_ONone(T_a)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_empty__upd__none,axiom, % 154.70/154.54 ! [V_xa_2,V_x_2,T_a,T_b] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a))),V_x_2),c_Option_Ooption_ONone(T_a)),V_xa_2) = c_Option_Ooption_ONone(T_a) ). % 154.70/154.54 % 154.70/154.54 fof(fact_dom__def,axiom, % 154.70/154.54 ! [V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,V_m_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,tc_Option_Ooption(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_a),c_fequal),V_m_2)),c_Option_Ooption_ONone(T_b)))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_domIff,axiom, % 154.70/154.54 ! [V_m_2,T_b,V_a_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2))) % 154.70/154.54 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_b) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_dom__empty,axiom, % 154.70/154.54 ! [T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_dom__eq__empty__conv,axiom, % 154.70/154.54 ! [V_f_2,T_b,T_a] : % 154.70/154.54 ( c_Map_Odom(T_a,T_b,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.54 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_restrict__map__def,axiom, % 154.70/154.54 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 154.70/154.54 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.54 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) ) % 154.70/154.54 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.54 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_restrict__out,axiom, % 154.70/154.54 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 154.70/154.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 154.70/154.54 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_restrict__map__empty,axiom, % 154.70/154.54 ! [V_x_2,V_D_2,T_a,T_b] : hAPP(c_Map_Orestrict__map(T_b,T_a,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a)),V_D_2),V_x_2) = c_Option_Ooption_ONone(T_a) ). % 154.70/154.54 % 154.70/154.54 fof(fact_restrict__map__to__empty,axiom, % 154.70/154.54 ! [V_x_2,V_m_2,T_a,T_b] : hAPP(c_Map_Orestrict__map(T_b,T_a,V_m_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2) = c_Option_Ooption_ONone(T_a) ). % 154.70/154.54 % 154.70/154.54 fof(fact_option_Osimps_I4_J,axiom, % 154.70/154.54 ! [V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_Option_Ooption_Ooption__case(T_a,T_b,V_f1_2,V_f2_2),c_Option_Ooption_ONone(T_b)) = V_f1_2 ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__upd__nonempty,axiom, % 154.70/154.54 ! [V_x_2,V_k_2,V_t_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) != hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_not__None__eq,axiom, % 154.70/154.54 ! [T_a,V_x_2] : % 154.70/154.54 ( V_x_2 != c_Option_Ooption_ONone(T_a) % 154.70/154.54 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_a),B_y) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_not__Some__eq,axiom, % 154.70/154.54 ! [T_a,V_x_2] : % 154.70/154.54 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_a),B_y) % 154.70/154.54 <=> V_x_2 = c_Option_Ooption_ONone(T_a) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_option_Osimps_I3_J,axiom, % 154.70/154.54 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ). % 154.70/154.54 % 154.70/154.54 fof(fact_option_Osimps_I2_J,axiom, % 154.70/154.54 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ). % 154.70/154.54 % 154.70/154.54 fof(fact_ran__empty,axiom, % 154.70/154.54 ! [T_a,T_b] : c_Map_Oran(T_b,T_a,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__of_Osimps_I1_J,axiom, % 154.70/154.54 ! [V_x_1,T_b,T_a] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),c_List_Olist_ONil(tc_prod(T_a,T_b))),V_x_1) = c_Option_Ooption_ONone(T_b) ). % 154.70/154.54 % 154.70/154.54 fof(fact_Option_Omap__def,axiom, % 154.70/154.54 ! [V_f_2,T_b,T_a] : hAPP(c_Option_Omap(T_a,T_b),V_f_2) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_a,c_Option_Ooption_ONone(T_b),hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_a),c_Option_Ooption_OSome(T_b)),V_f_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_option_Osize_I3_J,axiom, % 154.70/154.54 ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(fact_option_Osize_I1_J,axiom, % 154.70/154.54 ! [V_fa_2,T_a] : c_Option_Ooption_Ooption__size(T_a,V_fa_2,c_Option_Ooption_ONone(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(fact_dom__minus,axiom, % 154.70/154.54 ! [V_A_2,T_b,T_a,V_x_2,V_f_2] : % 154.70/154.54 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_a) % 154.70/154.54 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,V_f_2)),V_A_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_WT_OBody,axiom, % 154.70/154.54 ! [V_pn] : % 154.70/154.54 ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom) % 154.70/154.54 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_partition__P,axiom, % 154.70/154.54 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] : % 154.70/154.54 ( c_List_Opartition(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_yes_2),V_no_2) % 154.70/154.54 => ( ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_yes_2))) % 154.70/154.54 => hBOOL(hAPP(V_P_2,B_x)) ) % 154.70/154.54 & ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_no_2))) % 154.70/154.54 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_partition_Osimps_I1_J,axiom, % 154.70/154.54 ! [V_P_2,T_a] : c_List_Opartition(T_a,V_P_2,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(T_a)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_ran__map__upd,axiom, % 154.70/154.54 ! [V_b_2,T_b,T_a,V_a_2,V_m_2] : % 154.70/154.54 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_a) % 154.70/154.54 => c_Map_Oran(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__of__zip__is__None,axiom, % 154.70/154.54 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] : % 154.70/154.54 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 154.70/154.54 => ( hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)),V_x_2) = c_Option_Ooption_ONone(T_b) % 154.70/154.54 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_partition_Osimps_I2_J,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,V_P_2,T_a] : c_List_Opartition(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_List_Olist(T_a)),hAPP(c_If(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(V_P_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_List_Olist_OCons(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),c_COMBB(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_List_Olist(T_a))),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(c_List_Olist_OCons(T_a),V_x_2)))),c_List_Opartition(T_a,V_P_2,V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_dom__fun__upd,axiom, % 154.70/154.54 ! [V_x_2,V_f_2,T_b,T_a,V_y_2] : % 154.70/154.54 ( ( V_y_2 = c_Option_Ooption_ONone(T_a) % 154.70/154.54 => c_Map_Odom(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) % 154.70/154.54 & ( V_y_2 != c_Option_Ooption_ONone(T_a) % 154.70/154.54 => c_Map_Odom(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Map_Odom(T_b,T_a,V_f_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_restrict__complement__singleton__eq,axiom, % 154.70/154.54 ! [V_x_2,V_f_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,V_f_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),c_Option_Ooption_ONone(T_b)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__of__eq__None__iff,axiom, % 154.70/154.54 ! [V_x_2,V_xys_2,T_a,T_b] : % 154.70/154.54 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_a) % 154.70/154.54 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xys_2)))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_UNIV__option__conv,axiom, % 154.70/154.54 ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)),hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_a),c_Option_Ooption_OSome(T_a)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_dom__eq__singleton__conv,axiom, % 154.70/154.54 ! [V_x_2,V_f_2,T_b,T_a] : % 154.70/154.54 ( c_Map_Odom(T_a,T_b,V_f_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) % 154.70/154.54 <=> ? [B_v] : V_f_2 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),B_v)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_fun__upd__None__restrict,axiom, % 154.70/154.54 ! [V_m_2,T_b,V_D_2,V_x_2,T_a] : % 154.70/154.54 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 154.70/154.54 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_b)) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ) % 154.70/154.54 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 154.70/154.54 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_b)) = c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_lists__Int__eq,axiom, % 154.70/154.54 ! [V_B_2,V_A_2,T_a] : c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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_A_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),c_List_Olists(T_a,V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),c_List_Olists(T_a,V_B_2))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_lists__IntI,axiom, % 154.70/154.54 ! [V_B_2,V_A_2,V_l_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_A_2))) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_B_2))) % 154.70/154.54 => hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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_A_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_l_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_listsp_ONil,axiom, % 154.70/154.54 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_append__in__listsp__conv,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,V_A_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) % 154.70/154.54 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) % 154.70/154.54 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_ys_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_listsp_Oequations_I2_J,axiom, % 154.70/154.54 ! [V_a2_2,V_a1_2,V_A_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a2_2))) % 154.70/154.54 <=> ( hBOOL(hAPP(V_A_2,V_a1_2)) % 154.70/154.54 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_a2_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_in__listsp__conv__set,axiom, % 154.70/154.54 ! [V_xs_2,V_A_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) % 154.70/154.54 <=> ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_listsp__conj__eq,axiom, % 154.70/154.54 ! [V_x_2,V_B_2,V_A_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_A_2)),V_B_2)),V_x_2)) % 154.70/154.54 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_x_2)) % 154.70/154.54 & hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_x_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_listsp__inf__eq,axiom, % 154.70/154.54 ! [V_B_2,V_A_2,T_a] : c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),c_List_Olistsp(T_a,V_A_2)),c_List_Olistsp(T_a,V_B_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_listsp__infI,axiom, % 154.70/154.54 ! [V_B_2,V_l_2,V_A_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_l_2)) % 154.70/154.54 => ( hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_l_2)) % 154.70/154.54 => hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_l_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_listsp_Oequations_I1_J,axiom, % 154.70/154.54 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_listsp__mono,axiom, % 154.70/154.54 ! [V_B_2,V_A_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 154.70/154.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),c_List_Olistsp(T_a,V_A_2)),c_List_Olistsp(T_a,V_B_2))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_listsp__lists__eq,axiom, % 154.70/154.54 ! [V_x_2,V_A_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),V_x_2)) % 154.70/154.54 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_x_2),c_List_Olists(T_a,V_A_2))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_,axiom, % 154.70/154.54 ! [V_y_2,V_x_2,T_a] : c_Smallcheck_Oorelse(T_a,V_x_2,V_y_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_a,V_y_2,c_Option_Ooption_OSome(T_a)),V_x_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_product_Osimps_I2_J,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,V_x_2,T_b,T_a] : c_Enum_Oproduct(T_a,T_b,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_a,T_b)),hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2)),V_ys_2)),c_Enum_Oproduct(T_a,T_b,V_xs_2,V_ys_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_product_Osimps_I1_J,axiom, % 154.70/154.54 ! [V_uu,T_b,T_a] : c_Enum_Oproduct(T_a,T_b,c_List_Olist_ONil(T_a),V_uu) = c_List_Olist_ONil(tc_prod(T_a,T_b)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_distinct__product,axiom, % 154.70/154.54 ! [V_ys,T_b,V_xs,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 154.70/154.54 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys)) % 154.70/154.54 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_product__list__set,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_List_Oset(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_List_Oset(T_b),V_ys_2))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sublists__powset,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : hAPP(c_Set_Oimage(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),c_List_Oset(T_a)),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_Osublists(T_a,V_xs_2))) = hAPP(c_Set_OPow(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_length__sublists,axiom, % 154.70/154.54 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sublists_Osimps_I1_J,axiom, % 154.70/154.54 ! [T_a] : c_Enum_Osublists(T_a,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sublists_Osimps_I2_J,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,T_a] : c_Enum_Osublists(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs_2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(T_a)),tc_fun(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),tc_List_Olist(tc_List_Olist(T_a))),c_List_Oappend(tc_List_Olist(T_a))),hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(c_List_Olist_OCons(T_a),V_x_2)))),c_COMBI(tc_List_Olist(tc_List_Olist(T_a))))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_distinct__set__sublists,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 154.70/154.54 => hBOOL(hAPP(c_List_Odistinct(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),c_List_Oset(T_a)),c_Enum_Osublists(T_a,V_xs_2)))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_set__n__lists,axiom, % 154.70/154.54 ! [V_xs_2,V_n_2,T_a] : hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,V_xs_2)) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),hAPP(c_List_Oset(T_a),V_xs_2)))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_enum__the__def,axiom, % 154.70/154.54 ! [V_P_2,T_a] : c_Enum_Oenum__the(T_a,V_P_2) = c_HOL_OThe(T_a,V_P_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_distinct__n__lists,axiom, % 154.70/154.54 ! [V_n,V_xs,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 154.70/154.54 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_n__lists_Osimps_I1_J,axiom, % 154.70/154.54 ! [V_xs,T_a] : c_Enum_On__lists(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xs) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_n__lists__Nil,axiom, % 154.70/154.54 ! [T_a,V_n] : % 154.70/154.54 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.54 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ) % 154.70/154.54 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.54 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_length__n__lists,axiom, % 154.70/154.54 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_On__lists(T_a,V_n,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n) ). % 154.70/154.54 % 154.70/154.54 fof(fact_length__n__lists__elem,axiom, % 154.70/154.54 ! [V_xs_2,V_n_2,V_ys_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,V_xs_2)))) % 154.70/154.54 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_full__small__int__def,axiom, % 154.70/154.54 ! [V_d_2,V_f_2] : c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,V_f_2,V_d_2) = c_Smallcheck_Ofull__small_H(V_f_2,hAPP(c_Code__Numeral_Oint__of,V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,V_d_2))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_small_H_Osimps,axiom, % 154.70/154.54 ! [V_f_2,V_i_2,V_d_2] : % 154.70/154.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 154.70/154.54 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 154.70/154.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 154.70/154.54 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_small_H_Opsimps,axiom, % 154.70/154.54 ! [V_i_2,V_d_2,V_f_2] : % 154.70/154.54 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),V_f_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2)))) % 154.70/154.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 154.70/154.54 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 154.70/154.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 154.70/154.54 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2)) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_small__int__def,axiom, % 154.70/154.54 ! [V_d_2,V_f_2] : hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),V_f_2),V_d_2) = c_Smallcheck_Osmall_H(V_f_2,hAPP(c_Code__Numeral_Oint__of,V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,V_d_2))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_small__prod__def,axiom, % 154.70/154.54 ! [V_d_2,V_f_2,T_a,T_b] : % 154.70/154.54 ( ( class_Smallcheck_Osmall(T_b) % 154.70/154.54 & class_Smallcheck_Osmall(T_a) ) % 154.70/154.54 => hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(T_a,T_b)),V_f_2),V_d_2) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(T_a),hAPP(hAPP(c_COMBC(T_a,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_a),c_Smallcheck_Osmall__class_Osmall(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),T_b),V_f_2)),c_Product__Type_OPair(T_a,T_b)))),V_d_2)),V_d_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_small_H_Opinduct,axiom, % 154.70/154.54 ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] : % 154.70/154.54 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),V_a0_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a1_2),V_a2_2)))) % 154.70/154.54 => ( ! [B_f,B_d,B_i] : % 154.70/154.54 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),B_f),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i)))) % 154.70/154.54 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) % 154.70/154.54 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) % 154.70/154.54 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) % 154.70/154.54 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i)) ) ) % 154.70/154.54 => hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__of__zip__enum__inject,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,T_a,T_b] : % 154.70/154.54 ( ( class_Enum_Oenum(T_b) % 154.70/154.54 & class_Enum_Oenum(T_a) ) % 154.70/154.54 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b)) % 154.70/154.54 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b)) % 154.70/154.54 => ( hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),c_Enum_Oenum__class_Oenum(T_b)),V_xs_2))) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),c_Enum_Oenum__class_Oenum(T_b)),V_ys_2))) % 154.70/154.54 => V_xs_2 = V_ys_2 ) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_enum__prod__def,axiom, % 154.70/154.54 ! [T_b,T_a] : % 154.70/154.54 ( ( class_Enum_Oenum(T_a) % 154.70/154.54 & class_Enum_Oenum(T_b) ) % 154.70/154.54 => c_Enum_Oenum__class_Oenum(tc_prod(T_a,T_b)) = c_Enum_Oproduct(T_a,T_b,c_Enum_Oenum__class_Oenum(T_a),c_Enum_Oenum__class_Oenum(T_b)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_UNIV__enum,axiom, % 154.70/154.54 ! [T_a] : % 154.70/154.54 ( class_Enum_Oenum(T_a) % 154.70/154.54 => c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_enum__UNIV,axiom, % 154.70/154.54 ! [T_a] : % 154.70/154.54 ( class_Enum_Oenum(T_a) % 154.70/154.54 => hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_in__enum,axiom, % 154.70/154.54 ! [V_x_2,T_a] : % 154.70/154.54 ( class_Enum_Oenum(T_a) % 154.70/154.54 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_enum__option__def,axiom, % 154.70/154.54 ! [T_a] : % 154.70/154.54 ( class_Enum_Oenum(T_a) % 154.70/154.54 => c_Enum_Oenum__class_Oenum(tc_Option_Ooption(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)),hAPP(hAPP(c_List_Omap(T_a,tc_Option_Ooption(T_a)),c_Option_Ooption_OSome(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_enum__distinct,axiom, % 154.70/154.54 ! [T_a] : % 154.70/154.54 ( class_Enum_Oenum(T_a) % 154.70/154.54 => hBOOL(hAPP(c_List_Odistinct(T_a),c_Enum_Oenum__class_Oenum(T_a))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_enum__fun__code,axiom, % 154.70/154.54 ! [T_b,T_a] : % 154.70/154.54 ( ( class_Enum_Oenum(T_a) % 154.70/154.54 & class_HOL_Oequal(T_a) % 154.70/154.54 & class_Enum_Oenum(T_b) ) % 154.70/154.54 => c_Enum_Oenum__class_Oenum(tc_fun(T_a,T_b)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),c_Enum_On__lists(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a)),c_Enum_Oenum__class_Oenum(T_b))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_enum__fun__def,axiom, % 154.70/154.54 ! [T_b,T_a] : % 154.70/154.54 ( ( class_Enum_Oenum(T_a) % 154.70/154.54 & class_Enum_Oenum(T_b) ) % 154.70/154.54 => c_Enum_Oenum__class_Oenum(tc_fun(T_a,T_b)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),c_Enum_On__lists(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a)),c_Enum_Oenum__class_Oenum(T_b))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_all__n__lists__def,axiom, % 154.70/154.54 ! [V_n_2,V_P_2,T_a] : % 154.70/154.54 ( class_Enum_Oenum(T_a) % 154.70/154.54 => ( c_Enum_Oall__n__lists(T_a,V_P_2,V_n_2) % 154.70/154.54 <=> ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,c_Enum_Oenum__class_Oenum(T_a))))) % 154.70/154.54 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_ex__n__lists__def,axiom, % 154.70/154.54 ! [V_n_2,V_P_2,T_a] : % 154.70/154.54 ( class_Enum_Oenum(T_a) % 154.70/154.54 => ( c_Enum_Oex__n__lists(T_a,V_P_2,V_n_2) % 154.70/154.54 <=> ? [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,c_Enum_Oenum__class_Oenum(T_a))))) % 154.70/154.54 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_enum__all__fun__def,axiom, % 154.70/154.54 ! [V_P_2,T_a,T_b] : % 154.70/154.54 ( ( class_Enum_Oenum(T_b) % 154.70/154.54 & class_Enum_Oenum(T_a) ) % 154.70/154.54 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2)) % 154.70/154.54 <=> c_Enum_Oall__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_enum__ex__fun__def,axiom, % 154.70/154.54 ! [V_P_2,T_a,T_b] : % 154.70/154.54 ( ( class_Enum_Oenum(T_b) % 154.70/154.54 & class_Enum_Oenum(T_a) ) % 154.70/154.54 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2)) % 154.70/154.54 <=> c_Enum_Oex__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_enum__all__prod__def,axiom, % 154.70/154.54 ! [V_P_2,T_a,T_b] : % 154.70/154.54 ( ( class_Enum_Oenum(T_b) % 154.70/154.54 & class_Enum_Oenum(T_a) ) % 154.70/154.54 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_a,T_b)),V_P_2)) % 154.70/154.54 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_Enum_Oenum__class_Oenum__all(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b))))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_enum__ex__prod__def,axiom, % 154.70/154.54 ! [V_P_2,T_a,T_b] : % 154.70/154.54 ( ( class_Enum_Oenum(T_b) % 154.70/154.54 & class_Enum_Oenum(T_a) ) % 154.70/154.54 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_a,T_b)),V_P_2)) % 154.70/154.54 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_Enum_Oenum__class_Oenum__ex(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b))))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_all__code,axiom, % 154.70/154.54 ! [V_P_2,T_a] : % 154.70/154.54 ( class_Enum_Oenum(T_a) % 154.70/154.54 => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 154.70/154.54 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_exists__code,axiom, % 154.70/154.54 ! [V_P_2,T_a] : % 154.70/154.54 ( class_Enum_Oenum(T_a) % 154.70/154.54 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 154.70/154.54 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_enum__all,axiom, % 154.70/154.54 ! [V_P_2,T_a] : % 154.70/154.54 ( class_Enum_Oenum(T_a) % 154.70/154.54 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) % 154.70/154.54 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_enum__ex,axiom, % 154.70/154.54 ! [V_P_2,T_a] : % 154.70/154.54 ( class_Enum_Oenum(T_a) % 154.70/154.54 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) % 154.70/154.54 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_enum__all__option__def,axiom, % 154.70/154.54 ! [V_P_2,T_a] : % 154.70/154.54 ( class_Enum_Oenum(T_a) % 154.70/154.54 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(T_a)),V_P_2)) % 154.70/154.54 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) % 154.70/154.54 & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_HOL_Obool,T_a),V_P_2),c_Option_Ooption_OSome(T_a)))) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_enum__ex__option__def,axiom, % 154.70/154.54 ! [V_P_2,T_a] : % 154.70/154.54 ( class_Enum_Oenum(T_a) % 154.70/154.54 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(T_a)),V_P_2)) % 154.70/154.54 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) % 154.70/154.54 | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_HOL_Obool,T_a),V_P_2),c_Option_Ooption_OSome(T_a)))) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_order__fun_I1_J,axiom, % 154.70/154.54 ! [V_g_2,V_f_2,T_a,T_b] : % 154.70/154.54 ( ( class_Orderings_Oorder(T_b) % 154.70/154.54 & class_Enum_Oenum(T_a) ) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 154.70/154.54 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBS(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_f_2)),V_g_2))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_order__fun_I2_J,axiom, % 154.70/154.54 ! [V_g_2,V_f_2,T_a,T_b] : % 154.70/154.54 ( ( class_Orderings_Oorder(T_b) % 154.70/154.54 & class_Enum_Oenum(T_a) ) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 154.70/154.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 154.70/154.54 & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBS(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_g_2)))) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_enum__ex__fun__code,axiom, % 154.70/154.54 ! [V_P_2,T_a,T_b] : % 154.70/154.54 ( ( class_Enum_Oenum(T_b) % 154.70/154.54 & class_Enum_Oenum(T_a) % 154.70/154.54 & class_HOL_Oequal(T_a) ) % 154.70/154.54 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2)) % 154.70/154.54 <=> c_Enum_Oex__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_enum__all__fun__code,axiom, % 154.70/154.54 ! [V_P_2,T_a,T_b] : % 154.70/154.54 ( ( class_Enum_Oenum(T_b) % 154.70/154.54 & class_Enum_Oenum(T_a) % 154.70/154.54 & class_HOL_Oequal(T_a) ) % 154.70/154.54 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2)) % 154.70/154.54 <=> c_Enum_Oall__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__of__zip__enum__is__Some,axiom, % 154.70/154.54 ! [V_x,V_ys,T_b,T_a] : % 154.70/154.54 ( class_Enum_Oenum(T_a) % 154.70/154.54 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a)) % 154.70/154.54 => ? [B_y] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a)),V_ys)),V_x) = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all2__def,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 154.70/154.54 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 154.70/154.54 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 154.70/154.54 & ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) % 154.70/154.54 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all2__lengthD,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 154.70/154.54 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 154.70/154.54 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all2__dropI,axiom, % 154.70/154.54 ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_b,T_a] : % 154.70/154.54 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,V_bs_2) % 154.70/154.54 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_bs_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all2__takeI,axiom, % 154.70/154.54 ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 154.70/154.54 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 154.70/154.54 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_ys_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all2__eq,axiom, % 154.70/154.54 ! [T_a,V_ys_2,V_xs_2] : % 154.70/154.54 ( V_xs_2 = V_ys_2 % 154.70/154.54 <=> c_List_Olist__all2(T_a,T_a,c_fequal,V_xs_2,V_ys_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all2__appendI,axiom, % 154.70/154.54 ! [V_d_2,V_c_2,V_b_2,V_a_2,V_P_2,T_b,T_a] : % 154.70/154.54 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) % 154.70/154.54 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_c_2,V_d_2) % 154.70/154.54 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_a_2),V_c_2),hAPP(hAPP(c_List_Oappend(T_b),V_b_2),V_d_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all2__Nil,axiom, % 154.70/154.54 ! [V_ys_2,V_P_2,T_b,T_a] : % 154.70/154.54 ( c_List_Olist__all2(T_a,T_b,V_P_2,c_List_Olist_ONil(T_a),V_ys_2) % 154.70/154.54 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all2__Nil2,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_b,T_a] : % 154.70/154.54 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,c_List_Olist_ONil(T_b)) % 154.70/154.54 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all2__append,axiom, % 154.70/154.54 ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_b,V_xs_2,T_a] : % 154.70/154.54 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 154.70/154.54 => ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2)) % 154.70/154.54 <=> ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 154.70/154.54 & c_List_Olist__all2(T_a,T_b,V_P_2,V_us_2,V_vs_2) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all2__map2,axiom, % 154.70/154.54 ! [V_bs_2,V_f_2,T_c,V_as_2,V_P_2,T_b,T_a] : % 154.70/154.54 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_bs_2)) % 154.70/154.54 <=> c_List_Olist__all2(T_a,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_c)),V_P_2)),V_f_2),V_as_2,V_bs_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all2__map1,axiom, % 154.70/154.54 ! [V_bs_2,V_as_2,V_f_2,T_c,V_P_2,T_b,T_a] : % 154.70/154.54 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_as_2),V_bs_2) % 154.70/154.54 <=> c_List_Olist__all2(T_c,T_b,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),V_P_2),V_f_2),V_as_2,V_bs_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all2__Cons,axiom, % 154.70/154.54 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_b,T_a] : % 154.70/154.54 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) % 154.70/154.54 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 154.70/154.54 & c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all2__nthD2,axiom, % 154.70/154.54 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 154.70/154.54 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))) % 154.70/154.54 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),V_p_2))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all2__nthD,axiom, % 154.70/154.54 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 154.70/154.54 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.54 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),V_p_2))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all2__conv__all__nth,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 154.70/154.54 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 154.70/154.54 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 154.70/154.54 & ! [B_i] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.54 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i))) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all2__update__cong2,axiom, % 154.70/154.54 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 154.70/154.54 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))) % 154.70/154.54 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_b,V_ys_2),V_i_2),V_y_2)) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all2__update__cong,axiom, % 154.70/154.54 ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_b,V_xs_2,T_a,V_i_2] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.54 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 154.70/154.54 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_b,V_ys_2),V_i_2),V_y_2)) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all2I,axiom, % 154.70/154.54 ! [V_P_2,V_b_2,V_a_2,T_b,T_a] : % 154.70/154.54 ( ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_a_2),V_b_2)))) % 154.70/154.54 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) % 154.70/154.54 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_b_2) % 154.70/154.54 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_all__nth__imp__all__set,axiom, % 154.70/154.54 ! [V_x_2,V_P_2,V_xs_2,T_a] : % 154.70/154.54 ( ! [B_i] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.54 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_fun__left__comm_Ofold__set__remdups,axiom, % 154.70/154.54 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] : % 154.70/154.54 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 154.70/154.54 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),V_f_2),V_y_2),c_List_Oremdups(T_a,V_xs_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__removeAll__inj__on,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 154.70/154.54 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_b,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_distinct__remdups,axiom, % 154.70/154.54 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_length__remdups__leq,axiom, % 154.70/154.54 ! [V_xs,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_removeAll__id,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2) = V_xs_2 ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_remdups__id__iff__distinct,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : % 154.70/154.54 ( c_List_Oremdups(T_a,V_xs_2) = V_xs_2 % 154.70/154.54 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_distinct__removeAll,axiom, % 154.70/154.54 ! [V_x,V_xs,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 154.70/154.54 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_distinct__remdups__id,axiom, % 154.70/154.54 ! [V_xs,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 154.70/154.54 => c_List_Oremdups(T_a,V_xs) = V_xs ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_remove1__remdups,axiom, % 154.70/154.54 ! [V_x,V_xs,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 154.70/154.54 => c_List_Oremove1(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oremove1(T_a,V_x,V_xs)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_length__remdups__eq,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : % 154.70/154.54 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) % 154.70/154.54 <=> c_List_Oremdups(T_a,V_xs_2) = V_xs_2 ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_set__remdups,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_remdups__remdups,axiom, % 154.70/154.54 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ). % 154.70/154.54 % 154.70/154.54 fof(fact_removeAll__append,axiom, % 154.70/154.54 ! [V_ys,V_xs,V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)),hAPP(c_List_OremoveAll(T_a,V_x),V_ys)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_remdups_Osimps_I1_J,axiom, % 154.70/154.54 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 154.70/154.54 % 154.70/154.54 fof(fact_remdups__eq__nil__right__iff,axiom, % 154.70/154.54 ! [V_x_2,T_a] : % 154.70/154.54 ( c_List_Olist_ONil(T_a) = c_List_Oremdups(T_a,V_x_2) % 154.70/154.54 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_removeAll_Osimps_I1_J,axiom, % 154.70/154.54 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 154.70/154.54 % 154.70/154.54 fof(fact_remdups__eq__nil__iff,axiom, % 154.70/154.54 ! [V_x_2,T_a] : % 154.70/154.54 ( c_List_Oremdups(T_a,V_x_2) = c_List_Olist_ONil(T_a) % 154.70/154.54 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_remdups__map__remdups,axiom, % 154.70/154.54 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oremdups(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oremdups(T_b,V_xs_2))) = c_List_Oremdups(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_removeAll_Osimps_I2_J,axiom, % 154.70/154.54 ! [V_xs,T_a,V_y,V_x] : % 154.70/154.54 ( ( V_x = V_y % 154.70/154.54 => hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) % 154.70/154.54 & ( V_x != V_y % 154.70/154.54 => hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_distinct__remove1__removeAll,axiom, % 154.70/154.54 ! [V_x,V_xs,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 154.70/154.54 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_remdups_Osimps_I2_J,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.54 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => c_List_Oremdups(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_Oremdups(T_a,V_xs_2) ) % 154.70/154.54 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => c_List_Oremdups(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oremdups(T_a,V_xs_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_length__remdups__card__conv,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__removeAll__inj,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 154.70/154.54 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 154.70/154.54 => hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_b,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_set__removeAll,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_length__remdups__concat,axiom, % 154.70/154.54 ! [V_xss_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,c_List_Oconcat(T_a,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2)),c_List_Oset(T_a))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__list__of__set__sort__remdups,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(c_List_Oset(T_a),V_xs_2)) = c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),c_List_Oremdups(T_a,V_xs_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_concat_Osimps_I2_J,axiom, % 154.70/154.54 ! [V_xs,V_x,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),V_x),c_List_Oconcat(T_a,V_xs)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__concat,axiom, % 154.70/154.54 ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_Nil__eq__concat__conv,axiom, % 154.70/154.54 ! [V_xss_2,T_a] : % 154.70/154.54 ( c_List_Olist_ONil(T_a) = c_List_Oconcat(T_a,V_xss_2) % 154.70/154.54 <=> ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) % 154.70/154.54 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_concat__eq__Nil__conv,axiom, % 154.70/154.54 ! [V_xss_2,T_a] : % 154.70/154.54 ( c_List_Oconcat(T_a,V_xss_2) = c_List_Olist_ONil(T_a) % 154.70/154.54 <=> ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) % 154.70/154.54 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sort__key__simps_I1_J,axiom, % 154.70/154.54 ! [V_f_2,T_a,T_b] : % 154.70/154.54 ( class_Orderings_Olinorder(T_b) % 154.70/154.54 => c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_concat_Osimps_I1_J,axiom, % 154.70/154.54 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ). % 154.70/154.54 % 154.70/154.54 fof(fact_concat__conv__foldl,axiom, % 154.70/154.54 ! [V_xss_2,T_a] : c_List_Oconcat(T_a,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_xss_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_foldl__conv__concat,axiom, % 154.70/154.54 ! [V_xss_2,V_xs_2,T_a] : hAPP(c_List_Ofoldl(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Oappend(T_a),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_Oconcat(T_a,V_xss_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_set__sort,axiom, % 154.70/154.54 ! [V_xs_2,V_f_2,T_a,T_b] : % 154.70/154.54 ( class_Orderings_Olinorder(T_b) % 154.70/154.54 => hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_length__sort,axiom, % 154.70/154.54 ! [V_xs_2,V_f_2,T_a,T_b] : % 154.70/154.54 ( class_Orderings_Olinorder(T_b) % 154.70/154.54 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_distinct__sort,axiom, % 154.70/154.54 ! [V_xs_2,V_f_2,T_a,T_b] : % 154.70/154.54 ( class_Orderings_Olinorder(T_b) % 154.70/154.54 => ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2))) % 154.70/154.54 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_length__concat,axiom, % 154.70/154.54 ! [V_xss_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oconcat(T_a,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xss_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_set__concat,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oconcat(T_a,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)),c_List_Oset(T_a)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sort__key__simps_I2_J,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 154.70/154.54 ( class_Orderings_Olinorder(T_b) % 154.70/154.54 => c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_concat__append,axiom, % 154.70/154.54 ! [V_ys,V_xs,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Oappend(tc_List_Olist(T_a)),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oconcat(T_a,V_xs)),c_List_Oconcat(T_a,V_ys)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sort__foldl__insort,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),T_a,hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a))),c_List_Olist_ONil(T_a)),V_xs_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_concat__eq__concat__iff,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,T_a] : % 154.70/154.54 ( ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)))) % 154.70/154.54 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),B_x)) ) % 154.70/154.54 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_ys_2) % 154.70/154.54 => ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2) % 154.70/154.54 <=> V_xs_2 = V_ys_2 ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_concat__injective,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,T_a] : % 154.70/154.54 ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2) % 154.70/154.54 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_ys_2) % 154.70/154.54 => ( ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)))) % 154.70/154.54 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),B_x)) ) % 154.70/154.54 => V_xs_2 = V_ys_2 ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_concat__map__singleton,axiom, % 154.70/154.54 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_b),c_List_Olist_OCons(T_a)),V_f_2)),c_List_Olist_ONil(T_a))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_n__lists_Osimps_I2_J,axiom, % 154.70/154.54 ! [V_xs_2,V_n_2,T_a] : c_Enum_On__lists(T_a,hAPP(c_Nat_OSuc,V_n_2),V_xs_2) = c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_List_Omap(T_a,tc_List_Olist(T_a))),hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)))),V_xs_2)),c_Enum_On__lists(T_a,V_n_2,V_xs_2))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_transpose_Osimps_I3_J,axiom, % 154.70/154.54 ! [V_xss_2,V_xs_2,V_x_2,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)))),c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2))))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_transpose__aux__filter__head,axiom, % 154.70/154.54 ! [V_xss_2,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),c_List_Ohd(T_a)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xss_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_filter__concat,axiom, % 154.70/154.54 ! [V_xs_2,V_p_2,T_a] : hAPP(c_List_Ofilter(T_a,V_p_2),c_List_Oconcat(T_a,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Ofilter(T_a,V_p_2)),V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_filter__sort,axiom, % 154.70/154.54 ! [V_xs_2,V_f_2,V_P_2,T_a,T_b] : % 154.70/154.54 ( class_Orderings_Olinorder(T_b) % 154.70/154.54 => hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_transpose_Osimps_I2_J,axiom, % 154.70/154.54 ! [V_xss,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss)) = c_List_Otranspose(T_a,V_xss) ). % 154.70/154.54 % 154.70/154.54 fof(fact_partition__filter2,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Opartition(T_a,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_a,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot),V_P_2)),V_xs_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_distinct__filter,axiom, % 154.70/154.54 ! [V_P_2,V_xs_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 154.70/154.54 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sum__length__filter__compl,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_length__filter__le,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_filter__is__subset,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_filter__id__conv,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : % 154.70/154.54 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = V_xs_2 % 154.70/154.54 <=> ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_filter__insort__triv,axiom, % 154.70/154.54 ! [V_xs_2,V_f_2,T_a,V_x_2,V_P_2,T_b] : % 154.70/154.54 ( class_Orderings_Olinorder(T_b) % 154.70/154.54 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 154.70/154.54 => hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_remove1__filter__not,axiom, % 154.70/154.54 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 154.70/154.54 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 154.70/154.54 => c_List_Oremove1(T_a,V_x_2,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_filter__remove1,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,V_Q_2,T_a] : hAPP(c_List_Ofilter(T_a,V_Q_2),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = c_List_Oremove1(T_a,V_x_2,hAPP(c_List_Ofilter(T_a,V_Q_2),V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_filter__filter,axiom, % 154.70/154.54 ! [V_xs_2,V_Q_2,V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(c_List_Ofilter(T_a,V_Q_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_Q_2)),V_P_2)),V_xs_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_partition__filter1,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Opartition(T_a,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_filter__append,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)),hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_transpose_Osimps_I1_J,axiom, % 154.70/154.54 ! [T_a] : c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_filter_Osimps_I1_J,axiom, % 154.70/154.54 ! [V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 154.70/154.54 % 154.70/154.54 fof(fact_filter__empty__conv,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : % 154.70/154.54 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = c_List_Olist_ONil(T_a) % 154.70/154.54 <=> ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_filter_Osimps_I2_J,axiom, % 154.70/154.54 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 154.70/154.54 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 154.70/154.54 => hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) ) % 154.70/154.54 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 154.70/154.54 => hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_filter__map,axiom, % 154.70/154.54 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2)),V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_removeAll__filter__not,axiom, % 154.70/154.54 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 154.70/154.54 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 154.70/154.54 => hAPP(c_List_OremoveAll(T_a,V_x_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_remdups__filter,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : c_List_Oremdups(T_a,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Oremdups(T_a,V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_removeAll__filter__not__eq,axiom, % 154.70/154.54 ! [V_x_2,T_a] : c_List_OremoveAll(T_a,V_x_2) = c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(c_fequal,V_x_2))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_nth__transpose,axiom, % 154.70/154.54 ! [V_xs_2,T_a,V_i_2] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)))) % 154.70/154.54 => hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),c_List_Otranspose(T_a,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,T_a),c_List_Onth(T_a)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_xs_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_transpose__map__map,axiom, % 154.70/154.54 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),c_List_Otranspose(T_b,V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_set__filter,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(c_List_Oset(T_a),V_xs_2)))),V_P_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_length__filter__map,axiom, % 154.70/154.54 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2)),V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_length__filter__less,axiom, % 154.70/154.54 ! [V_P_2,V_xs_2,V_x_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 154.70/154.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_partition__filter__conv,axiom, % 154.70/154.54 ! [V_xs_2,V_f_2,T_a] : c_List_Opartition(T_a,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_a,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot),V_f_2)),V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_set__minus__filter__out,axiom, % 154.70/154.54 ! [V_y_2,V_xs_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_a),hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_filter__in__sublist,axiom, % 154.70/154.54 ! [V_s_2,V_xs_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 154.70/154.54 => hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_a,V_xs_2,V_s_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_transpose__empty,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : % 154.70/154.54 ( c_List_Otranspose(T_a,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_a)) % 154.70/154.54 <=> ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.54 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_length__filter__conv__card,axiom, % 154.70/154.54 ! [V_xs_2,V_p_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_p_2),V_xs_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_a),V_xs_2))))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_transpose__aux__filter__tail,axiom, % 154.70/154.54 ! [V_xss_2,T_a] : c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Otl(T_a)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xss_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_transpose_Opsimps_I3_J,axiom, % 154.70/154.54 ! [V_xss_2,V_xs_2,V_x_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2))) % 154.70/154.54 => c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)))),c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2))))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__filter__def,axiom, % 154.70/154.54 ! [V_xs_2,V_f_2,T_a,T_b] : c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),V_f_2)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_Option_Ooption(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool),T_b),c_fequal),V_f_2)),c_Option_Ooption_ONone(T_a)))),V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__filter__simps_I2_J,axiom, % 154.70/154.54 ! [V_f_2,T_a,T_b] : c_List_Omap__filter(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__of__filter__in,axiom, % 154.70/154.54 ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_a,T_b] : % 154.70/154.54 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_z_2) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2)) % 154.70/154.54 => hAPP(hAPP(c_Map_Omap__of(T_b,T_a),hAPP(c_List_Ofilter(tc_prod(T_b,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_HOL_Obool),V_P_2)),V_xs_2)),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_z_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__filter__simps_I1_J,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : c_List_Omap__filter(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(T_a),T_a,c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2))),hAPP(V_f_2,V_x_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sublist__shift__lemma__Suc,axiom, % 154.70/154.54 ! [V_is_2,V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_a,tc_Nat_Onat)),V_P_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_a,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_a,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_a,tc_Nat_Onat)),V_P_2),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_select__weigth__drop__zero,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : c_Random_Oselect__weight(T_a,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Oselect__weight(T_a,V_xs_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_pick__drop__zero,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : c_Random_Opick(T_a,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Opick(T_a,V_xs_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_transpose_Opsimps_I1_J,axiom, % 154.70/154.54 ! [T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a)))) % 154.70/154.54 => c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__filter__map__filter,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = c_List_Omap__filter(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,tc_Option_Ooption(T_a),tc_Option_Ooption(T_a)),hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_Option_Ooption(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_Option_Ooption(T_a))),T_b),c_If(tc_Option_Ooption(T_a))),V_P_2)),hAPP(hAPP(c_COMBB(T_a,tc_Option_Ooption(T_a),T_b),c_Option_Ooption_OSome(T_a)),V_f_2))),c_Option_Ooption_ONone(T_a)),V_xs_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_transpose_Opsimps_I2_J,axiom, % 154.70/154.54 ! [V_xss_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss_2))) % 154.70/154.54 => c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss_2)) = c_List_Otranspose(T_a,V_xss_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_transpose__max__length,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : c_List_Ofoldr(tc_List_Olist(T_a),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_a)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_transpose__aux__max,axiom, % 154.70/154.54 ! [V_xss_2,T_b,V_xs_2,T_a] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xss_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_foldr__append,axiom, % 154.70/154.54 ! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,c_List_Ofoldr(T_b,T_a,V_f_2,V_ys_2,V_a_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_foldr_Osimps_I1_J,axiom, % 154.70/154.54 ! [V_a_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b),V_a_2) = V_a_2 ). % 154.70/154.54 % 154.70/154.54 fof(fact_foldr_Osimps_I2_J,axiom, % 154.70/154.54 ! [V_a_2,V_xs_2,V_x_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,V_a_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_foldr__conv__foldl,axiom, % 154.70/154.54 ! [V_a_2,V_xs_2,T_a] : % 154.70/154.54 ( class_Groups_Oab__semigroup__add(T_a) % 154.70/154.54 => c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_xs_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_foldr__map,axiom, % 154.70/154.54 ! [V_a_2,V_xs_2,V_f_2,T_c,V_g_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_g_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_c,T_a,hAPP(c_Fun_Ocomp(T_b,tc_fun(T_a,T_a),T_c,V_g_2),V_f_2),V_xs_2,V_a_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_foldl__foldr1,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : % 154.70/154.54 ( class_Groups_Omonoid__add(T_a) % 154.70/154.54 => hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_xs_2) = c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_foldl__foldr1__lemma,axiom, % 154.70/154.54 ! [V_xs_2,V_a_2,T_a] : % 154.70/154.54 ( class_Groups_Omonoid__add(T_a) % 154.70/154.54 => hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,c_Groups_Ozero__class_Ozero(T_a))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_length__transpose,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = c_List_Ofoldr(tc_List_Olist(T_a),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_a)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sublist__def,axiom, % 154.70/154.54 ! [V_A_2,V_xs_2,T_a] : c_List_Osublist(T_a,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sublist__shift__lemma,axiom, % 154.70/154.54 ! [V_i_2,V_xs_2,V_A_2,T_a] : hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),c_List_Oupt(V_i_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_a,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(T_a,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_atLeastLessThan__upt,axiom, % 154.70/154.54 ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_set__upt,axiom, % 154.70/154.54 ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_length__upt,axiom, % 154.70/154.54 ! [V_j,V_i] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i) ). % 154.70/154.54 % 154.70/154.54 fof(fact_upt__Suc__append,axiom, % 154.70/154.54 ! [V_j,V_i] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 154.70/154.54 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_upt__Suc,axiom, % 154.70/154.54 ! [V_j,V_i] : % 154.70/154.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 154.70/154.54 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) ) % 154.70/154.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 154.70/154.54 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_upt__rec,axiom, % 154.70/154.54 ! [V_j,V_i] : % 154.70/154.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 154.70/154.54 => c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) ) % 154.70/154.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 154.70/154.54 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_upt__conv__Cons,axiom, % 154.70/154.54 ! [V_j,V_i] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 154.70/154.54 => c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_upt__conv__Nil,axiom, % 154.70/154.54 ! [V_i,V_j] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 154.70/154.54 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_upt__eq__Nil__conv,axiom, % 154.70/154.54 ! [V_j_2,V_i_2] : % 154.70/154.54 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat) % 154.70/154.54 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_upt__0,axiom, % 154.70/154.54 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(fact_upt__add__eq__append,axiom, % 154.70/154.54 ! [V_k,V_j,V_i] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 154.70/154.54 => c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),c_List_Oupt(V_j,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__list__of__set__range,axiom, % 154.70/154.54 ! [V_n_2,V_m_2] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = c_List_Oupt(V_m_2,V_n_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_take__upt,axiom, % 154.70/154.54 ! [V_n,V_m,V_i] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)),V_n)) % 154.70/154.54 => hAPP(hAPP(c_List_Otake(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_n)) = c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_hd__upt,axiom, % 154.70/154.54 ! [V_j,V_i] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 154.70/154.54 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_drop__upt,axiom, % 154.70/154.54 ! [V_j,V_i,V_m] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_j)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m),V_j) ). % 154.70/154.54 % 154.70/154.54 fof(fact_distinct__upt,axiom, % 154.70/154.54 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_upt__rec__number__of,axiom, % 154.70/154.54 ! [V_n,V_m] : % 154.70/154.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) % 154.70/154.54 => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) ) % 154.70/154.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) % 154.70/154.54 => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_upt__eq__Cons__conv,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,V_j_2,V_i_2] : % 154.70/154.54 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2) % 154.70/154.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) % 154.70/154.54 & V_i_2 = V_x_2 % 154.70/154.54 & c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_j_2) = V_xs_2 ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_last__upt,axiom, % 154.70/154.54 ! [V_j,V_i] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 154.70/154.54 => c_List_Olast(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__Suc__upt,axiom, % 154.70/154.54 ! [V_n_2,V_m_2] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(V_m_2,V_n_2)) = c_List_Oupt(hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_atLeastAtMost__upt,axiom, % 154.70/154.54 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_n_2,hAPP(c_Nat_OSuc,V_m_2))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_atLeast__upt,axiom, % 154.70/154.54 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_nth__upt,axiom, % 154.70/154.54 ! [V_j,V_k,V_i] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j)) % 154.70/154.54 => hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_greaterThanAtMost__upt,axiom, % 154.70/154.54 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_greaterThanLessThan__upt,axiom, % 154.70/154.54 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),V_m_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_atMost__upto,axiom, % 154.70/154.54 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__nth,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),hAPP(c_List_Onth(T_a),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) = V_xs_2 ). % 154.70/154.54 % 154.70/154.54 fof(fact_interv__listsum__conv__setsum__set__nat,axiom, % 154.70/154.54 ! [V_n_2,V_m_2,V_f_2,T_a] : % 154.70/154.54 ( class_Groups_Ocomm__monoid__add(T_a) % 154.70/154.54 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),V_f_2),c_List_Oupt(V_m_2,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_setsum__set__upt__conv__listsum__nat,axiom, % 154.70/154.54 ! [V_n_2,V_m_2,V_f_2,T_a] : % 154.70/154.54 ( class_Groups_Ocomm__monoid__add(T_a) % 154.70/154.54 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),V_f_2),c_List_Oupt(V_m_2,V_n_2))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_nth__map__upt,axiom, % 154.70/154.54 ! [V_f_2,T_a,V_m_2,V_n_2,V_i_2] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2))) % 154.70/154.54 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),V_f_2),c_List_Oupt(V_m_2,V_n_2))),V_i_2) = hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_i_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_transpose__rectangle,axiom, % 154.70/154.54 ! [V_n_2,T_a,V_xs_2] : % 154.70/154.54 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a)) % 154.70/154.54 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 154.70/154.54 => ( ! [B_i] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2))) % 154.70/154.54 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),B_i)) = V_n_2 ) % 154.70/154.54 => c_List_Otranspose(T_a,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_a)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_a)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_Nat_Onat,T_a),tc_Nat_Onat),c_List_Onth(T_a)),hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_insort__key__remove1,axiom, % 154.70/154.54 ! [V_f_2,V_xs_2,V_a_2,T_a,T_b] : % 154.70/154.54 ( class_Orderings_Olinorder(T_b) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) % 154.70/154.54 => ( hAPP(c_List_Ohd(T_a),hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_a),hAPP(c_fequal,hAPP(V_f_2,V_a_2))),V_f_2)),V_xs_2)) = V_a_2 % 154.70/154.54 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_a_2),c_List_Oremove1(T_a,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted_ONil,axiom, % 154.70/154.54 ! [T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__single,axiom, % 154.70/154.54 ! [V_x,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__upt,axiom, % 154.70/154.54 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__Cons,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 154.70/154.54 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 154.70/154.54 & ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__sort,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__insort,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)) % 154.70/154.54 <=> c_List_Olinorder__class_Osorted(T_a,V_xs_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__drop,axiom, % 154.70/154.54 ! [V_n,V_xs,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 154.70/154.54 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__remove1,axiom, % 154.70/154.54 ! [V_a,V_xs,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 154.70/154.54 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__upto,axiom, % 154.70/154.54 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__take,axiom, % 154.70/154.54 ! [V_n,V_xs,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 154.70/154.54 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__tl,axiom, % 154.70/154.54 ! [V_xs,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 154.70/154.54 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__insort__insert,axiom, % 154.70/154.54 ! [V_x_2,V_xs_2,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 154.70/154.54 => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__butlast,axiom, % 154.70/154.54 ! [V_xs,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( V_xs != c_List_Olist_ONil(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 154.70/154.54 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted_Oequations_I1_J,axiom, % 154.70/154.54 ! [T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__many,axiom, % 154.70/154.54 ! [V_zs,V_y,V_x,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs)) % 154.70/154.54 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__many__eq,axiom, % 154.70/154.54 ! [V_zs_2,V_y_2,V_x_2,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2))) % 154.70/154.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 154.70/154.54 & c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2)) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__remdups,axiom, % 154.70/154.54 ! [V_l,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,V_l) % 154.70/154.54 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__distinct__set__unique,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 154.70/154.54 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,V_ys_2) % 154.70/154.54 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2)) % 154.70/154.54 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2) % 154.70/154.54 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__sort__key,axiom, % 154.70/154.54 ! [V_xs_2,V_f_2,T_b,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olinorder__class_Osort__key(T_b,T_a,V_f_2,V_xs_2))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__insort__insert__key,axiom, % 154.70/154.54 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 154.70/154.54 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__map__remove1,axiom, % 154.70/154.54 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 154.70/154.54 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__insort__key,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2))) % 154.70/154.54 <=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__map__same,axiom, % 154.70/154.54 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,tc_HOL_Obool),T_b),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__filter,axiom, % 154.70/154.54 ! [V_P_2,V_xs_2,V_f_2,T_b,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 154.70/154.54 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__same,axiom, % 154.70/154.54 ! [V_xs_2,V_g_2,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__append,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 154.70/154.54 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 154.70/154.54 & c_List_Olinorder__class_Osorted(T_a,V_ys_2) % 154.70/154.54 & ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => ! [B_xa] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),V_ys_2))) % 154.70/154.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) ) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_filter__insort,axiom, % 154.70/154.54 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_b,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 154.70/154.54 => ( hBOOL(hAPP(V_P_2,V_x_2)) % 154.70/154.54 => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted_Oequations_I2_J,axiom, % 154.70/154.54 ! [V_a1_2,V_a2_2,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a1_2)) % 154.70/154.54 <=> ( ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_a1_2))) % 154.70/154.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a2_2),B_x)) ) % 154.70/154.54 & c_List_Olinorder__class_Osorted(T_a,V_a1_2) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__list__of__set,axiom, % 154.70/154.54 ! [V_A_2,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.54 => ( hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) = V_A_2 % 154.70/154.54 & c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) % 154.70/154.54 & hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_insort__remove1,axiom, % 154.70/154.54 ! [V_xs_2,V_a_2,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 154.70/154.54 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_a_2),c_List_Oremove1(T_a,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__equals__nth__mono,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 154.70/154.54 <=> ! [B_j] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.54 => ! [B_i] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 154.70/154.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j))) ) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__nth__mono,axiom, % 154.70/154.54 ! [V_j,V_i,V_xs,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j))) ) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__sorted__distinct__set__unique,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 154.70/154.54 ( class_Orderings_Olinorder(T_b) % 154.70/154.54 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2))) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) % 154.70/154.54 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)) % 154.70/154.54 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2))) % 154.70/154.54 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2) % 154.70/154.54 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_transpose__column,axiom, % 154.70/154.54 ! [V_i_2,V_xs_2,T_a] : % 154.70/154.54 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2))) % 154.70/154.54 => hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,T_a),c_List_Onth(T_a)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_List_Otranspose(T_a,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),V_i_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_nth__nth__transpose__sorted,axiom, % 154.70/154.54 ! [V_j_2,V_i_2,V_xs_2,T_a] : % 154.70/154.54 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)))) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_xs_2)))) % 154.70/154.54 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),c_List_Otranspose(T_a,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),V_j_2)),V_i_2) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_inj__on__rev,axiom, % 154.70/154.54 ! [V_A_2,T_a] : c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Orev(T_a),V_A_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_distinct__rev,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orev(T_a),V_xs_2))) % 154.70/154.54 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_rev__append,axiom, % 154.70/154.54 ! [V_ys,V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys)),hAPP(c_List_Orev(T_a),V_xs)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_rev_Osimps_I1_J,axiom, % 154.70/154.54 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 154.70/154.54 % 154.70/154.54 fof(fact_Nil__is__rev__conv,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : % 154.70/154.54 ( c_List_Olist_ONil(T_a) = hAPP(c_List_Orev(T_a),V_xs_2) % 154.70/154.54 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_rev__is__Nil__conv,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : % 154.70/154.54 ( hAPP(c_List_Orev(T_a),V_xs_2) = c_List_Olist_ONil(T_a) % 154.70/154.54 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_singleton__rev__conv,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.54 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) = hAPP(c_List_Orev(T_a),V_xs_2) % 154.70/154.54 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_rev__singleton__conv,axiom, % 154.70/154.54 ! [V_x_2,V_xs_2,T_a] : % 154.70/154.54 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) % 154.70/154.54 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_rev_Osimps_I2_J,axiom, % 154.70/154.54 ! [V_xs,V_x,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_rev__eq__Cons__iff,axiom, % 154.70/154.54 ! [V_ys_2,V_y_2,V_xs_2,T_a] : % 154.70/154.54 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2) % 154.70/154.54 <=> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_rev__concat,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : hAPP(c_List_Orev(T_a),c_List_Oconcat(T_a,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Orev(T_a)),hAPP(c_List_Orev(tc_List_Olist(T_a)),V_xs_2))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_rev__map,axiom, % 154.70/154.54 ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Orev(T_b),V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_rev__filter,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(c_List_Orev(T_a),V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_zip__rev,axiom, % 154.70/154.54 ! [V_ys,T_b,V_xs,T_a] : % 154.70/154.54 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys) % 154.70/154.54 => hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(c_List_Orev(T_a),V_xs)),hAPP(c_List_Orev(T_b),V_ys)) = hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_set__rev,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all2__rev1,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 154.70/154.54 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),V_ys_2) % 154.70/154.54 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,hAPP(c_List_Orev(T_b),V_ys_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all2__rev,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 154.70/154.54 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),hAPP(c_List_Orev(T_b),V_ys_2)) % 154.70/154.54 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_listsum__rev,axiom, % 154.70/154.54 ! [V_xs,T_a] : % 154.70/154.54 ( class_Groups_Ocomm__monoid__add(T_a) % 154.70/154.54 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_rev__is__rev__conv,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,T_a] : % 154.70/154.54 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Orev(T_a),V_ys_2) % 154.70/154.54 <=> V_xs_2 = V_ys_2 ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_rev__swap,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,T_a] : % 154.70/154.54 ( hAPP(c_List_Orev(T_a),V_xs_2) = V_ys_2 % 154.70/154.54 <=> V_xs_2 = hAPP(c_List_Orev(T_a),V_ys_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_rev__rev__ident,axiom, % 154.70/154.54 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ). % 154.70/154.54 % 154.70/154.54 fof(fact_length__rev,axiom, % 154.70/154.54 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ). % 154.70/154.54 % 154.70/154.54 fof(fact_foldl__foldr,axiom, % 154.70/154.54 ! [V_xs_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_a),V_f_2),hAPP(c_List_Orev(T_b),V_xs_2),V_a_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_foldr__foldl,axiom, % 154.70/154.54 ! [V_a_2,V_xs_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),V_f_2),V_a_2),hAPP(c_List_Orev(T_b),V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_last__rev,axiom, % 154.70/154.54 ! [T_a,V_xs] : % 154.70/154.54 ( V_xs != c_List_Olist_ONil(T_a) % 154.70/154.54 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_hd__rev,axiom, % 154.70/154.54 ! [T_a,V_xs] : % 154.70/154.54 ( V_xs != c_List_Olist_ONil(T_a) % 154.70/154.54 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__transpose,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_rev__foldl__cons,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),T_a,hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a)),V_xs_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_rev__drop,axiom, % 154.70/154.54 ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_rev__take,axiom, % 154.70/154.54 ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_rotate__rev,axiom, % 154.70/154.54 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Orev(T_a),hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))),V_xs)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_rev__nth,axiom, % 154.70/154.54 ! [V_xs,T_a,V_n] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.54 => hAPP(hAPP(c_List_Onth(T_a),hAPP(c_List_Orev(T_a),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_OSuc,V_n))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_rev__update,axiom, % 154.70/154.54 ! [V_y,V_xs,T_a,V_k] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.54 => hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_y)) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_k)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_y) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__rev__nth__mono,axiom, % 154.70/154.54 ! [V_j,V_i,V_xs,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs)) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i))) ) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_foldr__max__sorted,axiom, % 154.70/154.54 ! [V_y_2,V_xs_2,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs_2)) % 154.70/154.54 => ( ( V_xs_2 = c_List_Olist_ONil(T_a) % 154.70/154.54 => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = V_y_2 ) % 154.70/154.54 & ( V_xs_2 != c_List_Olist_ONil(T_a) % 154.70/154.54 => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2) ) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_length__transpose__sorted,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : % 154.70/154.54 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 154.70/154.54 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a)) % 154.70/154.54 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 154.70/154.54 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_a)) % 154.70/154.54 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_transpose__column__length,axiom, % 154.70/154.54 ! [V_i_2,V_xs_2,T_a] : % 154.70/154.54 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2))) % 154.70/154.54 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_List_Otranspose(T_a,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),V_i_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_transpose__transpose,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : % 154.70/154.54 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 154.70/154.54 => c_List_Otranspose(T_a,c_List_Otranspose(T_a,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a))),V_xs_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_transfer__nat__int__list__functions_I2_J,axiom, % 154.70/154.54 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__takeWhile,axiom, % 154.70/154.54 ! [V_P_2,V_xs_2,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 154.70/154.54 => c_List_Olinorder__class_Osorted(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_length__takeWhile__le,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_takeWhile__eq__all__conv,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : % 154.70/154.54 ( c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = V_xs_2 % 154.70/154.54 <=> ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_set__takeWhileD,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,V_x_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_zip__takeWhile__fst,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,tc_prod(T_a,T_b),V_P_2),c_Product__Type_Ofst(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_zip__takeWhile__snd,axiom, % 154.70/154.54 ! [V_ys_2,V_P_2,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),c_List_OtakeWhile(T_b,V_P_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_a,T_b),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_a,T_b),V_P_2),c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_takeWhile__map,axiom, % 154.70/154.54 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_OtakeWhile(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2),V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_takeWhile__tail,axiom, % 154.70/154.54 ! [V_l_2,V_xs_2,T_a,V_x_2,V_P_2] : % 154.70/154.54 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 154.70/154.54 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_l_2))) = c_List_OtakeWhile(T_a,V_P_2,V_xs_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_takeWhile_Osimps_I2_J,axiom, % 154.70/154.54 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 154.70/154.54 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 154.70/154.54 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) ) % 154.70/154.54 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 154.70/154.54 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_a) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_takeWhile_Osimps_I1_J,axiom, % 154.70/154.54 ! [V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 154.70/154.54 % 154.70/154.54 fof(fact_takeWhile__eq__take,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),V_xs_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_distinct__takeWhile,axiom, % 154.70/154.54 ! [V_P_2,V_xs_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 154.70/154.54 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_return__list__def,axiom, % 154.70/154.54 ! [V_l_2] : c_List_Oreturn__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),V_l_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_takeWhile__append1,axiom, % 154.70/154.54 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 154.70/154.54 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_a,V_P_2,V_xs_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_nth__length__takeWhile,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.54 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_takeWhile__nth,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a,V_j_2] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) % 154.70/154.54 => hAPP(hAPP(c_List_Onth(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_j_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_takeWhile__not__last,axiom, % 154.70/154.54 ! [T_a,V_xs_2] : % 154.70/154.54 ( V_xs_2 != c_List_Olist_ONil(T_a) % 154.70/154.54 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 154.70/154.54 => c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),c_List_Olast(T_a,V_xs_2))),V_xs_2) = c_List_Obutlast(T_a,V_xs_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_filter__equals__takeWhile__sorted__rev,axiom, % 154.70/154.54 ! [V_t_2,V_xs_2,V_f_2,T_b,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) % 154.70/154.54 => hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,T_b),hAPP(c_Orderings_Oord__class_Oless(T_a),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,T_b),hAPP(c_Orderings_Oord__class_Oless(T_a),V_t_2)),V_f_2),V_xs_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_transfer__nat__int__list__return__embed,axiom, % 154.70/154.54 ! [V_l] : % 154.70/154.54 ( c_List_Onat__list(V_l) % 154.70/154.54 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_transfer__nat__int__list__functions_I1_J,axiom, % 154.70/154.54 ! [V_m,V_l] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),V_l),V_m) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(V_l)),c_List_Oembed__list(V_m))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_embed__list__def,axiom, % 154.70/154.54 ! [V_l_2] : c_List_Oembed__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_l_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_takeWhile__neq__rev,axiom, % 154.70/154.54 ! [V_x_2,V_xs_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(c_List_Orev(T_a),hAPP(c_List_Otl(T_a),c_List_OdropWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_dropWhile__neq__rev,axiom, % 154.70/154.54 ! [V_x_2,V_xs_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => c_List_OdropWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(c_List_Orev(T_a),c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_takeWhile__dropWhile__id,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),c_List_OdropWhile(T_a,V_P_2,V_xs_2)) = V_xs_2 ). % 154.70/154.54 % 154.70/154.54 fof(fact_dropWhile__map,axiom, % 154.70/154.54 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_OdropWhile(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2),V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__dropWhile,axiom, % 154.70/154.54 ! [V_P_2,V_xs_2,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 154.70/154.54 => c_List_Olinorder__class_Osorted(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_length__dropWhile__le,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OdropWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_dropWhile__eq__Nil__conv,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : % 154.70/154.54 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = c_List_Olist_ONil(T_a) % 154.70/154.54 <=> ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_dropWhile_Osimps_I2_J,axiom, % 154.70/154.54 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 154.70/154.54 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 154.70/154.54 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_OdropWhile(T_a,V_P_2,V_xs_2) ) % 154.70/154.54 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 154.70/154.54 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_hd__dropWhile,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : % 154.70/154.54 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) != c_List_Olist_ONil(T_a) % 154.70/154.54 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_dropWhile_Osimps_I1_J,axiom, % 154.70/154.54 ! [V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 154.70/154.54 % 154.70/154.54 fof(fact_distinct__dropWhile,axiom, % 154.70/154.54 ! [V_P_2,V_xs_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 154.70/154.54 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_dropWhile__append1,axiom, % 154.70/154.54 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 154.70/154.54 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)),V_ys_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_dropWhile__eq__Cons__conv,axiom, % 154.70/154.54 ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_a] : % 154.70/154.54 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2) % 154.70/154.54 <=> ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)) % 154.70/154.54 & ~ hBOOL(hAPP(V_P_2,V_y_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_dropWhile__eq__drop,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),V_xs_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_dropWhile__nth,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a,V_j_2] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) % 154.70/154.54 => hAPP(hAPP(c_List_Onth(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_listsum__map__filter,axiom, % 154.70/154.54 ! [V_f_2,V_P_2,V_xs_2,T_a,T_b] : % 154.70/154.54 ( class_Groups_Omonoid__add(T_b) % 154.70/154.54 => ( ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => ( ~ hBOOL(hAPP(V_P_2,B_x)) % 154.70/154.54 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) % 154.70/154.54 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted__nth__monoI,axiom, % 154.70/154.54 ! [V_xs,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( ! [B_i,B_j] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 154.70/154.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_j))) ) ) % 154.70/154.54 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_takeWhile__eq__filter,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : % 154.70/154.54 ( ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) % 154.70/154.54 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 154.70/154.54 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_takeWhile__eq__take__P__nth,axiom, % 154.70/154.54 ! [V_P_2,V_xs_2,T_a,V_n_2] : % 154.70/154.54 ( ! [B_i] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.54 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) % 154.70/154.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.54 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) % 154.70/154.54 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_length__takeWhile__less__P__nth,axiom, % 154.70/154.54 ! [V_xs_2,T_a,V_P_2,V_j_2] : % 154.70/154.54 ( ! [B_i] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2)) % 154.70/154.54 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted_Osimps,axiom, % 154.70/154.54 ! [V_a_2,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,V_a_2) % 154.70/154.54 <=> ( V_a_2 = c_List_Olist_ONil(T_a) % 154.70/154.54 | ? [B_xs,B_x] : % 154.70/154.54 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) % 154.70/154.54 & ! [B_xa] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),B_xs))) % 154.70/154.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) % 154.70/154.54 & c_List_Olinorder__class_Osorted(T_a,B_xs) ) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__upds__def,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) = c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_Map_Omap__of(T_a,T_b),hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__comp__def,axiom, % 154.70/154.54 ! [V_k_2,V_g_2,V_f_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,V_f_2,V_g_2,V_k_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_b,c_Option_Ooption_ONone(T_a),V_f_2),hAPP(V_g_2,V_k_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__of__append,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),V_xs_2),V_ys_2)) = c_Map_Omap__add(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2),hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__comp__empty_I1_J,axiom, % 154.70/154.54 ! [V_x_2,V_m_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_x_2) = c_Option_Ooption_ONone(T_a) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__comp__empty_I2_J,axiom, % 154.70/154.54 ! [V_x_2,V_m_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a)),V_m_2,V_x_2) = c_Option_Ooption_ONone(T_a) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__comp__simps_I2_J,axiom, % 154.70/154.54 ! [V_m1_2,T_b,T_c,V_k_H_2,T_a,V_k_2,V_m2_2] : % 154.70/154.54 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_k_H_2) % 154.70/154.54 => c_Map_Omap__comp(T_a,T_c,T_b,V_m1_2,V_m2_2,V_k_2) = hAPP(V_m1_2,V_k_H_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__add__find__right,axiom, % 154.70/154.54 ! [V_m_2,T_b,V_xx_2,T_a,V_k_2,V_n_2] : % 154.70/154.54 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2) % 154.70/154.54 => hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__comp__Some__iff,axiom, % 154.70/154.54 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] : % 154.70/154.54 ( c_Map_Omap__comp(T_b,T_a,T_c,V_m1_2,V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2) % 154.70/154.54 <=> ? [B_k_H] : % 154.70/154.54 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H) % 154.70/154.54 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__add__upd,axiom, % 154.70/154.54 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_f_2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_g_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__add(T_a,T_b,V_f_2,V_g_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__add__SomeD,axiom, % 154.70/154.54 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] : % 154.70/154.54 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 154.70/154.54 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 154.70/154.54 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 154.70/154.54 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__add__Some__iff,axiom, % 154.70/154.54 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] : % 154.70/154.54 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 154.70/154.54 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 154.70/154.54 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 154.70/154.54 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__comp__simps_I1_J,axiom, % 154.70/154.54 ! [V_m1_2,T_b,T_c,T_a,V_k_2,V_m2_2] : % 154.70/154.54 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 154.70/154.54 => c_Map_Omap__comp(T_a,T_c,T_b,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_c) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__add__None,axiom, % 154.70/154.54 ! [V_k_2,V_n_2,V_m_2,T_a,T_b] : % 154.70/154.54 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_a) % 154.70/154.54 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 154.70/154.54 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_a) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__add__empty,axiom, % 154.70/154.54 ! [V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))) = V_m_2 ). % 154.70/154.54 % 154.70/154.54 fof(fact_empty__map__add,axiom, % 154.70/154.54 ! [V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)),V_m_2) = V_m_2 ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__add__upds,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,V_m2_2,V_m1_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m1_2,c_Map_Omap__upds(T_a,T_b,V_m2_2,V_xs_2,V_ys_2)) = c_Map_Omap__upds(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2),V_xs_2,V_ys_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_dom__map__add,axiom, % 154.70/154.54 ! [V_n_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m_2,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_n_2)),c_Map_Odom(T_a,T_b,V_m_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__add__dom__app__simps_I2_J,axiom, % 154.70/154.54 ! [V_l2_2,V_l1_2,T_b,V_m_2,T_a] : % 154.70/154.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l1_2))) % 154.70/154.54 => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__add__dom__app__simps_I3_J,axiom, % 154.70/154.54 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] : % 154.70/154.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2))) % 154.70/154.54 => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l1_2,V_m_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__add__dom__app__simps_I1_J,axiom, % 154.70/154.54 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2))) % 154.70/154.54 => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__add__assoc,axiom, % 154.70/154.54 ! [V_m3_2,V_m2_2,V_m1_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m1_2,c_Map_Omap__add(T_a,T_b,V_m2_2,V_m3_2)) = c_Map_Omap__add(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2),V_m3_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_inj__on__map__add__dom,axiom, % 154.70/154.54 ! [V_m_H_2,V_m_2,T_b,T_a] : % 154.70/154.54 ( c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_b),c_Map_Omap__add(T_a,T_b,V_m_2,V_m_H_2),c_Map_Odom(T_a,T_b,V_m_H_2)) % 154.70/154.54 <=> c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_b),V_m_H_2,c_Map_Odom(T_a,T_b,V_m_H_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__add__def,axiom, % 154.70/154.54 ! [V_x_2,V_m2_2,V_m1_2,T_a,T_b] : hAPP(c_Map_Omap__add(T_b,T_a,V_m1_2,V_m2_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_a,hAPP(V_m1_2,V_x_2),c_Option_Ooption_OSome(T_a)),hAPP(V_m2_2,V_x_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__add__comm,axiom, % 154.70/154.54 ! [V_m2_2,V_m1_2,T_b,T_a] : % 154.70/154.54 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_m1_2)),c_Map_Odom(T_a,T_b,V_m2_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 154.70/154.54 => c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2) = c_Map_Omap__add(T_a,T_b,V_m2_2,V_m1_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__comp__None__iff,axiom, % 154.70/154.54 ! [V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] : % 154.70/154.54 ( c_Map_Omap__comp(T_b,T_a,T_c,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 154.70/154.54 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 154.70/154.54 | ? [B_k_H] : % 154.70/154.54 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H) % 154.70/154.54 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_a) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__add__map__of__foldr,axiom, % 154.70/154.54 ! [V_ps_2,V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_Map_Omap__of(T_a,T_b),V_ps_2)) = c_List_Ofoldr(tc_prod(T_a,T_b),tc_fun(T_a,tc_Option_Ooption(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b))))),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b))),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)))),T_a),c_COMBC(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),hAPP(c_COMBC(tc_fun(T_a,tc_Option_Ooption(T_b)),T_a,tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)))))),c_Option_Ooption_OSome(T_b))),V_ps_2,V_m_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__add__upd__left,axiom, % 154.70/154.54 ! [V_u1_2,V_e1_2,V_e2_2,T_b,V_m_2,T_a] : % 154.70/154.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_e2_2))) % 154.70/154.54 => c_Map_Omap__add(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_e1_2),V_m_2),hAPP(c_Option_Ooption_OSome(T_b),V_u1_2)),V_e2_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__add(T_a,T_b,V_e1_2,V_e2_2)),V_m_2),hAPP(c_Option_Ooption_OSome(T_b),V_u1_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_finite__range__map__of__map__add,axiom, % 154.70/154.54 ! [V_l_2,V_f_2,T_b,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) % 154.70/154.54 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),c_Map_Omap__add(T_b,T_a,V_f_2,hAPP(c_Map_Omap__of(T_b,T_a),V_l_2))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_List_Oinsert__def,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.54 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) % 154.70/154.54 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_not__in__set__insert,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_distinct__insert,axiom, % 154.70/154.54 ! [V_x,V_xs,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 154.70/154.54 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_insert__remdups,axiom, % 154.70/154.54 ! [V_xs,V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oinsert(T_a,V_x,V_xs)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_in__set__insert,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_List_Oset__insert,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oinsert(T_a,V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_insert__Nil,axiom, % 154.70/154.54 ! [V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_concat__map__maps,axiom, % 154.70/154.54 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),V_f_2),V_xs_2)) = c_List_Omaps(T_b,T_a,V_f_2,V_xs_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_maps__def,axiom, % 154.70/154.54 ! [V_xs_2,V_f_2,T_a,T_b] : c_List_Omaps(T_b,T_a,V_f_2,V_xs_2) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),V_f_2),V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_maps__simps_I2_J,axiom, % 154.70/154.54 ! [V_f_2,T_a,T_b] : c_List_Omaps(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a) ). % 154.70/154.54 % 154.70/154.54 fof(fact_maps__simps_I1_J,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : c_List_Omaps(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_b,T_a,V_f_2,V_xs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_distinct__concat,axiom, % 154.70/154.54 ! [V_xs_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),V_xs_2)) % 154.70/154.54 => ( ! [B_ys] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.54 => hBOOL(hAPP(c_List_Odistinct(T_a),B_ys)) ) % 154.70/154.54 => ( ! [B_ys] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.54 => ! [B_zs] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.54 => ( B_ys != B_zs % 154.70/154.54 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),B_ys)),hAPP(c_List_Oset(T_a),B_zs)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) % 154.70/154.54 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oconcat(T_a,V_xs_2))) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_ran__restrictD,axiom, % 154.70/154.54 ! [V_A_2,V_m_2,T_b,V_y_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),c_Map_Oran(T_b,T_a,c_Map_Orestrict__map(T_b,T_a,V_m_2,V_A_2)))) % 154.70/154.54 => ? [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 154.70/154.54 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_measures__lesseq,axiom, % 154.70/154.54 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 154.70/154.54 => ( 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_List_Omeasures(T_a,V_fs_2))) % 154.70/154.54 => 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_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_in__measures_I2_J,axiom, % 154.70/154.54 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_a] : % 154.70/154.54 ( 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_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2)))) % 154.70/154.54 <=> ( 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))) % 154.70/154.54 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 154.70/154.54 & 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_List_Omeasures(T_a,V_fs_2))) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_wf__measures,axiom, % 154.70/154.54 ! [V_fs_2,T_a] : c_Wellfounded_Owf(T_a,c_List_Omeasures(T_a,V_fs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_in__measures_I1_J,axiom, % 154.70/154.54 ! [V_y_2,V_x_2,T_a] : ~ 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_List_Omeasures(T_a,c_List_Olist_ONil(tc_fun(T_a,tc_Nat_Onat))))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_measures__def,axiom, % 154.70/154.54 ! [V_fs_2,T_a] : c_List_Omeasures(T_a,V_fs_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),T_a),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(tc_fun(T_a,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(T_a,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),T_a),c_List_Omap(tc_fun(T_a,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(T_a,tc_Nat_Onat),T_a,tc_Nat_Onat),c_COMBI(tc_fun(T_a,tc_Nat_Onat))))),V_fs_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_measures__less,axiom, % 154.70/154.54 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] : % 154.70/154.54 ( 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))) % 154.70/154.54 => 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_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_foldl__apply,axiom, % 154.70/154.54 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_b,T_c,V_xs_2,T_a] : % 154.70/154.54 ( ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => hAPP(c_Fun_Ocomp(T_c,T_c,T_b,hAPP(V_f_2,B_x)),V_h_2) = hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_h_2),hAPP(V_g_2,B_x)) ) % 154.70/154.54 => hAPP(c_List_Ofoldl(T_c,T_a,hAPP(c_COMBC(T_a,T_c,T_c),V_f_2),hAPP(V_h_2,V_s_2)),V_xs_2) = hAPP(V_h_2,hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),V_g_2),V_s_2),V_xs_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_zip__obtain__same__length,axiom, % 154.70/154.54 ! [V_P_2,V_ys_2,T_b,V_xs_2,T_a] : % 154.70/154.54 ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_ys_2)) % 154.70/154.54 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_xs_2)),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_ys_2)))) ) % 154.70/154.54 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_map__of__eqI,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,T_b,T_a] : % 154.70/154.54 ( hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2)) = hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_ys_2)) % 154.70/154.54 => ( ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2)))) % 154.70/154.54 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2),B_x) = hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2),B_x) ) % 154.70/154.54 => hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_pos__not__random__dseq__def,axiom, % 154.70/154.54 ! [V_seed_2,V_size_2,V_nrandom_2,V_R_2] : c_New__Random__Sequence_Opos__not__random__dseq(V_R_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_dropWhile__append2,axiom, % 154.70/154.54 ! [V_ys_2,V_P_2,V_xs_2,T_a] : % 154.70/154.54 ( ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => hBOOL(hAPP(V_P_2,B_x)) ) % 154.70/154.54 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_a,V_P_2,V_ys_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all2__all__nthI,axiom, % 154.70/154.54 ! [V_P_2,V_b_2,T_b,V_a_2,T_a] : % 154.70/154.54 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_b_2) % 154.70/154.54 => ( ! [B_n] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_a_2))) % 154.70/154.54 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_b_2),B_n))) ) % 154.70/154.54 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_finite__map__freshness,axiom, % 154.70/154.54 ! [V_f_2,T_b,T_a] : % 154.70/154.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,V_f_2))) % 154.70/154.54 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 154.70/154.54 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_b) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_finite__sorted__distinct__unique,axiom, % 154.70/154.54 ! [V_A_2,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 154.70/154.54 => ? [B_x] : % 154.70/154.54 ( hAPP(c_List_Oset(T_a),B_x) = V_A_2 % 154.70/154.54 & c_List_Olinorder__class_Osorted(T_a,B_x) % 154.70/154.54 & hBOOL(hAPP(c_List_Odistinct(T_a),B_x)) % 154.70/154.54 & ! [B_y] : % 154.70/154.54 ( ( hAPP(c_List_Oset(T_a),B_y) = V_A_2 % 154.70/154.54 & c_List_Olinorder__class_Osorted(T_a,B_y) % 154.70/154.54 & hBOOL(hAPP(c_List_Odistinct(T_a),B_y)) ) % 154.70/154.54 => B_y = B_x ) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_takeWhile__append2,axiom, % 154.70/154.54 ! [V_ys_2,V_P_2,V_xs_2,T_a] : % 154.70/154.54 ( ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => hBOOL(hAPP(V_P_2,B_x)) ) % 154.70/154.54 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_OtakeWhile(T_a,V_P_2,V_ys_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_insort__is__Cons,axiom, % 154.70/154.54 ! [V_a_2,V_f_2,V_xs_2,T_a,T_b] : % 154.70/154.54 ( class_Orderings_Olinorder(T_b) % 154.70/154.54 => ( ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) ) % 154.70/154.54 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_a_2),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_xs_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_filter__eq__Cons__iff,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_a] : % 154.70/154.54 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) % 154.70/154.54 <=> ? [B_us,B_vs] : % 154.70/154.54 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_vs)) % 154.70/154.54 & ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) % 154.70/154.54 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 154.70/154.54 & hBOOL(hAPP(V_P_2,V_x_2)) % 154.70/154.54 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_Cons__eq__filter__iff,axiom, % 154.70/154.54 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 154.70/154.54 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2) % 154.70/154.54 <=> ? [B_us,B_vs] : % 154.70/154.54 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_vs)) % 154.70/154.54 & ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) % 154.70/154.54 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 154.70/154.54 & hBOOL(hAPP(V_P_2,V_x_2)) % 154.70/154.54 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__ball__nth,axiom, % 154.70/154.54 ! [V_P_2,V_xs_2,T_a,V_n_2] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.54 => ( ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => hBOOL(hAPP(V_P_2,B_x)) ) % 154.70/154.54 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_sorted_OCons,axiom, % 154.70/154.54 ! [V_x_2,V_xs_2,T_a] : % 154.70/154.54 ( class_Orderings_Olinorder(T_a) % 154.70/154.54 => ( ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) % 154.70/154.54 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 154.70/154.54 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__ex__length,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : % 154.70/154.54 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 154.70/154.54 <=> ? [B_n] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.54 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_in__set__conv__decomp__first,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 <=> ? [B_ys] : % 154.70/154.54 ( ? [B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs)) % 154.70/154.54 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_ys))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__ex__simps_I2_J,axiom, % 154.70/154.54 ! [V_P_2,T_a] : ~ c_List_Olist__ex(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__ex__append,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,V_P_2,T_a] : % 154.70/154.54 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 154.70/154.54 <=> ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 154.70/154.54 | c_List_Olist__ex(T_a,V_P_2,V_ys_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__ex__iff,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : % 154.70/154.54 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 154.70/154.54 <=> ? [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__ex__rev,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : % 154.70/154.54 ( c_List_Olist__ex(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2)) % 154.70/154.54 <=> c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__ex__simps_I1_J,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 154.70/154.54 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 154.70/154.54 <=> ( hBOOL(hAPP(V_P_2,V_x_2)) % 154.70/154.54 | c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_in__set__conv__decomp,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 <=> ? [B_ys,B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_in__set__conv__decomp__last,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 <=> ? [B_ys,B_zs] : % 154.70/154.54 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs)) % 154.70/154.54 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_zs))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_option_Orecs_I2_J,axiom, % 154.70/154.54 ! [V_a_2,V_f2_2,V_f1_2,T_b,T_a] : c_Option_Ooption_Ooption__rec(T_a,T_b,V_f1_2,V_f2_2,hAPP(c_Option_Ooption_OSome(T_b),V_a_2)) = hAPP(V_f2_2,V_a_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_option_Orecs_I1_J,axiom, % 154.70/154.54 ! [V_f2_2,V_f1_2,T_b,T_a] : c_Option_Ooption_Ooption__rec(T_a,T_b,V_f1_2,V_f2_2,c_Option_Ooption_ONone(T_b)) = V_f1_2 ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all__length,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : % 154.70/154.54 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 154.70/154.54 <=> ! [B_n] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 154.70/154.54 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_measure__function__int,axiom, % 154.70/154.54 c_FunDef_Ois__measure(tc_Int_Oint,hAPP(c_Fun_Ocomp(tc_Int_Oint,tc_Nat_Onat,tc_Int_Oint,c_Int_Onat),c_Groups_Oabs__class_Oabs(tc_Int_Oint))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all__simps_I1_J,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 154.70/154.54 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 154.70/154.54 <=> ( hBOOL(hAPP(V_P_2,V_x_2)) % 154.70/154.54 & c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all__rev,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : % 154.70/154.54 ( c_List_Olist__all(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2)) % 154.70/154.54 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_Ball__set__list__all,axiom, % 154.70/154.54 ! [V_P_2,V_xs_2,T_a] : % 154.70/154.54 ( ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => hBOOL(hAPP(V_P_2,B_x)) ) % 154.70/154.54 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_measure__fst,axiom, % 154.70/154.54 ! [T_b,V_f_2,T_a] : % 154.70/154.54 ( c_FunDef_Ois__measure(T_a,V_f_2) % 154.70/154.54 => c_FunDef_Ois__measure(tc_prod(T_a,T_b),hAPP(hAPP(c_COMBB(T_a,tc_Nat_Onat,tc_prod(T_a,T_b)),V_f_2),c_Product__Type_Ofst(T_a,T_b))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_measure__snd,axiom, % 154.70/154.54 ! [T_b,V_f_2,T_a] : % 154.70/154.54 ( c_FunDef_Ois__measure(T_a,V_f_2) % 154.70/154.54 => c_FunDef_Ois__measure(tc_prod(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,tc_Nat_Onat,tc_prod(T_b,T_a)),V_f_2),c_Product__Type_Osnd(T_b,T_a))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all__iff,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : % 154.70/154.54 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 154.70/154.54 <=> ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_is__measure_Osimps,axiom, % 154.70/154.54 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_is__measure_Oequations,axiom, % 154.70/154.54 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_is__measure_Ointros,axiom, % 154.70/154.54 ! [V_f_2,T_a] : c_FunDef_Ois__measure(T_a,V_f_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_measure__size,axiom, % 154.70/154.54 ! [T_a] : % 154.70/154.54 ( class_Nat_Osize(T_a) % 154.70/154.54 => c_FunDef_Ois__measure(T_a,c_Nat_Osize__class_Osize(T_a)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all__append,axiom, % 154.70/154.54 ! [V_ys_2,V_xs_2,V_P_2,T_a] : % 154.70/154.54 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 154.70/154.54 <=> ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 154.70/154.54 & c_List_Olist__all(T_a,V_P_2,V_ys_2) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all__simps_I2_J,axiom, % 154.70/154.54 ! [V_P_2,T_a] : c_List_Olist__all(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__all__iff__raw,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : % 154.70/154.54 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 154.70/154.54 <=> ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__ex1__simps_I2_J,axiom, % 154.70/154.54 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 154.70/154.54 ( c_List_Olist__ex1(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 154.70/154.54 <=> ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 154.70/154.54 => c_List_Olist__all(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2))),hAPP(c_fequal,V_x_2)),V_xs_2) ) % 154.70/154.54 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 154.70/154.54 => c_List_Olist__ex1(T_a,V_P_2,V_xs_2) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_equal__fun__def,axiom, % 154.70/154.54 ! [V_g_2,V_f_2,T_a,T_b] : % 154.70/154.54 ( ( class_HOL_Oequal(T_b) % 154.70/154.54 & class_Enum_Oenum(T_a) ) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 154.70/154.54 <=> ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) % 154.70/154.54 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__ex1__simps_I1_J,axiom, % 154.70/154.54 ! [V_P_2,T_a] : ~ c_List_Olist__ex1(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_equal,axiom, % 154.70/154.54 ! [T_a] : % 154.70/154.54 ( class_HOL_Oequal(T_a) % 154.70/154.54 => c_HOL_Oequal__class_Oequal(T_a) = c_fequal ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_equal__refl,axiom, % 154.70/154.54 ! [V_x,T_a] : % 154.70/154.54 ( class_HOL_Oequal(T_a) % 154.70/154.54 => hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x),V_x)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_equal__eq,axiom, % 154.70/154.54 ! [V_y_2,V_x_2,T_a] : % 154.70/154.54 ( class_HOL_Oequal(T_a) % 154.70/154.54 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x_2),V_y_2)) % 154.70/154.54 <=> V_x_2 = V_y_2 ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_eq__equal,axiom, % 154.70/154.54 ! [T_a] : % 154.70/154.54 ( class_HOL_Oequal(T_a) % 154.70/154.54 => c_fequal = c_HOL_Oequal__class_Oequal(T_a) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_exists1__code,axiom, % 154.70/154.54 ! [V_P_2,T_a] : % 154.70/154.54 ( class_Enum_Oenum(T_a) % 154.70/154.54 => ( ? [B_x] : % 154.70/154.54 ( hBOOL(hAPP(V_P_2,B_x)) % 154.70/154.54 & ! [B_y] : % 154.70/154.54 ( hBOOL(hAPP(V_P_2,B_y)) % 154.70/154.54 => B_y = B_x ) ) % 154.70/154.54 <=> c_List_Olist__ex1(T_a,V_P_2,c_Enum_Oenum__class_Oenum(T_a)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_bool_Osize_I3_J,axiom, % 154.70/154.54 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(fact_bool_Osize_I4_J,axiom, % 154.70/154.54 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(fact_list__ex1__iff,axiom, % 154.70/154.54 ! [V_xs_2,V_P_2,T_a] : % 154.70/154.54 ( c_List_Olist__ex1(T_a,V_P_2,V_xs_2) % 154.70/154.54 <=> ? [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 & hBOOL(hAPP(V_P_2,B_x)) % 154.70/154.54 & ! [B_y] : % 154.70/154.54 ( ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),hAPP(c_List_Oset(T_a),V_xs_2))) % 154.70/154.54 & hBOOL(hAPP(V_P_2,B_y)) ) % 154.70/154.54 => B_y = B_x ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_size__code,axiom, % 154.70/154.54 ! [V_xq_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),V_xq_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),T_a),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(c_Lazy__Sequence_Oyield(T_a),V_xq_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_transfer__morphism__int__nat,axiom, % 154.70/154.54 c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_eq__int__code_I7_J,axiom, % 154.70/154.54 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k2))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_eq__int__code_I11_J,axiom, % 154.70/154.54 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OMin)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_eq__int__code_I13_J,axiom, % 154.70/154.54 ! [V_k2_2,V_k1_2] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 154.70/154.54 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_eq__int__code_I1_J,axiom, % 154.70/154.54 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_eq__int__code_I16_J,axiom, % 154.70/154.54 ! [V_k2_2,V_k1_2] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 154.70/154.54 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_eq__number__of__int__code,axiom, % 154.70/154.54 ! [V_l_2,V_k_2] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2))) % 154.70/154.54 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_eq__int__code_I6_J,axiom, % 154.70/154.54 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_eq__int__code_I4_J,axiom, % 154.70/154.54 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k2))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_eq__int__code_I10_J,axiom, % 154.70/154.54 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OPls)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_equal__int__def,axiom, % 154.70/154.54 ! [V_l_2,V_k_2] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) % 154.70/154.54 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_eq__int__code_I14_J,axiom, % 154.70/154.54 ! [V_k2,V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OBit1(V_k2))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_eq__int__code_I15_J,axiom, % 154.70/154.54 ! [V_k2,V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OBit0(V_k2))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_eq__int__code_I3_J,axiom, % 154.70/154.54 ! [V_k2_2] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k2_2))) % 154.70/154.54 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),V_k2_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_eq__int__code_I9_J,axiom, % 154.70/154.54 ! [V_k1_2] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OPls)) % 154.70/154.54 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OPls)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_eq__int__code_I8_J,axiom, % 154.70/154.54 ! [V_k2_2] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k2_2))) % 154.70/154.54 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),V_k2_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_eq__int__code_I12_J,axiom, % 154.70/154.54 ! [V_k1_2] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OMin)) % 154.70/154.54 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OMin)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_eq__int__code_I5_J,axiom, % 154.70/154.54 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_eq__int__code_I2_J,axiom, % 154.70/154.54 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_lazy__sequence__size__code,axiom, % 154.70/154.54 ! [V_xq_2,V_s_2,T_a] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_s_2),V_xq_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),hAPP(hAPP(c_COMBC(T_a,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),T_a),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),T_a),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),T_a),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),T_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_s_2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_s_2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(T_a),V_xq_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_seq__case,axiom, % 154.70/154.54 ! [V_xq_2,V_g_2,V_f_2,T_b,T_a] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_a,T_b,V_f_2,V_g_2,V_xq_2) = hAPP(c_Option_Ooption_Ooption__case(T_a,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),T_a),V_g_2)),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_eq__int__refl,axiom, % 154.70/154.54 ! [V_k] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k),V_k)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_yieldn__def,axiom, % 154.70/154.54 ! [T_a] : c_Lazy__Sequence_Oyieldn(T_a) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(T_a),T_a,c_Lazy__Sequence_Oyield(T_a)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_lazy__sequence_Osize_I2_J,axiom, % 154.70/154.54 ! [V_lazy__sequence_2,V_a_2,V_fa_2,T_a] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_fa_2),V_lazy__sequence_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_lazy__sequence_Osimps_I5_J,axiom, % 154.70/154.54 ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_b,T_a] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_a,T_b,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_lazy__sequence_Oinject,axiom, % 154.70/154.54 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_a] : % 154.70/154.54 ( c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_2,V_lazy__sequence_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H_2,V_lazy__sequence_H_2) % 154.70/154.54 <=> ( V_a_2 = V_a_H_2 % 154.70/154.54 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact__01,axiom, % 154.70/154.54 ! [V_xq,V_x,T_a] : hAPP(c_Lazy__Sequence_Oyield(T_a),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq)) = hAPP(c_Option_Ooption_OSome(tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_Product__Type_OPair(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),V_x),V_xq)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_lazy__sequence_Osize_I4_J,axiom, % 154.70/154.54 ! [V_lazy__sequence,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a,V_lazy__sequence)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),V_lazy__sequence)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_New__DSequence_Opos__decr__bind__def,axiom, % 154.70/154.54 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] : % 154.70/154.54 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 154.70/154.54 => hAPP(c_New__DSequence_Opos__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_a) ) % 154.70/154.54 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 154.70/154.54 => hAPP(c_New__DSequence_Opos__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_b,T_a,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a)),V_f_2),V_i_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom, % 154.70/154.54 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] : % 154.70/154.54 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 154.70/154.54 => hAPP(c_New__DSequence_Oneg__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_a) ) % 154.70/154.54 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 154.70/154.54 => hAPP(c_New__DSequence_Oneg__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_b,T_a,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))),V_f_2),V_i_2)) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom, % 154.70/154.54 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : c_New__Random__Sequence_Opos__decr__bind(T_b,T_a,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom, % 154.70/154.54 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : c_New__Random__Sequence_Oneg__decr__bind(T_b,T_a,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_New__DSequence_Oneg__bind__def,axiom, % 154.70/154.54 ! [V_i_2,V_f_2,V_x_2,T_a,T_b] : hAPP(c_New__DSequence_Oneg__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_b,T_a,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))),V_f_2),V_i_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_New__DSequence_Opos__empty__def,axiom, % 154.70/154.54 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ). % 154.70/154.54 % 154.70/154.54 fof(fact_pos__empty__def,axiom, % 154.70/154.54 ! [V_seed_2,V_size_2,V_nrandom_2,T_a] : c_New__Random__Sequence_Opos__empty(T_a,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_a) ). % 154.70/154.54 % 154.70/154.54 fof(fact_neg__bind__def,axiom, % 154.70/154.54 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_b,T_a,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_New__DSequence_Opos__bind__def,axiom, % 154.70/154.54 ! [V_i_2,V_f_2,V_x_2,T_a,T_b] : hAPP(c_New__DSequence_Opos__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_b,T_a,hAPP(V_x_2,V_i_2)),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a)),V_f_2),V_i_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_neg__map__def,axiom, % 154.70/154.54 ! [V_P_2,V_f_2,T_a,T_b] : c_New__Random__Sequence_Oneg__map(T_b,T_a,V_f_2,V_P_2) = c_New__Random__Sequence_Oneg__bind(T_b,T_a,V_P_2,hAPP(c_Fun_Ocomp(T_a,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))))),T_b,c_New__Random__Sequence_Oneg__single(T_a)),V_f_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_neg__single__def,axiom, % 154.70/154.54 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_a] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_a),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_a,V_x_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_pos__bind__def,axiom, % 154.70/154.54 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_b,T_a,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_New__DSequence_Oneg__single__def,axiom, % 154.70/154.54 ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Oneg__single(T_a,V_x),V_i_1) = c_Lazy__Sequence_Ohb__single(T_a,V_x) ). % 154.70/154.54 % 154.70/154.54 fof(fact_pos__map__def,axiom, % 154.70/154.54 ! [V_P_2,V_f_2,T_a,T_b] : c_New__Random__Sequence_Opos__map(T_b,T_a,V_f_2,V_P_2) = c_New__Random__Sequence_Opos__bind(T_b,T_a,V_P_2,hAPP(c_Fun_Ocomp(T_a,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))))),T_b,c_New__Random__Sequence_Opos__single(T_a)),V_f_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_pos__single__def,axiom, % 154.70/154.54 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_a] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_a),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_a,V_x_2) ). % 154.70/154.54 % 154.70/154.54 fof(fact_length__splice,axiom, % 154.70/154.54 ! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osplice(T_a,V_xs,V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_splice_Osimps_I3_J,axiom, % 154.70/154.54 ! [V_ys,V_y,V_xs,V_x,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Osplice(T_a,V_xs,V_ys))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_splice__Nil2,axiom, % 154.70/154.54 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ). % 154.70/154.54 % 154.70/154.54 fof(fact_splice_Osimps_I1_J,axiom, % 154.70/154.54 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ). % 154.70/154.54 % 154.70/154.54 fof(fact_splice_Osimps_I2_J,axiom, % 154.70/154.54 ! [V_va,V_v,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va) ). % 154.70/154.54 % 154.70/154.54 fof(fact_New__DSequence_Opos__single__def,axiom, % 154.70/154.54 ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Opos__single(T_a,V_x),V_i_1) = hAPP(c_Lazy__Sequence_Osingle(T_a),V_x) ). % 154.70/154.54 % 154.70/154.54 fof(fact_acyclicP__converse,axiom, % 154.70/154.54 ! [V_r_2,T_a] : % 154.70/154.54 ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_Predicate_Oconversep(T_a,T_a,V_r_2)))) % 154.70/154.54 <=> c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_converse__meet,axiom, % 154.70/154.54 ! [V_s_2,V_r_2,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),c_Predicate_Oconversep(T_b,T_a,V_r_2)),c_Predicate_Oconversep(T_b,T_a,V_s_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_conversep__eq,axiom, % 154.70/154.54 ! [T_a] : c_Predicate_Oconversep(T_a,T_a,c_fequal) = c_fequal ). % 154.70/154.54 % 154.70/154.54 fof(fact_conversep__conversep,axiom, % 154.70/154.54 ! [V_r_2,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,c_Predicate_Oconversep(T_a,T_b,V_r_2)) = V_r_2 ). % 154.70/154.54 % 154.70/154.54 fof(fact_conversep__iff,axiom, % 154.70/154.54 ! [V_b_2,V_a_2,V_r_2,T_b,T_a] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a_2),V_b_2)) % 154.70/154.54 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_conversep_Oequations,axiom, % 154.70/154.54 ! [V_a1_2,V_a2_2,V_r_2,T_b,T_a] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a2_2),V_a1_2)) % 154.70/154.54 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_conversep_Ointros,axiom, % 154.70/154.54 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 154.70/154.54 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_b_2),V_a_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_conversepD,axiom, % 154.70/154.54 ! [V_b_2,V_a_2,V_r_2,T_b,T_a] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a_2),V_b_2)) % 154.70/154.54 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_conversep__noteq,axiom, % 154.70/154.54 ! [V_y_2,V_x_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_a,hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot)),c_fequal)),V_x_2),V_y_2)) % 154.70/154.54 <=> V_x_2 != V_y_2 ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_converse__pred__comp,axiom, % 154.70/154.54 ! [V_s_2,V_r_2,T_c,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,c_Predicate_Opred__comp(T_b,T_c,T_a,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_a,T_c,T_b,c_Predicate_Oconversep(T_c,T_a,V_s_2),c_Predicate_Oconversep(T_b,T_c,V_r_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_converse__join,axiom, % 154.70/154.54 ! [V_s_2,V_r_2,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),c_Predicate_Oconversep(T_b,T_a,V_r_2)),c_Predicate_Oconversep(T_b,T_a,V_s_2)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_conversep__converse__eq,axiom, % 154.70/154.54 ! [V_y_2,V_x_2,V_r_2,T_b,T_a] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,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(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(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),hAPP(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)),V_x_2),V_y_2)) % 154.70/154.54 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2))) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact__02,axiom, % 154.70/154.54 ! [V_s2_2,V_s1_2,T_b,T_a] : c_Lazy__Sequence_Oproduct(T_a,T_b,V_s1_2,V_s2_2) = hAPP(c_Lazy__Sequence_Obind(T_a,tc_prod(T_a,T_b),V_s1_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b)),T_a),c_Lazy__Sequence_Obind(T_b,tc_prod(T_a,T_b),V_s2_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b)),T_b),c_Lazy__Sequence_Osingle(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))) ). % 154.70/154.54 % 154.70/154.54 fof(fact_tl__replicate,axiom, % 154.70/154.54 ! [V_x,T_a,V_n] : % 154.70/154.54 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.54 => hAPP(c_List_Otl(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_x) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_zip__replicate,axiom, % 154.70/154.54 ! [V_y,V_j,V_x,V_i,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Oreplicate(T_a,V_i,V_x)),c_List_Oreplicate(T_b,V_j,V_y)) = c_List_Oreplicate(tc_prod(T_a,T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_j),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_replicate__app__Cons__same,axiom, % 154.70/154.54 ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_xs)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_replicate__Suc,axiom, % 154.70/154.54 ! [V_x,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(c_Nat_OSuc,V_n),V_x) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_n,V_x)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_rev__replicate,axiom, % 154.70/154.54 ! [V_x,V_n,T_a] : hAPP(c_List_Orev(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,V_n,V_x) ). % 154.70/154.54 % 154.70/154.54 fof(fact_last__replicate,axiom, % 154.70/154.54 ! [V_x,T_a,V_n] : % 154.70/154.54 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.54 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_drop__replicate,axiom, % 154.70/154.54 ! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_k),V_i),V_x) ). % 154.70/154.54 % 154.70/154.54 fof(fact_hd__replicate,axiom, % 154.70/154.54 ! [V_x,T_a,V_n] : % 154.70/154.54 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.54 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_take__replicate,axiom, % 154.70/154.54 ! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_k),V_x) ). % 154.70/154.54 % 154.70/154.54 fof(fact_Ball__set__replicate,axiom, % 154.70/154.54 ! [V_P_2,V_a_2,V_n_2,T_a] : % 154.70/154.54 ( ! [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_a_2)))) % 154.70/154.54 => hBOOL(hAPP(V_P_2,B_x)) ) % 154.70/154.54 <=> ( hBOOL(hAPP(V_P_2,V_a_2)) % 154.70/154.54 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_Bex__set__replicate,axiom, % 154.70/154.54 ! [V_P_2,V_a_2,V_n_2,T_a] : % 154.70/154.54 ( ? [B_x] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_a_2)))) % 154.70/154.54 & hBOOL(hAPP(V_P_2,B_x)) ) % 154.70/154.54 <=> ( hBOOL(hAPP(V_P_2,V_a_2)) % 154.70/154.54 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_replicate__eq__replicate,axiom, % 154.70/154.54 ! [V_y_2,V_n_2,V_x_2,V_m_2,T_a] : % 154.70/154.54 ( c_List_Oreplicate(T_a,V_m_2,V_x_2) = c_List_Oreplicate(T_a,V_n_2,V_y_2) % 154.70/154.54 <=> ( V_m_2 = V_n_2 % 154.70/154.54 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 154.70/154.54 => V_x_2 = V_y_2 ) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_nth__replicate,axiom, % 154.70/154.54 ! [V_x,T_a,V_n,V_i] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 154.70/154.54 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_in__set__replicate,axiom, % 154.70/154.54 ! [V_y_2,V_n_2,V_x_2,T_a] : % 154.70/154.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_y_2)))) % 154.70/154.54 <=> ( V_x_2 = V_y_2 % 154.70/154.54 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 154.70/154.54 % 154.70/154.54 fof(fact_replicate__add,axiom, % 154.70/154.54 ! [V_x,V_m,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_x) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_m,V_x)) ). % 154.70/154.54 % 154.70/154.54 fof(fact_append__replicate__commute,axiom, % 154.70/154.54 ! [V_k,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_k,V_x)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_k,V_x)),c_List_Oreplicate(T_a,V_n,V_x)) ). % 154.70/154.54 % 154.70/154.54 %----Arity declarations (231) % 154.70/154.54 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom, % 154.70/154.54 class_Lattices_Obounded__lattice(tc_HOL_Obool) ). % 154.70/154.54 % 154.70/154.54 fof(arity_fun__Lattices_Obounded__lattice,axiom, % 154.70/154.54 ! [T_2,T_1] : % 154.70/154.54 ( class_Lattices_Obounded__lattice(T_1) % 154.70/154.54 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom, % 154.70/154.54 ! [T_2,T_1] : % 154.70/154.54 ( class_Complete__Lattice_Ocomplete__lattice(T_1) % 154.70/154.54 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_fun__Lattices_Obounded__lattice__top,axiom, % 154.70/154.54 ! [T_2,T_1] : % 154.70/154.54 ( class_Lattices_Obounded__lattice(T_1) % 154.70/154.54 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom, % 154.70/154.54 ! [T_2,T_1] : % 154.70/154.54 ( class_Lattices_Obounded__lattice(T_1) % 154.70/154.54 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_fun__Lattices_Osemilattice__sup,axiom, % 154.70/154.54 ! [T_2,T_1] : % 154.70/154.54 ( class_Lattices_Olattice(T_1) % 154.70/154.54 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_fun__Lattices_Osemilattice__inf,axiom, % 154.70/154.54 ! [T_2,T_1] : % 154.70/154.54 ( class_Lattices_Olattice(T_1) % 154.70/154.54 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_fun__Lattices_Odistrib__lattice,axiom, % 154.70/154.54 ! [T_2,T_1] : % 154.70/154.54 ( class_Lattices_Odistrib__lattice(T_1) % 154.70/154.54 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_fun__Lattices_Oboolean__algebra,axiom, % 154.70/154.54 ! [T_2,T_1] : % 154.70/154.54 ( class_Lattices_Oboolean__algebra(T_1) % 154.70/154.54 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_fun__Orderings_Opreorder,axiom, % 154.70/154.54 ! [T_2,T_1] : % 154.70/154.54 ( class_Orderings_Opreorder(T_1) % 154.70/154.54 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_fun__Finite__Set_Ofinite,axiom, % 154.70/154.54 ! [T_1,T_2] : % 154.70/154.54 ( ( class_Finite__Set_Ofinite(T_2) % 154.70/154.54 & class_Finite__Set_Ofinite(T_1) ) % 154.70/154.54 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_fun__Lattices_Olattice,axiom, % 154.70/154.54 ! [T_2,T_1] : % 154.70/154.54 ( class_Lattices_Olattice(T_1) % 154.70/154.54 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_fun__Orderings_Oorder,axiom, % 154.70/154.54 ! [T_2,T_1] : % 154.70/154.54 ( class_Orderings_Oorder(T_1) % 154.70/154.54 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_fun__Orderings_Otop,axiom, % 154.70/154.54 ! [T_2,T_1] : % 154.70/154.54 ( class_Orderings_Otop(T_1) % 154.70/154.54 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_fun__Orderings_Oord,axiom, % 154.70/154.54 ! [T_2,T_1] : % 154.70/154.54 ( class_Orderings_Oord(T_1) % 154.70/154.54 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_fun__Orderings_Obot,axiom, % 154.70/154.54 ! [T_2,T_1] : % 154.70/154.54 ( class_Orderings_Obot(T_1) % 154.70/154.54 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_fun__Groups_Ouminus,axiom, % 154.70/154.54 ! [T_2,T_1] : % 154.70/154.54 ( class_Groups_Ouminus(T_1) % 154.70/154.54 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_fun__Groups_Ominus,axiom, % 154.70/154.54 ! [T_2,T_1] : % 154.70/154.54 ( class_Groups_Ominus(T_1) % 154.70/154.54 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_fun__HOL_Oequal,axiom, % 154.70/154.54 ! [T_1,T_2] : % 154.70/154.54 ( ( class_Enum_Oenum(T_2) % 154.70/154.54 & class_HOL_Oequal(T_1) ) % 154.70/154.54 => class_HOL_Oequal(tc_fun(T_2,T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_fun__Enum_Oenum,axiom, % 154.70/154.54 ! [T_1,T_2] : % 154.70/154.54 ( ( class_Enum_Oenum(T_2) % 154.70/154.54 & class_Enum_Oenum(T_1) ) % 154.70/154.54 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Com__Ocom__HOL_Oequal,axiom, % 154.70/154.54 class_HOL_Oequal(tc_Com_Ocom) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Com__Ocom__Nat_Osize,axiom, % 154.70/154.54 class_Nat_Osize(tc_Com_Ocom) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 154.70/154.54 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 154.70/154.54 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 154.70/154.54 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom, % 154.70/154.54 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom, % 154.70/154.54 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom, % 154.70/154.54 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom, % 154.70/154.54 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom, % 154.70/154.54 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom, % 154.70/154.54 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom, % 154.70/154.54 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom, % 154.70/154.54 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom, % 154.70/154.54 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom, % 154.70/154.54 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom, % 154.70/154.54 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom, % 154.70/154.54 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom, % 154.70/154.54 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom, % 154.70/154.54 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom, % 154.70/154.54 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom, % 154.70/154.54 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom, % 154.70/154.54 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom, % 154.70/154.54 class_Rings_Olinordered__semiring(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom, % 154.70/154.54 class_Rings_Olinordered__semidom(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom, % 154.70/154.54 class_Lattices_Osemilattice__sup(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom, % 154.70/154.54 class_Lattices_Osemilattice__inf(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom, % 154.70/154.54 class_Lattices_Odistrib__lattice(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom, % 154.70/154.54 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom, % 154.70/154.54 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom, % 154.70/154.54 class_Groups_Oab__semigroup__add(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom, % 154.70/154.54 class_Rings_Oordered__semiring(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom, % 154.70/154.54 class_Rings_Oordered__ring__abs(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom, % 154.70/154.54 class_Rings_Ono__zero__divisors(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom, % 154.70/154.54 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom, % 154.70/154.54 class_Rings_Olinordered__ring(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom, % 154.70/154.54 class_Rings_Olinordered__idom(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom, % 154.70/154.54 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom, % 154.70/154.54 class_Groups_Osemigroup__add(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Divides_Osemiring__div,axiom, % 154.70/154.54 class_Divides_Osemiring__div(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom, % 154.70/154.54 class_Rings_Ocomm__semiring(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom, % 154.70/154.54 class_Nat_Osemiring__char__0(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Oab__group__add,axiom, % 154.70/154.54 class_Groups_Oab__group__add(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom, % 154.70/154.54 class_Rings_Ozero__neq__one(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Oordered__ring,axiom, % 154.70/154.54 class_Rings_Oordered__ring(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Orderings_Opreorder,axiom, % 154.70/154.54 class_Orderings_Opreorder(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Orderings_Olinorder,axiom, % 154.70/154.54 class_Orderings_Olinorder(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom, % 154.70/154.54 class_Groups_Omonoid__mult(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom, % 154.70/154.54 class_Rings_Ocomm__ring__1(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Omonoid__add,axiom, % 154.70/154.54 class_Groups_Omonoid__add(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Smallcheck_Osmall,axiom, % 154.70/154.54 class_Smallcheck_Osmall(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Osemiring__1,axiom, % 154.70/154.54 class_Rings_Osemiring__1(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Osemiring__0,axiom, % 154.70/154.54 class_Rings_Osemiring__0(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Lattices_Olattice,axiom, % 154.70/154.54 class_Lattices_Olattice(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Ogroup__add,axiom, % 154.70/154.54 class_Groups_Ogroup__add(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Divides_Oring__div,axiom, % 154.70/154.54 class_Divides_Oring__div(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Omult__zero,axiom, % 154.70/154.54 class_Rings_Omult__zero(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Orderings_Oorder,axiom, % 154.70/154.54 class_Orderings_Oorder(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Int_Oring__char__0,axiom, % 154.70/154.54 class_Int_Oring__char__0(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Int_Onumber__ring,axiom, % 154.70/154.54 class_Int_Onumber__ring(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Osemiring,axiom, % 154.70/154.54 class_Rings_Osemiring(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Orderings_Oord,axiom, % 154.70/154.54 class_Orderings_Oord(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Ouminus,axiom, % 154.70/154.54 class_Groups_Ouminus(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Osgn__if,axiom, % 154.70/154.54 class_Groups_Osgn__if(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Oabs__if,axiom, % 154.70/154.54 class_Groups_Oabs__if(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Oring__1,axiom, % 154.70/154.54 class_Rings_Oring__1(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Ominus,axiom, % 154.70/154.54 class_Groups_Ominus(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Power_Opower,axiom, % 154.70/154.54 class_Power_Opower(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Ozero,axiom, % 154.70/154.54 class_Groups_Ozero(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Oring,axiom, % 154.70/154.54 class_Rings_Oring(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Rings_Oidom,axiom, % 154.70/154.54 class_Rings_Oidom(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Int_Onumber,axiom, % 154.70/154.54 class_Int_Onumber(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__Groups_Oone,axiom, % 154.70/154.54 class_Groups_Oone(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Int__Oint__HOL_Oequal,axiom, % 154.70/154.54 class_HOL_Oequal(tc_Int_Oint) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 154.70/154.54 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 154.70/154.54 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 154.70/154.54 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom, % 154.70/154.54 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom, % 154.70/154.54 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom, % 154.70/154.54 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 154.70/154.54 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 154.70/154.54 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 154.70/154.54 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom, % 154.70/154.54 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom, % 154.70/154.54 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 154.70/154.54 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom, % 154.70/154.54 class_Rings_Olinordered__semiring(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 154.70/154.54 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom, % 154.70/154.54 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom, % 154.70/154.54 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom, % 154.70/154.54 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom, % 154.70/154.54 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom, % 154.70/154.54 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 154.70/154.54 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom, % 154.70/154.54 class_Rings_Oordered__semiring(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom, % 154.70/154.54 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 154.70/154.54 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 154.70/154.54 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom, % 154.70/154.54 class_Groups_Osemigroup__add(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom, % 154.70/154.54 class_Divides_Osemiring__div(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom, % 154.70/154.54 class_Rings_Ocomm__semiring(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Orderings_Owellorder,axiom, % 154.70/154.54 class_Orderings_Owellorder(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom, % 154.70/154.54 class_Nat_Osemiring__char__0(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom, % 154.70/154.54 class_Rings_Ozero__neq__one(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 154.70/154.54 class_Orderings_Opreorder(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 154.70/154.54 class_Orderings_Olinorder(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom, % 154.70/154.54 class_Groups_Omonoid__mult(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 154.70/154.54 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom, % 154.70/154.54 class_Rings_Osemiring__1(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom, % 154.70/154.54 class_Rings_Osemiring__0(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Lattices_Olattice,axiom, % 154.70/154.54 class_Lattices_Olattice(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Rings_Omult__zero,axiom, % 154.70/154.54 class_Rings_Omult__zero(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 154.70/154.54 class_Orderings_Oorder(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Rings_Osemiring,axiom, % 154.70/154.54 class_Rings_Osemiring(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 154.70/154.54 class_Orderings_Oord(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Orderings_Obot,axiom, % 154.70/154.54 class_Orderings_Obot(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Groups_Ominus,axiom, % 154.70/154.54 class_Groups_Ominus(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Power_Opower,axiom, % 154.70/154.54 class_Power_Opower(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 154.70/154.54 class_Groups_Ozero(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Int_Onumber,axiom, % 154.70/154.54 class_Int_Onumber(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Groups_Oone,axiom, % 154.70/154.54 class_Groups_Oone(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__HOL_Oequal,axiom, % 154.70/154.54 class_HOL_Oequal(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Nat__Onat__Nat_Osize,axiom, % 154.70/154.54 class_Nat_Osize(tc_Nat_Onat) ). % 154.70/154.54 % 154.70/154.54 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom, % 154.70/154.54 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ). % 154.70/154.54 % 154.70/154.54 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom, % 154.70/154.54 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ). % 154.70/154.54 % 154.70/154.54 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom, % 154.70/154.54 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ). % 154.70/154.54 % 154.70/154.54 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom, % 154.70/154.54 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ). % 154.70/154.54 % 154.70/154.54 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom, % 154.70/154.54 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ). % 154.70/154.54 % 154.70/154.54 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom, % 154.70/154.54 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ). % 154.70/154.54 % 154.70/154.54 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom, % 154.70/154.54 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ). % 154.70/154.54 % 154.70/154.54 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 154.70/154.54 class_Orderings_Opreorder(tc_HOL_Obool) ). % 154.70/154.54 % 154.70/154.54 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom, % 154.70/154.54 class_Finite__Set_Ofinite(tc_HOL_Obool) ). % 154.70/154.54 % 154.70/154.54 fof(arity_HOL__Obool__Lattices_Olattice,axiom, % 154.70/154.54 class_Lattices_Olattice(tc_HOL_Obool) ). % 154.70/154.54 % 154.70/154.54 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 154.70/154.54 class_Orderings_Oorder(tc_HOL_Obool) ). % 154.70/154.54 % 154.70/154.54 fof(arity_HOL__Obool__Orderings_Otop,axiom, % 154.70/154.54 class_Orderings_Otop(tc_HOL_Obool) ). % 154.70/154.54 % 154.70/154.54 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 154.70/154.54 class_Orderings_Oord(tc_HOL_Obool) ). % 154.70/154.54 % 154.70/154.54 fof(arity_HOL__Obool__Orderings_Obot,axiom, % 154.70/154.54 class_Orderings_Obot(tc_HOL_Obool) ). % 154.70/154.54 % 154.70/154.54 fof(arity_HOL__Obool__Groups_Ouminus,axiom, % 154.70/154.54 class_Groups_Ouminus(tc_HOL_Obool) ). % 154.70/154.54 % 154.70/154.54 fof(arity_HOL__Obool__Groups_Ominus,axiom, % 154.70/154.54 class_Groups_Ominus(tc_HOL_Obool) ). % 154.70/154.54 % 154.70/154.54 fof(arity_HOL__Obool__HOL_Oequal,axiom, % 154.70/154.54 class_HOL_Oequal(tc_HOL_Obool) ). % 154.70/154.54 % 154.70/154.54 fof(arity_HOL__Obool__Enum_Oenum,axiom, % 154.70/154.54 class_Enum_Oenum(tc_HOL_Obool) ). % 154.70/154.54 % 154.70/154.54 fof(arity_HOL__Obool__Nat_Osize,axiom, % 154.70/154.54 class_Nat_Osize(tc_HOL_Obool) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Com__Ostate__HOL_Oequal,axiom, % 154.70/154.54 class_HOL_Oequal(tc_Com_Ostate) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Com__Ostate__Nat_Osize,axiom, % 154.70/154.54 class_Nat_Osize(tc_Com_Ostate) ). % 154.70/154.54 % 154.70/154.54 fof(arity_List__Olist__HOL_Oequal,axiom, % 154.70/154.54 ! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)) ). % 154.70/154.54 % 154.70/154.54 fof(arity_List__Olist__Nat_Osize,axiom, % 154.70/154.54 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ). % 154.70/154.54 % 154.70/154.54 fof(arity_sum__Finite__Set_Ofinite,axiom, % 154.70/154.54 ! [T_1,T_2] : % 154.70/154.54 ( ( class_Finite__Set_Ofinite(T_2) % 154.70/154.54 & class_Finite__Set_Ofinite(T_1) ) % 154.70/154.54 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_sum__HOL_Oequal,axiom, % 154.70/154.54 ! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)) ). % 154.70/154.54 % 154.70/154.54 fof(arity_sum__Enum_Oenum,axiom, % 154.70/154.54 ! [T_1,T_2] : % 154.70/154.54 ( ( class_Enum_Oenum(T_2) % 154.70/154.54 & class_Enum_Oenum(T_1) ) % 154.70/154.54 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_sum__Nat_Osize,axiom, % 154.70/154.54 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom, % 154.70/154.54 ! [T_1] : % 154.70/154.54 ( class_Finite__Set_Ofinite(T_1) % 154.70/154.54 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Option__Ooption__HOL_Oequal,axiom, % 154.70/154.54 ! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Option__Ooption__Enum_Oenum,axiom, % 154.70/154.54 ! [T_1] : % 154.70/154.54 ( class_Enum_Oenum(T_1) % 154.70/154.54 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Option__Ooption__Nat_Osize,axiom, % 154.70/154.54 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ). % 154.70/154.54 % 154.70/154.54 fof(arity_prod__Finite__Set_Ofinite,axiom, % 154.70/154.54 ! [T_1,T_2] : % 154.70/154.54 ( ( class_Finite__Set_Ofinite(T_2) % 154.70/154.54 & class_Finite__Set_Ofinite(T_1) ) % 154.70/154.54 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_prod__Smallcheck_Osmall,axiom, % 154.70/154.54 ! [T_1,T_2] : % 154.70/154.54 ( ( class_Smallcheck_Osmall(T_2) % 154.70/154.54 & class_Smallcheck_Osmall(T_1) ) % 154.70/154.54 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_prod__HOL_Oequal,axiom, % 154.70/154.54 ! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)) ). % 154.70/154.54 % 154.70/154.54 fof(arity_prod__Enum_Oenum,axiom, % 154.70/154.54 ! [T_1,T_2] : % 154.70/154.54 ( ( class_Enum_Oenum(T_2) % 154.70/154.54 & class_Enum_Oenum(T_1) ) % 154.70/154.54 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ). % 154.70/154.54 % 154.70/154.54 fof(arity_prod__Nat_Osize,axiom, % 154.70/154.54 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom, % 154.70/154.54 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom, % 154.70/154.54 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Product____Type__Ounit__HOL_Oequal,axiom, % 154.70/154.54 class_HOL_Oequal(tc_Product__Type_Ounit) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom, % 154.70/154.54 class_Enum_Oenum(tc_Product__Type_Ounit) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Product____Type__Ounit__Nat_Osize,axiom, % 154.70/154.54 class_Nat_Osize(tc_Product__Type_Ounit) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Evaluation__Oterm__HOL_Oequal,axiom, % 154.70/154.54 class_HOL_Oequal(tc_Code__Evaluation_Oterm) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom, % 154.70/154.54 class_Nat_Osize(tc_Code__Evaluation_Oterm) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom, % 154.70/154.54 ! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom, % 154.70/154.54 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 154.70/154.54 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 154.70/154.54 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom, % 154.70/154.54 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom, % 154.70/154.54 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom, % 154.70/154.54 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom, % 154.70/154.54 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom, % 154.70/154.54 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom, % 154.70/154.54 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom, % 154.70/154.54 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom, % 154.70/154.54 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom, % 154.70/154.54 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom, % 154.70/154.54 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom, % 154.70/154.54 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom, % 154.70/154.54 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom, % 154.70/154.54 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom, % 154.70/154.54 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom, % 154.70/154.54 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom, % 154.70/154.54 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom, % 154.70/154.54 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom, % 154.70/154.54 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom, % 154.70/154.54 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom, % 154.70/154.54 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom, % 154.70/154.54 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom, % 154.70/154.54 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom, % 154.70/154.54 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom, % 154.70/154.54 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom, % 154.70/154.54 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom, % 154.70/154.54 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom, % 154.70/154.54 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom, % 154.70/154.54 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom, % 154.70/154.54 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom, % 154.70/154.54 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom, % 154.70/154.54 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom, % 154.70/154.54 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom, % 154.70/154.54 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom, % 154.70/154.54 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom, % 154.70/154.54 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom, % 154.70/154.54 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom, % 154.70/154.54 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom, % 154.70/154.54 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal,axiom, % 154.70/154.54 class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom, % 154.70/154.54 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom, % 154.70/154.54 ! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 154.70/154.54 % 154.70/154.54 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom, % 154.70/154.54 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 154.70/154.54 % 154.70/154.54 %----Helper facts (20) % 154.70/154.54 fof(help_c__COMBI__1,axiom, % 154.70/154.54 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ). % 154.70/154.54 % 154.70/154.54 fof(help_c__COMBK__1,axiom, % 154.70/154.54 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ). % 154.70/154.54 % 154.70/154.54 fof(help_c__COMBB__1,axiom, % 154.70/154.54 ! [V_R_2,V_Q_2,V_P_2,T_c,T_a,T_b] : hAPP(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)) ). % 154.70/154.54 % 154.70/154.54 fof(help_c__COMBC__1,axiom, % 154.70/154.54 ! [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) ). % 154.70/154.54 % 154.70/154.54 fof(help_c__COMBS__1,axiom, % 154.70/154.54 ! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(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)) ). % 154.70/154.54 % 154.70/154.54 fof(help_c__fequal__1,axiom, % 154.70/154.54 ! [V_y_2,V_x_2] : % 154.70/154.54 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) % 154.70/154.54 | V_x_2 = V_y_2 ) ). % 154.70/154.54 % 154.70/154.54 fof(help_c__fequal__2,axiom, % 154.70/154.54 ! [V_y_2,V_x_2] : % 154.70/154.54 ( V_x_2 != V_y_2 % 154.70/154.54 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(help_c__fFalse__1,axiom, % 154.70/154.54 ~ hBOOL(c_fFalse) ). % 154.70/154.54 % 154.70/154.54 fof(help_c__fTrue__1,axiom, % 154.70/154.54 hBOOL(c_fTrue) ). % 154.70/154.54 % 154.70/154.54 fof(help_c__fNot__1,axiom, % 154.70/154.54 ! [V_P_2] : % 154.70/154.54 ( ~ hBOOL(hAPP(c_fNot,V_P_2)) % 154.70/154.54 | ~ hBOOL(V_P_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(help_c__fNot__2,axiom, % 154.70/154.54 ! [V_P_2] : % 154.70/154.54 ( ~ ~ hBOOL(V_P_2) % 154.70/154.54 | hBOOL(hAPP(c_fNot,V_P_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(help_c__fconj__1,axiom, % 154.70/154.54 ! [V_Q_2,V_P_2] : % 154.70/154.54 ( ~ hBOOL(V_P_2) % 154.70/154.54 | ~ hBOOL(V_Q_2) % 154.70/154.54 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(help_c__fconj__2,axiom, % 154.70/154.54 ! [V_Q_2,V_P_2] : % 154.70/154.54 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) % 154.70/154.54 | hBOOL(V_P_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(help_c__fconj__3,axiom, % 154.70/154.54 ! [V_Q_2,V_P_2] : % 154.70/154.54 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) % 154.70/154.54 | hBOOL(V_Q_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(help_c__fdisj__1,axiom, % 154.70/154.54 ! [V_Q_2,V_P_2] : % 154.70/154.54 ( ~ hBOOL(V_P_2) % 154.70/154.54 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(help_c__fdisj__2,axiom, % 154.70/154.54 ! [V_P_2,V_Q_2] : % 154.70/154.54 ( ~ hBOOL(V_Q_2) % 154.70/154.54 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(help_c__fdisj__3,axiom, % 154.70/154.54 ! [V_Q_2,V_P_2] : % 154.70/154.54 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) % 154.70/154.54 | hBOOL(V_P_2) % 154.70/154.54 | hBOOL(V_Q_2) ) ). % 154.70/154.54 % 154.70/154.54 fof(help_c__fimplies__1,axiom, % 154.70/154.54 ! [V_Q_2,V_P_2] : % 154.70/154.54 ( hBOOL(V_P_2) % 154.70/154.54 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(help_c__fimplies__2,axiom, % 154.70/154.54 ! [V_P_2,V_Q_2] : % 154.70/154.54 ( ~ hBOOL(V_Q_2) % 154.70/154.54 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ). % 154.70/154.54 % 154.70/154.54 fof(help_c__fimplies__3,axiom, % 154.70/154.54 ! [V_Q_2,V_P_2] : % 154.70/154.54 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) % 154.70/154.54 | ~ hBOOL(V_P_2) % 154.70/154.54 | hBOOL(V_Q_2) ) ). % 154.70/154.54 % 154.70/154.54 %----Conjectures (3) % 154.70/154.54 fof(conj_0,hypothesis, % 154.70/154.54 c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal)),c_Com_Ocom_OBODY)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Opname),c_Natural_Oevalc),c_Com_Ocom_OBODY))),v_Procs)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Opname),c_Natural_Oevalc),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody)))),v_Procs)) ). % 154.70/154.54 % 154.70/154.54 fof(conj_1,hypothesis, % 154.70/154.54 c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal)),c_Com_Ocom_OBODY)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Opname),c_Natural_Oevalc),c_Com_Ocom_OBODY))),v_Procs)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ). % 154.70/154.54 % 154.70/154.54 fof(conj_2,conjecture, % 154.70/154.54 c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal)),c_Com_Ocom_OBODY)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Opname),c_Natural_Oevalc),c_Com_Ocom_OBODY))),v_Procs)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,v_pn)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ). % 154.70/154.54 % 154.70/154.54 %------------------------------------------------------------------------------ % 154.70/154.54 %------------------------------------------- % 154.70/154.54 % Proof found % 154.70/154.54 % SZS status Theorem for theBenchmark % 154.70/154.54 % SZS output start Proof % 154.70/154.55 %ClaNum:10210(EqnAxiom:2874) % 154.70/154.55 %VarNum:70242(SingletonVarNum:20482) % 154.70/154.55 %MaxLitNum:8 % 154.70/154.55 %MaxfuncDepth:15 % 154.70/154.55 %SharedTerms:1124 % 154.70/154.55 %goalClause: 4566 % 154.70/154.55 %singleGoalClaCount:1 % 154.70/154.55 [2878]P1(a191) % 154.70/154.55 [2879]P2(a870) % 154.70/154.55 [2880]P2(a875) % 154.70/154.55 [2881]P2(a1) % 154.70/154.55 [2882]P98(a870) % 154.70/154.55 [2883]P98(a875) % 154.70/154.55 [2884]P99(a870) % 154.70/154.55 [2885]P99(a875) % 154.70/154.55 [2886]P99(a1) % 154.70/154.55 [2887]P3(a870) % 154.70/154.55 [2888]P4(a870) % 154.70/154.55 [2889]P4(a878) % 154.70/154.55 [2890]P64(a870) % 154.70/154.55 [2891]P64(a875) % 154.70/154.55 [2892]P64(a1) % 154.70/154.55 [2893]P64(a103) % 154.70/154.55 [2894]P103(a1) % 154.70/154.55 [2895]P65(a1) % 154.70/154.55 [2896]P100(a870) % 154.70/154.55 [2897]P100(a875) % 154.70/154.55 [2898]P100(a1) % 154.70/154.55 [2899]P66(a875) % 154.70/154.55 [2900]P66(a1) % 154.70/154.55 [2901]P66(a103) % 154.70/154.55 [2902]P96(a870) % 154.70/154.55 [2903]P96(a875) % 154.70/154.55 [2904]P96(a1) % 154.70/154.55 [2905]P72(a1) % 154.70/154.55 [2906]P5(a870) % 154.70/154.55 [2907]P67(a875) % 154.70/154.55 [2908]P67(a1) % 154.70/154.55 [2909]P67(a103) % 154.70/154.55 [2910]P68(a875) % 154.70/154.55 [2911]P68(a1) % 154.70/154.55 [2912]P68(a103) % 154.70/154.55 [2913]P69(a875) % 154.70/154.55 [2914]P69(a1) % 154.70/154.55 [2915]P69(a103) % 154.70/154.55 [2916]P76(a875) % 154.70/154.55 [2917]P76(a1) % 154.70/154.55 [2918]P76(a103) % 154.70/154.55 [2919]P104(a870) % 154.70/154.55 [2920]P77(a875) % 154.70/154.55 [2921]P77(a1) % 154.70/154.55 [2922]P77(a103) % 154.70/154.55 [2923]P74(a1) % 154.70/154.55 [2924]P97(a870) % 154.70/154.55 [2925]P78(a875) % 154.70/154.55 [2926]P78(a1) % 154.70/154.55 [2927]P78(a103) % 154.70/154.55 [2928]P134(a875) % 154.70/154.55 [2929]P134(a1) % 154.70/154.55 [2930]P134(a103) % 154.70/154.55 [2931]P109(a875) % 154.70/154.55 [2932]P109(a1) % 154.70/154.55 [2933]P109(a103) % 154.70/154.55 [2934]P141(a875) % 154.70/154.55 [2935]P141(a1) % 154.70/154.55 [2936]P73(a875) % 154.70/154.55 [2937]P73(a1) % 154.70/154.55 [2938]P73(a103) % 154.70/154.55 [2939]P89(a1) % 154.70/154.55 [2940]P114(a1) % 154.70/154.55 [2941]P115(a875) % 154.70/154.55 [2942]P115(a1) % 154.70/154.55 [2943]P115(a103) % 154.70/154.55 [2944]P122(a875) % 154.70/154.55 [2945]P122(a1) % 154.70/154.55 [2946]P122(a103) % 154.70/154.55 [2947]P120(a1) % 154.70/154.55 [2948]P123(a875) % 154.70/154.55 [2949]P123(a1) % 154.70/154.55 [2950]P123(a103) % 154.70/154.55 [2951]P121(a1) % 154.70/154.55 [2952]P135(a1) % 154.70/154.55 [2953]P105(a875) % 154.70/154.55 [2954]P105(a1) % 154.70/154.55 [2955]P105(a103) % 154.70/154.55 [2956]P106(a870) % 154.70/154.55 [2957]P106(a875) % 154.70/154.55 [2958]P106(a1) % 154.70/154.55 [2959]P106(a103) % 154.70/154.55 [2960]P107(a870) % 154.70/154.55 [2961]P107(a875) % 154.70/154.55 [2962]P107(a1) % 154.70/154.55 [2963]P107(a103) % 154.70/154.55 [2964]P108(a870) % 154.70/154.55 [2965]P108(a875) % 154.70/154.55 [2966]P108(a1) % 154.70/154.55 [2967]P108(a103) % 154.70/154.55 [2968]P70(a875) % 154.70/154.55 [2969]P70(a1) % 154.70/154.55 [2970]P70(a103) % 154.70/154.55 [2971]P127(a1) % 154.70/154.55 [2972]P128(a875) % 154.70/154.55 [2973]P128(a1) % 154.70/154.55 [2974]P128(a103) % 154.70/154.55 [2975]P136(a1) % 154.70/154.55 [2976]P129(a875) % 154.70/154.55 [2977]P129(a1) % 154.70/154.55 [2978]P129(a103) % 154.70/154.55 [2979]P138(a875) % 154.70/154.55 [2980]P138(a1) % 154.70/154.55 [2981]P138(a103) % 154.70/154.55 [2982]P110(a875) % 154.70/154.55 [2983]P110(a1) % 154.70/154.55 [2984]P110(a103) % 154.70/154.55 [2985]P80(a875) % 154.70/154.55 [2986]P80(a1) % 154.70/154.55 [2987]P80(a103) % 154.70/154.55 [2988]P84(a875) % 154.70/154.55 [2989]P84(a1) % 154.70/154.55 [2990]P84(a103) % 154.70/154.55 [2991]P81(a1) % 154.70/154.55 [2992]P79(a875) % 154.70/154.55 [2993]P79(a1) % 154.70/154.55 [2994]P79(a103) % 154.70/154.55 [2995]P139(a875) % 154.70/154.55 [2996]P139(a1) % 154.70/154.55 [2997]P139(a103) % 154.70/154.55 [2998]P85(a875) % 154.70/154.55 [2999]P85(a1) % 154.70/154.55 [3000]P85(a103) % 154.70/154.55 [3001]P82(a875) % 154.70/154.55 [3002]P82(a1) % 154.70/154.55 [3003]P82(a103) % 154.70/154.55 [3004]P130(a875) % 154.70/154.55 [3005]P130(a1) % 154.70/154.55 [3006]P130(a103) % 154.70/154.55 [3007]P132(a875) % 154.70/154.55 [3008]P132(a1) % 154.70/154.55 [3009]P132(a103) % 154.70/154.55 [3010]P131(a875) % 154.70/154.55 [3011]P131(a1) % 154.70/154.55 [3012]P131(a103) % 154.70/154.55 [3013]P124(a875) % 154.70/154.55 [3014]P124(a1) % 154.70/154.55 [3015]P124(a103) % 154.70/154.55 [3016]P125(a1) % 154.70/154.55 [3017]P126(a1) % 154.70/154.55 [3018]P101(a875) % 154.70/154.55 [3019]P101(a1) % 154.70/154.55 [3020]P101(a103) % 154.70/154.55 [3021]P140(a875) % 154.70/154.55 [3022]P140(a1) % 154.70/154.55 [3023]P140(a103) % 154.70/154.55 [3024]P83(a1) % 154.70/154.55 [3025]P133(a1) % 154.70/154.55 [3026]P75(a875) % 154.70/154.55 [3027]P75(a1) % 154.70/154.55 [3028]P75(a103) % 154.70/154.55 [3029]P93(a870) % 154.70/154.55 [3030]P86(a870) % 154.70/154.55 [3031]P86(a1) % 154.70/154.55 [3032]P116(a1) % 154.70/154.55 [3033]P111(a1) % 154.70/154.55 [3034]P137(a1) % 154.70/154.55 [3035]P71(a1) % 154.70/154.55 [3036]P112(a875) % 154.70/154.55 [3037]P112(a1) % 154.70/154.55 [3038]P112(a103) % 154.70/154.55 [3039]P57(a875) % 154.70/154.55 [3040]P57(a1) % 154.70/154.55 [3041]P57(a103) % 154.70/154.55 [3042]P58(a1) % 154.70/154.55 [3043]P87(a1) % 154.70/154.55 [3044]P90(a1) % 154.70/154.55 [3045]P91(a875) % 154.70/154.55 [3046]P91(a1) % 154.70/154.55 [3047]P91(a103) % 154.70/154.55 [3048]P113(a875) % 154.70/154.55 [3049]P88(a875) % 154.70/154.55 [3050]P88(a1) % 154.70/154.55 [3051]P88(a103) % 154.70/154.55 [3052]P142(a878) % 154.70/154.55 [3053]P142(a1) % 154.70/154.55 [3054]P59(a870) % 154.70/154.55 [3055]P59(a878) % 154.70/154.55 [3056]P92(a870) % 154.70/154.55 [3057]P92(a871) % 154.70/154.55 [3058]P92(a872) % 154.70/154.55 [3059]P92(a875) % 154.70/154.55 [3060]P92(a878) % 154.70/154.55 [3061]P92(a1) % 154.70/154.55 [3062]P92(a103) % 154.70/154.55 [3063]P92(a324) % 154.70/154.55 [3064]P102(a870) % 154.70/154.55 [3065]P102(a871) % 154.70/154.55 [3066]P102(a872) % 154.70/154.55 [3067]P102(a875) % 154.70/154.55 [3068]P102(a878) % 154.70/154.55 [3069]P102(a103) % 154.70/154.55 [3070]P102(a324) % 154.70/154.55 [3071]P95(a870) % 154.70/154.55 [3091]P39(a875,a247) % 154.70/154.55 [3092]P39(a875,a318) % 154.70/154.55 [4459]~E(a101,a83) % 154.70/154.55 [4460]~P1(a246) % 154.70/154.55 [2875]E(f2(a1),a83) % 154.70/154.55 [2876]E(f104(a103),a3) % 154.70/154.55 [2877]E(f22(a103),a23) % 154.70/154.55 [3072]E(f192(a875),f2(a875)) % 154.70/154.55 [3073]E(f31(a24),f2(a875)) % 154.70/154.55 [3074]E(f105(a875),f240(a875)) % 154.70/154.55 [3075]E(f114(a875),f241(a875)) % 154.70/154.55 [3076]E(f106(a1),f34(a1)) % 154.70/154.55 [3077]E(f84(a246),f2(a875)) % 154.70/154.55 [3078]E(f84(a191),f2(a875)) % 154.70/154.55 [3079]P6(f2(a1)) % 154.70/154.55 [3080]P6(f78(a1)) % 154.70/154.55 [3129]P1(f328(a25,a24)) % 154.70/154.55 [3142]P39(f881(a875,a875),a35) % 154.70/154.55 [3494]E(f320(a875,a875,a247,a247),a35) % 154.70/154.55 [4461]~E(f78(a1),f2(a1)) % 154.70/154.55 [3081]E(f4(f2(a103)),f2(a875)) % 154.70/154.55 [3082]E(f115(f2(a875)),f2(a875)) % 154.70/154.55 [3094]E(f328(f79(a1),a83),a83) % 154.70/154.55 [3098]E(f328(a3,f2(a875)),f2(a103)) % 154.70/154.55 [3099]E(f328(a116,f2(a875)),f78(a875)) % 154.70/154.55 [3100]E(f328(a108,f78(a1)),f78(a875)) % 154.70/154.55 [3101]E(f328(a3,f78(a875)),f78(a103)) % 154.70/154.55 [3103]E(f328(f107(a1),a83),f2(a1)) % 154.70/154.55 [3104]E(f328(f107(a103),a83),f2(a103)) % 154.70/154.55 [3105]E(f328(a108,f2(a1)),f2(a875)) % 154.70/154.55 [3106]E(f328(f193(a870),a246),f2(a875)) % 154.70/154.55 [3107]E(f328(f193(a870),a191),f2(a875)) % 154.70/154.55 [3108]E(f328(f193(a871),a24),f2(a875)) % 154.70/154.55 [3109]E(f328(f107(a875),a83),f2(a875)) % 154.70/154.55 [3113]E(f328(f79(a1),f78(a1)),a101) % 154.70/154.55 [3121]E(f328(f193(a103),f2(a103)),f2(a875)) % 154.70/154.55 [3122]E(f328(f104(a1),f2(a875)),f2(a1)) % 154.70/154.55 [3123]E(f328(f104(a1),f78(a875)),f78(a1)) % 154.70/154.55 [3124]E(f328(f79(a1),f2(a1)),f2(a1)) % 154.70/154.55 [3138]E(f328(a108,f78(a1)),f328(a116,f2(a875))) % 154.70/154.55 [3139]E(f328(f176(a873,a871),a27),a28) % 154.70/154.55 [3140]E(f319(f881(a875,a875),a35),a36) % 154.70/154.55 [3141]E(f321(f881(a875,a875),a35),a68) % 154.70/154.55 [3163]E(f328(f249(a875),f2(a875)),f192(f882(a875,a870))) % 154.70/154.55 [3164]E(f328(f250(a875),f2(a875)),f251(f882(a875,a870))) % 154.70/154.55 [3172]P40(f192(f882(a1,a870))) % 154.70/154.55 [3208]E(f328(f328(f22(a103),f2(a103)),f78(a103)),f2(a103)) % 154.70/154.55 [3285]P1(f328(f328(f243(a1),a101),f2(a1))) % 154.70/154.55 [3310]P1(f328(f328(f243(a1),f2(a1)),f78(a1))) % 154.70/154.55 [3312]P1(f328(f328(f242(a1),f2(a1)),f78(a1))) % 154.70/154.55 [3486]P1(f328(f61(a873),f182(a873,a871,a28))) % 154.70/154.55 [3524]E(f328(f328(f285(a875,a875,a875),a318),f304(a875,a318)),a247) % 154.70/154.55 [3562]P42(a1,a875,a108,f328(f242(a1),f2(a1))) % 154.70/154.55 [3566]E(f328(f328(f41(a875,f882(a875,a870)),f251(f882(a875,a870))),f249(a875)),f251(f882(a875,a870))) % 154.70/154.55 [3567]E(f328(f328(f41(a875,f882(a875,a870)),f251(f882(a875,a870))),f297(a875)),f251(f882(a875,a870))) % 154.70/154.55 [3568]E(f328(f328(f41(a875,f882(a875,a870)),f251(f882(a875,a870))),f250(a875)),f251(f882(a875,a870))) % 154.70/154.55 [3569]E(f328(f328(f42(a875,f882(a875,a870)),f251(f882(a875,a870))),f300(a875)),f192(f882(a875,a870))) % 154.70/154.55 [3585]P27(a875,a1,f104(a1),f251(f882(a875,a870))) % 154.70/154.55 [3598]P42(a875,a1,f104(a1),f328(f16(a870,a875),a191)) % 154.70/154.55 [3733]E(f328(f73(a875,a103,a1,a3),a108),f107(a103)) % 154.70/154.55 [3958]P53(a103,a875,a19,a3,f251(f882(a875,a870))) % 154.70/154.55 [3967]P53(a1,f882(f881(a875,a875),a870),a110,a89,a102) % 154.70/154.55 [4232]E(f268(a1,a1,a1,a1,f34(a1),f79(a1)),a50) % 154.70/154.55 [4484]~E(f328(f107(a1),a101),f328(f107(a1),a83)) % 154.70/154.55 [4485]~P1(f328(a197,f2(a1))) % 154.70/154.55 [4486]~P1(f328(a197,f78(a1))) % 154.70/154.55 [4527]~P1(f328(f328(f243(a1),a83),f2(a1))) % 154.70/154.55 [3155]E(f328(f328(f22(a1),a101),a101),a83) % 154.70/154.55 [3170]E(f328(f104(a1),f328(a116,f2(a875))),f78(a1)) % 154.70/154.55 [3236]E(f328(f37(a878),f251(f882(a878,a870))),f78(a875)) % 154.70/154.55 [3257]P1(f328(a197,f328(f107(a1),a101))) % 154.70/154.55 [3258]P1(f328(f328(f243(a1),a101),a83)) % 154.70/154.55 [3260]P1(f328(f328(f242(a1),a101),a83)) % 154.70/154.55 [3321]E(f328(f328(f306(a875),f2(a875)),f192(f882(a875,a870))),f328(f297(a875),f2(a875))) % 154.70/154.55 [3378]P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),a83))) % 154.70/154.55 [3390]E(f328(f307(a875,a875,a116),f251(f882(a875,a870))),f328(f300(a875),f2(a875))) % 154.70/154.55 [3430]P8(f881(a875,a875),f251(f882(f881(a875,a875),a870)),a112) % 154.70/154.55 [3741]E(f328(f73(a875,a1,a103,f104(a1)),a19),a20) % 154.70/154.55 [3801]P39(a875,f328(f248(f881(a875,a875)),f328(f267(a875,a875,a870),f243(a875)))) % 154.70/154.55 [4516]~P1(f328(a197,f328(f107(a1),a83))) % 154.70/154.55 [4517]~P1(f328(f328(f243(a1),a83),a83)) % 154.70/154.55 [4518]~P1(f328(f328(f243(a1),a83),a101)) % 154.70/154.55 [4519]~P1(f328(f328(f243(a1),a101),a101)) % 154.70/154.55 [4520]~P1(f328(f328(f242(a1),a83),a101)) % 154.70/154.55 [4521]~P1(f328(f328(f91(a1),a83),a101)) % 154.70/154.55 [4522]~P1(f328(f328(f91(a1),a101),a83)) % 154.70/154.55 [4533]~P1(f328(f61(a875),f251(f882(a875,a870)))) % 154.70/154.55 [4534]~P1(f328(f61(a1),f251(f882(a1,a870)))) % 154.70/154.55 [4403]E(f328(f267(a1,a1,a870),f328(f328(f8(f882(a1,a870),f882(a1,a870),a1),f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a326),f328(f243(a1),f2(a1))))),f328(f328(f7(a1,a1,f882(a1,a870)),f328(f328(f8(f882(a1,f882(a1,a870)),f882(a1,f882(a1,a870)),a1),f7(a1,a1,a870)),f328(f328(f8(f882(a1,a1),f882(a1,f882(a1,a870)),a1),f328(f8(a1,f882(a1,a870),a1),a325)),a224))),f78(a1)))),a220) % 154.70/154.55 [3468]E(f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101),f328(f79(a1),a101)) % 154.70/154.55 [3507]E(f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101),f328(f328(f22(a1),a83),a101)) % 154.70/154.55 [3667]E(f328(f328(f60(f881(a875,a875)),f251(f882(f881(a875,a875),a870))),a112),a102) % 154.70/154.55 [3696]E(f328(f107(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f78(a1)) % 154.70/154.55 [3697]E(f328(f107(a103),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f78(a103)) % 154.70/154.55 [3698]E(f328(f107(a875),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f78(a875)) % 154.70/154.55 [3702]E(f328(f107(a875),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(a116,f2(a875))) % 154.70/154.55 [4092]E(f328(f328(f114(f882(f881(f881(a875,a875),f881(a875,a875)),a870)),a35),f304(f881(a875,a875),f192(f882(f881(f881(a875,a875),f881(a875,a875)),a870)))),a70) % 154.70/154.55 [4163]E(f328(a89,f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),f328(f328(f263(a875,a875),f2(a875)),f2(a875))),f192(f882(f881(a875,a875),a870))))),f2(a1)) % 154.70/154.55 [4164]E(f328(a89,f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),f328(f328(f263(a875,a875),f78(a875)),f2(a875))),f192(f882(f881(a875,a875),a870))))),f78(a1)) % 154.70/154.55 [4179]E(f328(f248(f881(a875,a875)),f328(f267(a875,a875,a870),f328(f328(f8(a875,f882(a875,a870),a875),f328(f7(a875,a875,a870),a325)),a116))),a318) % 154.70/154.55 [4149]E(f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),f328(a116,f328(a116,f2(a875)))) % 154.70/154.55 [4152]E(f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),f328(f328(f80(a875),f78(a875)),f78(a875))) % 154.70/154.55 [4153]E(f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),f328(f37(a870),f251(f882(a870,a870)))) % 154.70/154.55 [4218]P6(f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))) % 154.70/154.55 [4290]P28(f882(f881(a875,a875),a870),f328(f328(f263(f882(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),a870),f882(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),a870)),a36),a69)) % 154.70/154.55 [4291]P28(f882(f881(a875,a875),a870),f328(f328(f263(f882(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),a870),f882(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),a870)),a68),a71)) % 154.70/154.55 [4331]E(f328(f328(f114(f882(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),a870)),f321(f881(a875,a875),a70)),f328(f328(f306(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f328(f328(f263(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),f192(f882(f881(a875,a875),a870))),f192(f882(f881(a875,a875),a870)))),f192(f882(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),a870)))),a71) % 154.70/154.55 [4332]E(f328(f328(f114(f882(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),a870)),f319(f881(a875,a875),a70)),f328(f328(f306(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f328(f328(f263(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),f192(f882(f881(a875,a875),a870))),f192(f882(f881(a875,a875),a870)))),f192(f882(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),a870)))),a69) % 154.70/154.55 [4220]E(f328(a108,f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(a116,f328(a116,f2(a875)))) % 154.70/154.55 [4267]E(f328(f104(a1),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))) % 154.70/154.55 [4302]P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 154.70/154.55 [4303]E(f328(f107(a875),f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),a101)),f328(a116,f328(a116,f328(a116,f2(a875))))) % 154.70/154.55 [4345]P6(f328(f107(a1),f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),a101))) % 154.70/154.55 [4416]P26(a872,f328(f328(f114(f882(f874(a872),a870)),a883),f328(f307(a873,f874(a872),f328(f328(f18(a873,f882(a872,f882(a872,a870)),f874(a872)),f328(f328(f8(a871,f882(f882(a872,f882(a872,a870)),f874(a872)),a873),f328(f92(a872),a325)),a26)),f328(f328(f8(a871,f882(a872,f882(a872,a870)),a873),a198),a26))),a884)),f328(f328(f306(f874(a872)),f328(f328(f328(f92(a872),a325),f328(f239(a871),f328(a28,a885))),f328(a198,f328(f239(a871),f328(a28,a885))))),f192(f882(f874(a872),a870)))) % 154.70/154.55 [4425]P26(a872,f328(f328(f114(f882(f874(a872),a870)),a883),f328(f307(a873,f874(a872),f328(f328(f18(a873,f882(a872,f882(a872,a870)),f874(a872)),f328(f328(f8(a871,f882(f882(a872,f882(a872,a870)),f874(a872)),a873),f328(f92(a872),a325)),a26)),f328(f328(f8(a871,f882(a872,f882(a872,a870)),a873),a198),a26))),a884)),f328(f307(a873,f874(a872),f328(f328(f18(a873,f882(a872,f882(a872,a870)),f874(a872)),f328(f328(f8(a871,f882(f882(a872,f882(a872,a870)),f874(a872)),a873),f328(f92(a872),a325)),f328(f328(f8(f879(a871),a871,a873),f239(a871)),a28))),f328(f328(f8(a871,f882(a872,f882(a872,a870)),a873),a198),f328(f328(f8(f879(a871),a871,a873),f239(a871)),a28)))),a884)) % 154.70/154.55 [4566]~P26(a872,f328(f328(f114(f882(f874(a872),a870)),a883),f328(f307(a873,f874(a872),f328(f328(f18(a873,f882(a872,f882(a872,a870)),f874(a872)),f328(f328(f8(a871,f882(f882(a872,f882(a872,a870)),f874(a872)),a873),f328(f92(a872),a325)),a26)),f328(f328(f8(a871,f882(a872,f882(a872,a870)),a873),a198),a26))),a884)),f328(f328(f306(f874(a872)),f328(f328(f328(f92(a872),a325),f328(f239(a871),f328(a28,a885))),f328(a198,f328(a26,a885)))),f192(f882(f874(a872),a870)))) % 154.70/154.55 [4373]E(f328(f104(a1),f328(f107(a875),f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),a101))),f328(f107(a1),f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),a101))) % 154.70/154.55 [4388]P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),a101)))) % 154.70/154.55 [3093]P7(x30931,a325) % 154.70/154.55 [3495]P27(a875,a875,a116,x34951) % 154.70/154.55 [3083]P92(f874(x30831)) % 154.70/154.55 [3084]P92(f879(x30841)) % 154.70/154.55 [3085]P92(f876(x30851)) % 154.70/154.55 [3086]P92(f877(x30861)) % 154.70/154.55 [3087]P102(f874(x30871)) % 154.70/154.55 [3088]P102(f879(x30881)) % 154.70/154.55 [3089]P102(f876(x30891)) % 154.70/154.55 [3090]P102(f877(x30901)) % 154.70/154.55 [3110]P39(a1,f109(x31101)) % 154.70/154.55 [3111]P39(a1,f111(x31111)) % 154.70/154.55 [3160]P39(f882(x31601,a870),f303(x31601)) % 154.70/154.55 [3184]E(f252(x31841,x31841,a325),a325) % 154.70/154.55 [3199]E(f44(a1,x31991,x31991),f2(a1)) % 154.70/154.55 [3254]P17(x32541,f882(x32541,a870),f306(x32541)) % 154.70/154.55 [4463]~E(f328(a26,x44631),a24) % 154.70/154.55 [4465]~E(f328(a116,x44651),x44651) % 154.70/154.55 [4475]~E(f328(a116,x44751),f2(a875)) % 154.70/154.55 [3095]E(f328(f193(a875),x30951),x30951) % 154.70/154.55 [3096]E(f328(f107(a1),x30961),x30961) % 154.70/154.55 [3112]E(f328(a89,f329(x31121)),x31121) % 154.70/154.55 [3125]E(f118(x31251,f117(x31251)),f117(x31251)) % 154.70/154.55 [3126]E(f149(x31261,f117(x31261)),f117(x31261)) % 154.70/154.55 [3130]E(f31(f328(a26,x31301)),f2(a875)) % 154.70/154.55 [3135]E(f328(f165(x31351),f117(x31351)),f117(x31351)) % 154.70/154.55 [3136]E(f328(f169(x31361),f117(x31361)),f117(x31361)) % 154.70/154.55 [3137]E(f328(f166(x31371),f117(x31371)),f117(x31371)) % 154.70/154.55 [3143]E(f328(f107(a1),x31431),f328(f106(a1),x31431)) % 154.70/154.55 [3144]E(f328(a89,f328(a110,x31441)),x31441) % 154.70/154.55 [3146]E(f328(a3,f328(a19,x31461)),x31461) % 154.70/154.55 [3147]E(f328(a19,f328(a3,x31471)),x31471) % 154.70/154.55 [3148]P6(f328(f104(a1),x31481)) % 154.70/154.55 [3153]E(f328(f193(f879(x31531)),f205(x31531)),f2(a875)) % 154.70/154.55 [3154]E(f328(f193(f876(x31541)),f117(x31541)),f2(a875)) % 154.70/154.55 [3159]E(f328(f193(a871),f328(a26,x31591)),f2(a875)) % 154.70/154.55 [3168]E(f234(x31681,f205(x31681)),f192(f882(x31681,a870))) % 154.70/154.55 [3175]E(f328(f328(f22(a875),x31751),f2(a875)),x31751) % 154.70/154.55 [3176]E(f328(f328(f80(a875),x31761),f2(a875)),x31761) % 154.70/154.55 [3177]E(f328(f328(f80(a1),x31771),f2(a1)),x31771) % 154.70/154.55 [3178]E(f328(f328(f81(a875),x31781),f78(a875)),x31781) % 154.70/154.55 [3179]E(f328(f328(f81(a1),x31791),f78(a1)),x31791) % 154.70/154.55 [3180]E(f328(f328(f241(a875),x31801),f2(a875)),x31801) % 154.70/154.55 [3181]E(f328(f328(f81(a875),x31811),f2(a875)),f2(a875)) % 154.70/154.55 [3182]E(f328(f328(f240(a875),x31821),f2(a875)),f2(a875)) % 154.70/154.55 [3183]E(f328(f328(f38(a1),x31831),f2(a1)),f2(a1)) % 154.70/154.55 [3190]E(f328(f170(x31901),f117(x31901)),f192(f882(x31901,a870))) % 154.70/154.55 [3194]P1(f328(f134(x31941),f117(x31941))) % 154.70/154.55 [3200]E(f328(f151(x32001,x32001),f5(x32001)),f34(f876(x32001))) % 154.70/154.55 [3201]E(f328(f151(x32011,x32011),f34(x32011)),f34(f876(x32011))) % 154.70/154.55 [3202]E(f328(f206(x32021,x32021),f5(x32021)),f34(f879(x32021))) % 154.70/154.55 [3203]E(f328(f206(x32031,x32031),f34(x32031)),f34(f879(x32031))) % 154.70/154.55 [3204]E(f44(a1,x32041,f2(a1)),x32041) % 154.70/154.55 [3205]E(f328(f242(a875),f328(a116,x32051)),f328(f243(a875),x32051)) % 154.70/154.55 [3206]E(f328(f249(a875),f328(a116,x32061)),f328(f297(a875),x32061)) % 154.70/154.55 [3207]E(f328(f250(a875),f328(a116,x32071)),f328(f300(a875),x32071)) % 154.70/154.55 [3209]E(f44(a1,f2(a1),x32091),f2(a1)) % 154.70/154.55 [3220]E(f328(f328(f80(a875),x32201),f78(a875)),f328(a116,x32201)) % 154.70/154.55 [3230]E(f328(f298(a875,x32301),f2(a875)),f192(f882(a875,a870))) % 154.70/154.55 [3242]E(f299(a875,f2(a875),x32421),f328(f297(a875),x32421)) % 154.70/154.55 [3288]E(f328(f328(f22(a875),f328(a116,x32881)),f78(a875)),x32881) % 154.70/154.55 [3301]E(f46(f2(a1),x33011),f328(f328(f263(a1,a1),f2(a1)),f2(a1))) % 154.70/154.55 [3350]P1(f328(f328(f243(a875),x33501),f328(a116,x33501))) % 154.70/154.55 [3362]P1(f328(f328(f243(a875),f2(a875)),f328(a116,x33621))) % 154.70/154.55 [3653]E(f328(f328(f22(a103),f328(a3,f328(a116,f328(a19,x36531)))),f78(a103)),x36531) % 154.70/154.55 [3725]P1(f328(f328(f242(a1),f328(f79(a1),f328(f104(a1),x37251))),f2(a1))) % 154.70/154.55 [3874]P1(f328(f328(f243(a1),f328(f79(a1),f328(f104(a1),f328(a116,x38741)))),f2(a1))) % 154.70/154.55 [4491]~E(f251(f882(x44911,a870)),f192(f882(x44911,a870))) % 154.70/154.55 [4530]~P1(f328(f328(f243(a875),x45301),f2(a875))) % 154.70/154.55 [4542]~P1(f328(f328(f243(a1),f328(f104(a1),x45421)),f2(a1))) % 154.70/154.55 [3158]E(f178(x31581,f117(f876(x31581))),f117(f876(x31581))) % 154.70/154.55 [3161]E(f328(f328(f81(a1),a83),x31611),a83) % 154.70/154.55 [3162]E(f328(f328(f80(a1),a83),x31621),x31621) % 154.70/154.55 [3165]E(f328(a108,f328(f104(a1),x31651)),x31651) % 154.70/154.55 [3166]E(f328(f328(f22(a1),x31661),a83),x31661) % 154.70/154.55 [3167]E(f328(f328(f80(a1),x31671),a83),x31671) % 154.70/154.55 [3169]E(f328(f328(f22(a875),x31691),x31691),f2(a875)) % 154.70/154.55 [3173]E(f328(f37(a875),f328(f249(a875),x31731)),x31731) % 154.70/154.55 [3174]E(f328(f79(a1),f328(f79(a1),x31741)),x31741) % 154.70/154.55 [3185]E(f328(f328(f80(a875),f2(a875)),x31851),x31851) % 154.70/154.55 [3186]E(f328(f328(f80(a1),f2(a1)),x31861),x31861) % 154.70/154.55 [3187]E(f328(f328(f81(a875),f78(a875)),x31871),x31871) % 154.70/154.55 [3188]E(f328(f328(f81(a1),f78(a1)),x31881),x31881) % 154.70/154.55 [3189]E(f328(f328(f241(a875),f2(a875)),x31891),x31891) % 154.70/154.55 [3195]E(f328(f328(f22(a875),f2(a875)),x31951),f2(a875)) % 154.70/154.55 [3196]E(f328(f328(f81(a875),f2(a875)),x31961),f2(a875)) % 154.70/154.55 [3197]E(f328(f328(f240(a875),f2(a875)),x31971),f2(a875)) % 154.70/154.55 [3198]E(f328(f328(f38(a1),f2(a1)),x31981),f2(a1)) % 154.70/154.55 [3215]E(f328(f298(a875,f2(a875)),x32151),f328(f249(a875),x32151)) % 154.70/154.55 [3216]E(f328(f328(f81(a1),a101),x32161),f328(f79(a1),x32161)) % 154.70/154.55 [3222]E(f328(a108,f328(f107(a1),x32221)),f328(f107(a875),x32221)) % 154.70/154.55 [3223]E(f328(a19,f328(f107(a103),x32231)),f328(f107(a875),x32231)) % 154.70/154.55 [3224]E(f328(f37(a875),f328(f297(a875),x32241)),f328(a116,x32241)) % 154.70/154.55 [3234]E(f328(f328(f80(a875),f78(a875)),x32341),f328(a116,x32341)) % 154.70/154.55 [3238]E(f328(f75(a1),f328(f104(a1),x32381)),f328(f104(a1),x32381)) % 154.70/154.55 [3239]E(f328(f106(a1),f328(f104(a1),x32391)),f328(f104(a1),x32391)) % 154.70/154.55 [3244]E(f328(f37(x32441),f192(f882(x32441,a870))),f2(a875)) % 154.70/154.55 [3246]E(f328(f328(f38(a875),x32461),f328(a116,f2(a875))),x32461) % 154.70/154.55 [3255]E(f44(a875,x32551,f328(a116,f2(a875))),f2(a875)) % 154.70/154.55 [3256]E(f44(a1,x32561,f328(f107(a1),a101)),f2(a1)) % 154.70/154.55 [3272]E(f328(f328(f38(a1),x32721),f328(f107(a1),a101)),f328(f79(a1),x32721)) % 154.70/154.55 [3276]E(f136(a875,f328(f298(a875,x32761),f2(a875))),f117(a875)) % 154.70/154.55 [3277]E(f328(f328(f80(a1),x32771),f78(a1)),f328(f328(f22(a1),x32771),a101)) % 154.70/154.55 [3278]E(f328(f328(f22(a1),x32781),f78(a1)),f328(f328(f80(a1),x32781),a101)) % 154.70/154.55 [3282]P1(f328(f328(f242(a875),x32821),x32821)) % 154.70/154.55 [3283]P1(f328(f328(f242(a1),x32831),x32831)) % 154.70/154.55 [3284]P1(f328(f328(f91(a1),x32841),x32841)) % 154.70/154.55 [3289]E(f328(f79(a1),f328(f107(a1),x32891)),f328(f107(a1),f328(f79(a1),x32891))) % 154.70/154.55 [3290]P1(f328(f61(a875),f328(f249(a875),x32901))) % 154.70/154.55 [3291]P1(f328(f61(a875),f328(f297(a875),x32911))) % 154.70/154.55 [3299]E(f158(x32991,f251(f882(x32991,a870))),f251(f882(f876(x32991),a870))) % 154.70/154.55 [3304]P1(f328(f328(f242(a875),f2(a875)),x33041)) % 154.70/154.55 [3314]E(f328(f328(f80(a875),f115(x33141)),f328(a116,f2(a875))),f115(f328(a116,x33141))) % 154.70/154.55 [3315]E(f328(f248(x33151),f328(f16(a870,x33151),a246)),f192(f882(x33151,a870))) % 154.70/154.55 [3316]E(f328(f248(x33161),f328(f16(a870,x33161),a191)),f251(f882(x33161,a870))) % 154.70/154.55 [3320]E(f328(f328(f306(a875),x33201),f328(f249(a875),x33201)),f328(f249(a875),f328(a116,x33201))) % 154.70/154.55 [3332]E(f328(f328(f80(a1),f78(a1)),f328(f104(a1),x33321)),f328(f104(a1),f328(a116,x33321))) % 154.70/154.55 [3334]E(f328(f328(f148(f876(x33341)),f117(x33341)),f117(f876(x33341))),f53(x33341,f117(x33341))) % 154.70/154.55 [3353]E(f192(f882(f881(x33531,x33531),a870)),f260(x33531,f192(f882(x33531,a870)))) % 154.70/154.55 [3354]E(f328(f305(x33541),f251(f882(x33541,a870))),f251(f882(f882(x33541,a870),a870))) % 154.70/154.55 [3355]E(f328(f79(f882(x33551,a870)),f192(f882(x33551,a870))),f251(f882(x33551,a870))) % 154.70/154.55 [3356]E(f328(f79(f882(x33561,a870)),f251(f882(x33561,a870))),f192(f882(x33561,a870))) % 154.70/154.55 [3358]P1(f328(f61(x33581),f192(f882(x33581,a870)))) % 154.70/154.55 [3360]E(f328(f298(a875,x33601),f328(a116,x33601)),f328(f328(f306(a875),x33601),f192(f882(a875,a870)))) % 154.70/154.55 [3361]E(f85(f881(a875,a875),f47(x33611,f2(a875))),f328(f328(f263(a875,a875),f2(a875)),x33611)) % 154.70/154.55 [3373]P1(f328(f328(f328(a198,a24),x33731),x33731)) % 154.70/154.55 [3377]E(f328(f328(f306(a875),f328(a116,x33771)),f328(f297(a875),x33771)),f328(f297(a875),f328(a116,x33771))) % 154.70/154.55 [3381]P39(x33811,f192(f882(f881(x33811,x33811),a870))) % 154.70/154.55 [3384]P1(f328(f328(f242(a1),f2(a1)),f328(f104(a1),x33841))) % 154.70/154.55 [3392]E(f328(f328(f80(a875),f328(f193(a875),x33921)),f328(a116,f2(a875))),f328(f193(a875),f328(a116,x33921))) % 154.70/154.55 [3502]P40(f328(f307(a875,a1,f104(a1)),x35021)) % 154.70/154.55 [3540]P41(x35401,f192(f882(x35401,a870)),f192(f882(f881(x35401,x35401),a870))) % 154.70/154.55 [3559]E(f328(f328(f263(a1,a1),f328(f107(a1),a101)),f328(f328(f22(a1),x35591),f78(a1))),f49(f328(f107(a1),a101),x35591)) % 154.70/154.55 [3610]P56(x36101,f328(f16(f882(x36101,a870),x36101),f328(f16(a870,x36101),a246))) % 154.70/154.55 [3813]P1(f328(f328(f330(f882(f881(a875,a875),a870)),f329(x38131)),a102)) % 154.70/154.55 [3838]P1(f328(f328(f330(f882(f881(a875,a875),a870)),f328(a110,x38381)),a102)) % 154.70/154.55 [3976]P27(x39761,f882(x39761,a870),f328(f328(f7(x39761,f882(x39761,a870),f882(x39761,a870)),f306(x39761)),f192(f882(x39761,a870))),f251(f882(x39761,a870))) % 154.70/154.55 [4488]~E(f328(f328(f80(a1),x44881),x44881),a101) % 154.70/154.55 [4515]~E(f328(a3,f328(a116,f328(a19,x45151))),f2(a103)) % 154.70/154.55 [4523]~P1(f328(a197,f328(f104(a1),x45231))) % 154.70/154.55 [4526]~P1(f328(f328(f243(a875),x45261),x45261)) % 154.70/154.55 [4535]~P1(f328(f328(f242(a875),f328(a116,x45351)),x45351)) % 154.70/154.55 [3306]E(f328(a108,f328(f79(a1),f328(f104(a1),x33061))),f2(a875)) % 154.70/154.55 [3309]E(f328(f328(f80(a1),f328(f79(a1),x33091)),x33091),f2(a1)) % 154.70/154.55 [3313]E(f328(f37(a1),f328(f298(a1,f2(a1)),x33131)),f328(a108,x33131)) % 154.70/154.55 [3325]E(f328(f328(f253(a875),f328(a116,f2(a875))),x33251),f328(a116,f2(a875))) % 154.70/154.55 [3427]E(f328(f281(x34271),f192(f882(f881(x34271,x34271),a870))),f192(f882(x34271,a870))) % 154.70/154.55 [3435]E(f39(f882(x34351,a870),f192(f882(f882(x34351,a870),a870))),f192(f882(x34351,a870))) % 154.70/154.55 [3436]E(f39(f882(x34361,a870),f251(f882(f882(x34361,a870),a870))),f251(f882(x34361,a870))) % 154.70/154.55 [3437]E(f40(f882(x34371,a870),f192(f882(f882(x34371,a870),a870))),f251(f882(x34371,a870))) % 154.70/154.55 [3438]E(f40(f882(x34381,a870),f251(f882(f882(x34381,a870),a870))),f192(f882(x34381,a870))) % 154.70/154.55 [3484]E(f328(f328(f306(f876(x34841)),f117(x34841)),f192(f882(f876(x34841),a870))),f158(x34841,f192(f882(x34841,a870)))) % 154.70/154.55 [3485]E(f328(f328(f306(f876(x34851)),f117(x34851)),f192(f882(f876(x34851),a870))),f159(x34851,f117(f882(x34851,a870)))) % 154.70/154.55 [3523]E(f328(f328(f80(a875),f4(x35231)),f328(a116,f2(a875))),f4(f328(a3,f328(a116,f328(a19,x35231))))) % 154.70/154.55 [3551]E(f328(f37(a1),f328(f307(a875,a1,f104(a1)),x35511)),f328(f37(a875),x35511)) % 154.70/154.55 [3554]P1(f328(f328(f242(a875),x35541),f328(f328(f81(a875),x35541),x35541))) % 154.70/154.55 [3589]E(f328(f307(a1,a875,a108),f299(a1,f2(a1),f328(f104(a1),x35891))),f328(f297(a875),x35891)) % 154.70/154.55 [3605]E(f328(f328(f38(a875),f328(a116,f2(a875))),f328(f107(a875),x36051)),f328(a108,f328(f328(f38(a1),f78(a1)),f328(f107(a1),x36051)))) % 154.70/154.55 [3607]E(f328(f170(a875),f136(a875,f328(f298(a875,f2(a875)),f328(a116,x36071)))),f328(f297(a875),x36071)) % 154.70/154.55 [3608]E(f328(f328(f80(a875),f328(f193(a103),x36081)),f328(a116,f2(a875))),f328(f193(a103),f328(a3,f328(a116,f328(a19,x36081))))) % 154.70/154.55 [3627]E(f328(f307(a1,a875,a108),f328(f307(a875,a1,f104(a1)),x36271)),x36271) % 154.70/154.55 [3659]E(f328(f328(f306(a875),f2(a875)),f328(f307(a875,a875,a116),f328(f249(a875),x36591))),f328(f249(a875),f328(a116,x36591))) % 154.70/154.55 [3666]P51(x36661,x36661,f304(x36661,f192(f882(f881(x36661,x36661),a870)))) % 154.70/154.55 [3672]P1(f328(a197,f328(f79(a1),f328(f104(a1),f328(a116,x36721))))) % 154.70/154.55 [3683]E(f328(f328(f22(f882(a875,a870)),f328(f250(a875),x36831)),f328(f328(f306(a875),x36831),f192(f882(a875,a870)))),f328(f250(a875),f328(a116,x36831))) % 154.70/154.55 [3699]E(f328(f328(f80(a1),f328(f328(f22(a1),a83),x36991)),f328(f328(f22(a1),a83),x36991)),f328(f328(f22(a1),a83),f328(f328(f80(a1),x36991),x36991))) % 154.70/154.55 [3715]E(f328(f328(f306(f882(x37151,a870)),f192(f882(x37151,a870))),f192(f882(f882(x37151,a870),a870))),f328(f305(x37151),f192(f882(x37151,a870)))) % 154.70/154.55 [3742]E(f328(f328(f22(f882(a875,a870)),f328(f300(a875),x37421)),f328(f328(f306(a875),f328(a116,x37421)),f192(f882(a875,a870)))),f328(f300(a875),f328(a116,x37421))) % 154.70/154.55 [3751]E(f328(f328(f306(f879(x37511)),f205(x37511)),f328(f307(x37511,f879(x37511),f235(x37511)),f251(f882(x37511,a870)))),f251(f882(f879(x37511),a870))) % 154.70/154.55 [3850]E(f328(f107(a875),f328(f328(f80(a1),x38501),x38501)),f328(f328(f86(a875,a875),f328(f107(a875),x38501)),f328(f328(f18(a875,a875,a875),f80(a875)),f5(a875)))) % 154.70/154.55 [4241]P17(x42411,f882(x42411,a870),f328(f328(f8(f882(x42411,a870),f882(f882(x42411,a870),f882(x42411,a870)),x42411),f328(f7(f882(x42411,a870),f882(x42411,a870),f882(x42411,a870)),f22(f882(x42411,a870)))),f328(f328(f7(x42411,f882(x42411,a870),f882(x42411,a870)),f306(x42411)),f192(f882(x42411,a870))))) % 154.70/154.55 [4330]E(f328(f248(f881(a1,a1)),f328(f267(a1,a1,a870),f328(f328(f8(f882(a1,a870),f882(a1,a870),a1),f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a326),f328(f242(a1),x43301)))),f243(a1)))),f111(x43301)) % 154.70/154.55 [4363]E(f328(f248(f881(a1,a1)),f328(f267(a1,a1,a870),f328(f328(f18(a1,f882(a1,a870),f882(a1,a870)),f328(f328(f8(f882(a870,a870),f882(f882(a1,a870),f882(a1,a870)),a1),f8(a870,a870,a1)),f328(f328(f8(a870,f882(a870,a870),a1),a326),f328(f242(a1),x43631)))),f243(a1)))),f109(x43631)) % 154.70/154.55 [4419]E(f328(f248(f881(f882(x44191,a870),f882(x44191,a870))),f328(f267(f882(x44191,a870),f882(x44191,a870),a870),f328(f328(f7(f882(x44191,a870),f882(f882(x44191,a870),a870),f882(f882(x44191,a870),a870)),f328(f328(f8(f882(f882(x44191,a870),f882(a870,a870)),f882(f882(f882(x44191,a870),a870),f882(f882(x44191,a870),a870)),f882(x44191,a870)),f18(f882(x44191,a870),a870,a870)),f328(f328(f8(f882(f882(x44191,a870),a870),f882(f882(x44191,a870),f882(a870,a870)),f882(x44191,a870)),f328(f8(a870,f882(a870,a870),f882(x44191,a870)),a326)),f243(f882(x44191,a870))))),f61(x44191)))),f303(x44191)) % 154.70/154.55 [4539]~P1(f328(f61(f876(x45391)),f251(f882(f876(x45391),a870)))) % 154.70/154.55 [4544]~P1(f328(f328(f91(a1),a101),f328(f328(f80(a1),x45441),x45441))) % 154.70/154.55 [4554]~P1(f328(f328(f242(a1),f2(a1)),f328(f79(a1),f328(f104(a1),f328(a116,x45541))))) % 154.70/154.55 [3462]E(f328(f328(f22(a1),f328(f328(f80(a1),x34621),a101)),a101),x34621) % 154.70/154.55 [3478]E(f328(f170(a875),f136(a875,f328(f298(a875,f2(a875)),x34781))),f328(f249(a875),x34781)) % 154.70/154.55 [3721]E(f328(f328(f80(a1),f328(f328(f80(a1),f78(a1)),x37211)),x37211),f328(f328(f22(a1),f328(f328(f80(a1),x37211),x37211)),a101)) % 154.70/154.55 [3768]E(f328(f283(x37681,x37681),f304(x37681,f192(f882(f881(x37681,x37681),a870)))),f304(x37681,f192(f882(f881(x37681,x37681),a870)))) % 154.70/154.55 [3816]P1(f328(f328(f242(a875),x38161),f328(f328(f81(a875),x38161),f328(f328(f81(a875),x38161),x38161)))) % 154.70/154.55 [4096]P1(f328(f61(a875),f328(f248(a875),f328(f328(f7(a875,a875,a870),f243(a875)),x40961)))) % 154.70/154.55 [4097]P1(f328(f61(a875),f328(f248(a875),f328(f328(f7(a875,a875,a870),f242(a875)),x40971)))) % 154.70/154.55 [4383]E(f328(f248(f881(x43831,x43831)),f328(f328(f8(f882(x43831,a870),a870,f881(x43831,x43831)),f87(x43831)),f328(f328(f7(f881(x43831,x43831),f882(x43831,f881(x43831,x43831)),f882(x43831,a870)),f328(f328(f8(f882(f881(x43831,x43831),a870),f882(f882(x43831,f881(x43831,x43831)),f882(x43831,a870)),f881(x43831,x43831)),f8(f881(x43831,x43831),a870,x43831)),a325)),f328(f328(f18(x43831,x43831,f881(x43831,x43831)),f263(x43831,x43831)),f5(x43831))))),f304(x43831,f192(f882(f881(x43831,x43831),a870)))) % 154.70/154.55 [4541]~E(f328(f328(f22(a1),f328(f328(f80(a1),x45411),x45411)),a101),a83) % 154.70/154.55 [4543]~E(f328(f328(f80(a1),f328(f328(f80(a1),f78(a1)),x45431)),x45431),f2(a1)) % 154.70/154.55 [4551]~P1(f328(f328(f91(a1),f328(f328(f80(a1),x45511),x45511)),a101)) % 154.70/154.55 [3863]E(f328(f328(f80(a1),f328(f328(f22(a1),a101),x38631)),f328(f328(f22(a1),a101),x38631)),f328(f328(f22(a1),a101),f328(f328(f22(a1),f328(f328(f80(a1),x38631),x38631)),a101))) % 154.70/154.55 [3985]E(f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),a101),x39851)),f328(f328(f22(a1),a101),x39851))),a101),f328(f328(f22(a1),a101),f328(f328(f80(a1),x39851),x39851))) % 154.70/154.55 [4020]E(f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f80(a1),x40201),a101)),f328(f328(f80(a1),x40201),a101))),a101),f328(f328(f80(a1),f328(f328(f80(a1),x40201),x40201)),a101)) % 154.70/154.55 [4058]E(f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),a101),x40581)),f328(f328(f22(a1),a101),x40581))),a101),f328(f328(f22(a1),a83),f328(f328(f22(a1),f328(f328(f80(a1),x40581),x40581)),a101))) % 154.70/154.55 [4159]E(f328(a89,f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),f328(f328(f263(a875,a875),x41591),f2(a875))),f192(f882(f881(a875,a875),a870))))),f328(f104(a1),x41591)) % 154.70/154.55 [4169]E(f328(a89,f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),f328(f328(f263(a875,a875),f333(x41691)),f552(x41691))),f192(f882(f881(a875,a875),a870))))),x41691) % 154.70/154.55 [4203]E(f328(f248(a1),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a326),f328(f242(a1),f2(a1)))),x42031)),f328(f307(a875,a1,f104(a1)),f328(f248(a875),f328(f328(f8(a1,a870,a875),x42031),f104(a1))))) % 154.70/154.55 [4249]P40(f328(f248(a1),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a326),f328(f242(a1),f2(a1)))),x42491))) % 154.70/154.55 [4270]P1(f328(f328(f330(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f328(f328(f263(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),x42701),f192(f882(f881(a875,a875),a870)))),a71)) % 154.70/154.55 [4276]E(f328(f307(a1,a875,a108),f328(f248(a1),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a326),f328(f242(a1),f2(a1)))),f328(f328(f8(a875,a870,a1),x42761),a108)))),f328(f248(a875),x42761)) % 154.70/154.55 [4434]E(f309(a875,f328(f328(f41(f881(a875,a875),f882(a875,a870)),f328(a110,x44341)),f328(f267(a875,a875,f882(a875,a870)),f328(f328(f7(a875,f882(a875,a870),f882(a875,f882(a875,a870))),f328(f328(f8(f882(a875,f882(f882(a875,a870),f882(a875,a870))),f882(f882(a875,a870),f882(a875,f882(a875,a870))),a875),f7(a875,f882(a875,a870),f882(a875,a870))),f328(f328(f8(f882(a875,a875),f882(a875,f882(f882(a875,a870),f882(a875,a870))),a875),f328(f8(a875,f882(f882(a875,a870),f882(a875,a870)),a875),f306(a875))),f22(a875)))),f192(f882(a875,a870)))))),f328(a108,x44341)) % 154.70/154.55 [4556]~P1(f328(f328(f91(a1),a83),f328(f328(f22(a1),f328(f328(f80(a1),x45561),x45561)),a101))) % 154.70/154.55 [3908]E(f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),x39081),x39081)),a101)),a101),f328(f328(f80(a1),x39081),x39081)) % 154.70/154.55 [3959]E(f328(f328(f22(a1),f328(f328(f22(a1),f328(f328(f80(a1),x39591),x39591)),a101)),a101),f328(f328(f80(a1),f328(f328(f22(a1),x39591),a101)),f328(f328(f22(a1),x39591),a101))) % 154.70/154.55 [4177]E(f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f80(a1),f328(f79(a1),x41771)),a101)),f328(f328(f80(a1),f328(f79(a1),x41771)),a101))),a101),f328(f79(a1),f328(f328(f22(a1),f328(f328(f80(a1),x41771),x41771)),a101))) % 154.70/154.55 [4564]~P1(f328(f328(f91(a1),f328(f328(f22(a1),f328(f328(f80(a1),x45641),x45641)),a101)),a83)) % 154.70/154.55 [4221]E(f328(f328(f80(a875),x42211),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(a116,f328(a116,x42211))) % 154.70/154.55 [4222]E(f328(f328(f81(a875),x42221),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(f328(f80(a875),x42221),x42221)) % 154.70/154.55 [4223]E(f328(f328(f38(a875),f328(f328(f80(a875),x42231),x42231)),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x42231) % 154.70/154.55 [4305]E(f44(a875,f328(a116,f328(a116,x43051)),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f44(a875,x43051,f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 154.70/154.55 [4449]E(f328(a89,f328(f328(f41(f881(a875,a875),f882(f881(a875,a875),a870)),f328(a110,x44491)),f328(f267(a875,a875,f882(f881(a875,a875),a870)),f328(f328(f8(f882(a875,f882(f881(a875,a875),a870)),f882(a875,f882(f881(a875,a875),a870)),a875),f328(f8(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870),a875),f282(f881(a875,a875),f881(a875,a875),a112))),f328(f328(f7(a875,f882(f881(a875,a875),a870),f882(a875,f882(f881(a875,a875),a870))),f328(f328(f8(f882(a875,f882(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f882(f882(f881(a875,a875),a870),f882(a875,f882(f881(a875,a875),a870))),a875),f7(a875,f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f328(f328(f8(f882(a875,f881(a875,a875)),f882(a875,f882(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),a875),f328(f8(f881(a875,a875),f882(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),a875),f306(f881(a875,a875)))),f328(f7(a875,a875,f881(a875,a875)),f263(a875,a875))))),f192(f882(f881(a875,a875),a870))))))),f328(f79(a1),x44491)) % 154.70/154.55 [4300]E(f328(f328(f80(a875),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x43001),f328(a116,f328(a116,x43001))) % 154.70/154.55 [4301]E(f328(f328(f81(a875),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x43011),f328(f328(f80(a875),x43011),x43011)) % 154.70/154.55 [4335]E(f328(f328(f38(a875),f328(a116,f328(a116,x43351))),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(a116,f328(f328(f38(a875),x43351),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))) % 154.70/154.55 [4389]E(f328(f328(f80(a875),f328(f107(a875),f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),a101))),x43891),f328(a116,f328(a116,f328(a116,x43891)))) % 154.70/154.55 [4457]E(f328(f267(a1,a1,f881(a1,a1)),f328(f328(f18(a1,f882(a1,f881(a1,a1)),f882(a1,f881(a1,a1))),f328(f328(f8(f882(a1,f882(f881(a1,a1),f881(a1,a1))),f882(f882(a1,f881(a1,a1)),f882(a1,f881(a1,a1))),a1),f18(a1,f881(a1,a1),f881(a1,a1))),f328(f328(f8(f882(a1,f881(a1,a1)),f882(a1,f882(f881(a1,a1),f881(a1,a1))),a1),f328(f18(a1,f881(a1,a1),f882(f881(a1,a1),f881(a1,a1))),f328(f328(f8(a870,f882(f881(a1,a1),f882(f881(a1,a1),f881(a1,a1))),a1),f100(f881(a1,a1))),f328(f328(f8(a1,a870,a1),f328(f242(a1),f2(a1))),f328(f328(f7(a1,a1,a1),f22(a1)),x44571))))),f328(f328(f7(a1,f882(a1,a1),f882(a1,f881(a1,a1))),f328(f328(f8(f882(a1,f881(a1,a1)),f882(f882(a1,a1),f882(a1,f881(a1,a1))),a1),f8(a1,f881(a1,a1),a1)),f328(f328(f8(a1,f882(a1,f881(a1,a1)),a1),f263(a1,a1)),f328(f328(f7(a1,a1,a1),f328(f328(f8(a1,f882(a1,a1),a1),f80(a1)),f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))),f78(a1))))),f328(f328(f7(a1,a1,a1),f22(a1)),x44571))))),f328(f328(f8(a1,f882(a1,f881(a1,a1)),a1),f263(a1,a1)),f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))))),f43(x44571)) % 154.70/154.55 [3131]P92(f880(x31311,x31312)) % 154.70/154.55 [3132]P92(f881(x31321,x31322)) % 154.70/154.55 [3133]P102(f880(x31331,x31332)) % 154.70/154.55 [3134]P102(f881(x31341,x31342)) % 154.70/154.55 [3151]P16(a1,f177(x31511,x31512)) % 154.70/154.55 [3152]P39(x31521,f150(x31521,x31522)) % 154.70/154.55 [3217]P33(x32171,x32172,f117(x32171)) % 154.70/154.55 [3250]P41(x32501,x32502,f260(x32501,x32502)) % 154.70/154.55 [3251]P51(x32511,x32511,f260(x32511,x32512)) % 154.70/154.55 [3526]P27(x35261,x35261,f5(x35261),x35262) % 154.70/154.55 [3527]P27(x35271,x35271,f34(x35271),x35272) % 154.70/154.55 [3535]P34(x35351,x35352,f117(x35351),f117(x35351)) % 154.70/154.55 [3536]P27(x35361,f879(x35361),f235(x35361),x35362) % 154.70/154.55 [3545]P27(f876(x35451),f876(x35451),f166(x35451),x35452) % 154.70/154.55 [4468]~E(f33(x44681,x44682),a24) % 154.70/154.55 [4469]~E(f32(x44691,x44692),a24) % 154.70/154.55 [4498]~P35(x44981,x44982,f117(x44981)) % 154.70/154.55 [4499]~P37(x44991,x44992,f117(x44991)) % 154.70/154.55 [3114]E(f328(f5(x31141),x31142),x31142) % 154.70/154.55 [3115]E(f328(f248(x31151),x31152),x31152) % 154.70/154.55 [3117]E(f328(f34(x31171),x31172),x31172) % 154.70/154.55 [3127]E(f328(f195(x31271),x31272),f119(x31271)) % 154.70/154.55 [3149]E(f85(x31491,f328(a325,x31492)),x31492) % 154.70/154.55 [3150]E(f90(x31501,f328(a325,x31502)),x31502) % 154.70/154.55 [3171]E(f328(f133(x31711,x31712),f117(x31711)),f117(x31711)) % 154.70/154.55 [3191]E(f304(x31911,f304(x31911,x31912)),f304(x31911,x31912)) % 154.70/154.55 [3192]E(f149(x31921,f149(x31921,x31922)),f149(x31921,x31922)) % 154.70/154.55 [3212]E(f328(f328(f125(x32121),x32122),f117(x32121)),x32122) % 154.70/154.55 [3218]E(f171(x32181,x32182,f117(x32181)),x32182) % 154.70/154.55 [3219]E(f171(x32191,f117(x32191),x32192),x32192) % 154.70/154.55 [3225]E(f328(f328(f173(x32251),x32252),f117(x32251)),f117(x32251)) % 154.70/154.55 [3226]E(f328(f328(f135(x32261),x32262),f117(x32261)),f117(x32261)) % 154.70/154.55 [3228]E(f152(x32281,x32282,f117(x32281)),f2(a875)) % 154.70/154.55 [3229]E(f236(x32291,x32292,f205(x32291)),f2(a875)) % 154.70/154.55 [3231]E(f167(x32311,x32312,f117(x32311)),f117(x32311)) % 154.70/154.55 [3232]E(f175(x32321,x32322,f117(x32321)),f117(x32321)) % 154.70/154.55 [3233]E(f174(x32331,f117(x32331),x32332),f117(x32331)) % 154.70/154.55 [3237]E(f328(f170(x32371),f149(x32371,x32372)),f328(f170(x32371),x32372)) % 154.70/154.55 [3240]E(f328(f259(x32401,x32401),f260(x32401,x32402)),x32402) % 154.70/154.55 [3241]E(f328(f261(x32411,x32411),f260(x32411,x32412)),x32412) % 154.70/154.55 [3249]E(f328(f283(x32491,x32491),f260(x32491,x32492)),f260(x32491,x32492)) % 154.70/154.55 [3264]E(f304(f876(x32641),f154(x32641,x32642)),f155(x32641,f304(x32641,x32642))) % 154.70/154.55 [3266]P1(f328(f134(a1),f177(x32661,x32662))) % 154.70/154.55 [3274]E(f328(f259(x32741,x32741),f304(x32741,x32742)),f251(f882(x32741,a870))) % 154.70/154.55 [3275]E(f328(f261(x32751,x32751),f304(x32751,x32752)),f251(f882(x32751,a870))) % 154.70/154.55 [3279]P1(f328(f134(x32791),f149(x32791,x32792))) % 154.70/154.55 [3281]P1(f328(f157(x32811,x32812),f117(x32811))) % 154.70/154.55 [3287]E(f328(f170(a1),f177(x32871,x32872)),f299(a1,x32871,x32872)) % 154.70/154.55 [3302]P52(x33021,f192(f882(x33021,a870)),x33022) % 154.70/154.55 [3307]E(f328(f266(a1,a1),f45(x33071,x33072)),f44(a1,x33071,x33072)) % 154.70/154.55 [3308]E(f328(f298(a875,x33081),f328(a116,x33082)),f299(a875,x33081,x33082)) % 154.70/154.55 [3324]E(f328(f328(f148(x33241),x33242),f117(x33241)),f137(x33241,x33242,f117(x33241))) % 154.70/154.55 [3336]E(f299(a875,f328(a116,x33361),x33362),f301(a875,x33361,x33362)) % 154.70/154.55 [3339]P41(x33391,f251(f882(x33391,a870)),f304(x33391,x33392)) % 154.70/154.55 [3404]E(f328(f328(f22(a875),x34041),f328(a116,x34042)),f328(f37(a875),f302(a875,x34042,x34041))) % 154.70/154.55 [3463]E(f164(x34631,x34632,f117(x34631)),f328(f328(f263(f876(x34631),f876(x34631)),f117(x34631)),f117(x34631))) % 154.70/154.55 [3482]E(f328(f267(x34821,x34822,f881(x34821,x34822)),f263(x34821,x34822)),f34(f881(x34821,x34822))) % 154.70/154.55 [3487]P1(f328(f328(f330(f876(x34871)),f117(x34871)),f158(x34871,x34872))) % 154.70/154.55 [3488]E(f328(f193(f876(x34881)),f118(x34881,x34882)),f328(f328(f22(a875),f328(f193(f876(x34881)),x34882)),f78(a875))) % 154.70/154.55 [3496]P1(f328(f61(a875),f302(a875,x34961,x34962))) % 154.70/154.55 [3497]P1(f328(f61(a875),f301(a875,x34971,x34972))) % 154.70/154.55 [3498]P1(f328(f61(a875),f299(a875,x34981,x34982))) % 154.70/154.55 [3499]P1(f328(f61(a1),f302(a1,x34991,x34992))) % 154.70/154.55 [3500]P1(f328(f61(a1),f301(a1,x35001,x35002))) % 154.70/154.55 [3501]P1(f328(f61(a1),f299(a1,x35011,x35012))) % 154.70/154.55 [3604]E(f328(f307(a875,a875,a116),f299(a875,x36041,x36042)),f299(a875,f328(a116,x36041),f328(a116,x36042))) % 154.70/154.55 [3624]E(f328(f328(f285(x36241,x36241,x36241),f304(x36241,x36242)),f304(x36241,x36242)),f304(x36241,x36242)) % 154.70/154.55 [3657]E(f328(f328(f263(a1,a1),f328(f328(f38(a1),x36571),x36572)),f44(a1,x36571,x36572)),f45(x36571,x36572)) % 154.70/154.55 [3658]E(f328(f328(f263(a103,a103),f328(f328(f38(a103),x36581),x36582)),f44(a103,x36581,x36582)),f21(x36581,x36582)) % 154.70/154.55 [3687]E(f328(f328(f263(a875,a875),f328(f328(f38(a875),x36871),x36872)),f44(a875,x36871,x36872)),f85(f881(a875,a875),f47(x36871,x36872))) % 154.70/154.55 [3738]P1(f328(f328(f243(a875),f328(f328(f22(a875),x37381),x37382)),f328(a116,x37381))) % 154.70/154.55 [3837]E(f328(f328(f80(a1),f328(f328(f81(a1),x38371),f328(f328(f38(a1),x38372),x38371))),f44(a1,x38372,x38371)),x38372) % 154.70/154.55 [3841]E(f328(f328(f41(a875,f882(f881(f876(x38411),f876(x38411)),a870)),f251(f882(a875,a870))),f140(x38411,x38412)),f142(x38411,x38412)) % 154.70/154.55 [4071]P1(f328(f328(f330(f881(f876(x40711),f876(x40711))),f328(f328(f263(f876(x40711),f876(x40711)),f117(x40711)),f117(x40711))),f155(x40711,x40712))) % 154.70/154.55 [4234]E(f268(x42341,x42341,x42342,x42342,f5(x42341),f5(x42342)),f34(f881(x42341,x42342))) % 154.70/154.55 [4236]E(f268(x42361,x42361,x42362,x42362,f34(x42361),f34(x42362)),f34(f881(x42361,x42362))) % 154.70/154.55 [4477]~E(f328(f235(x44771),x44772),f205(x44771)) % 154.70/154.55 [3210]E(f328(f239(x32101),f328(f235(x32101),x32102)),x32102) % 154.70/154.55 [3211]E(f328(f166(x32111),f328(f166(x32111),x32112)),x32112) % 154.70/154.55 [3213]E(f328(f328(f135(x32131),f2(a875)),x32132),x32132) % 154.70/154.55 [3227]E(f328(f328(f173(x32271),f2(a875)),x32272),f117(x32271)) % 154.70/154.55 [3235]E(f328(f328(f125(x32351),f117(x32351)),x32352),x32352) % 154.70/154.55 [3243]E(f328(f193(f879(x32431)),f328(f235(x32431),x32432)),f2(a875)) % 154.70/154.55 [3245]E(f39(f882(x32451,a870),f328(f305(x32451),x32452)),x32452) % 154.70/154.55 [3247]E(f328(f170(x32471),f328(f165(x32471),x32472)),f328(f170(x32471),x32472)) % 154.70/154.55 [3248]E(f328(f170(x32481),f328(f166(x32481),x32482)),f328(f170(x32481),x32482)) % 154.70/154.55 [3253]E(f328(f328(f22(a103),x32531),x32532),f328(f328(a23,x32531),x32532)) % 154.70/154.55 [3268]E(f328(f328(f80(a875),x32681),x32682),f328(f328(f80(a875),x32682),x32681)) % 154.70/154.55 [3269]E(f328(f328(f80(a1),x32691),x32692),f328(f328(f80(a1),x32692),x32691)) % 154.70/154.55 [3270]E(f328(f328(f81(a875),x32701),x32702),f328(f328(f81(a875),x32702),x32701)) % 154.70/154.55 [3271]E(f328(f328(f81(a1),x32711),x32712),f328(f328(f81(a1),x32712),x32711)) % 154.70/154.55 [3294]E(f328(f328(f187(x32941,x32941),f2(a875)),x32942),f34(x32941)) % 154.70/154.55 [3295]E(f328(f193(f876(x32951)),f328(f165(x32951),x32952)),f328(f193(f876(x32951)),x32952)) % 154.70/154.55 [3296]E(f328(f193(f876(x32961)),f328(f166(x32961),x32962)),f328(f193(f876(x32961)),x32962)) % 154.70/154.55 [3297]E(f174(x32971,x32972,f192(f882(a875,a870))),f117(x32971)) % 154.70/154.55 [3298]E(f328(f328(f151(x32981,x32981),f5(x32981)),x32982),x32982) % 154.70/154.55 [3300]E(f328(f262(a1,a1),f45(x33001,x33002)),f328(f328(f38(a1),x33001),x33002)) % 154.70/154.55 [3317]E(f328(f193(f876(x33171)),f149(x33171,x33172)),f328(f37(x33171),f328(f170(x33171),x33172))) % 154.70/154.55 [3318]E(f31(f32(x33181,x33182)),f328(f328(f80(a875),f31(x33182)),f328(a116,f2(a875)))) % 154.70/154.55 [3319]E(f328(f281(x33191),f328(f283(x33191,x33191),x33192)),f328(f281(x33191),x33192)) % 154.70/154.55 [3323]P1(f328(f61(x33231),f328(f170(x33231),x33232))) % 154.70/154.55 [3331]E(f328(f328(f80(a1),x33311),f328(f79(a1),x33312)),f328(f328(f22(a1),x33311),x33312)) % 154.70/154.55 [3338]P26(x33381,x33382,f192(f882(f874(x33381),a870))) % 154.70/154.55 [3340]E(f328(f307(x33401,x33401,f5(x33401)),x33402),x33402) % 154.70/154.55 [3341]E(f328(f307(x33411,x33411,f34(x33411)),x33412),x33412) % 154.70/154.55 [3342]E(f328(f308(x33421,x33421,f5(x33421)),x33422),x33422) % 154.70/154.55 [3343]E(f328(f308(x33431,x33431,f34(x33431)),x33432),x33432) % 154.70/154.55 [3344]P1(f328(f251(f882(x33441,a870)),x33442)) % 154.70/154.55 [3346]E(f328(f37(a875),f328(f298(a875,x33461),x33462)),f328(f328(f22(a875),x33462),x33461)) % 154.70/154.55 [3347]E(f328(f298(a875,f328(a116,x33471)),x33472),f302(a875,x33471,x33472)) % 154.70/154.55 [3359]E(f328(f328(f306(x33591),x33592),f192(f882(x33591,a870))),f328(f248(x33591),f328(a325,x33592))) % 154.70/154.55 [3363]E(f328(f328(f306(x33631),x33632),f192(f882(x33631,a870))),f234(x33631,f328(f235(x33631),x33632))) % 154.70/154.55 [3365]E(f304(x33651,f328(f283(x33651,x33651),x33652)),f328(f283(x33651,x33651),f304(x33651,x33652))) % 154.70/154.55 [3370]E(f328(f328(f80(a875),f328(a116,x33701)),x33702),f328(f328(f80(a875),x33701),f328(a116,x33702))) % 154.70/154.55 [3371]E(f328(f328(f22(a875),f328(a116,x33711)),f328(a116,x33712)),f328(f328(f22(a875),x33711),x33712)) % 154.70/154.55 [3379]E(f54(x33791,f2(a875),x33792),f328(f328(f148(f876(x33791)),f117(x33791)),f117(f876(x33791)))) % 154.70/154.55 [3380]E(f328(f37(a875),f301(a875,x33801,x33802)),f328(f328(f22(a875),x33802),x33801)) % 154.70/154.55 [3389]P39(x33891,f328(f328(f284(a875,x33891),a247),x33892)) % 154.70/154.55 [3391]P16(a875,f136(a875,f328(f298(a875,x33911),x33912))) % 154.70/154.55 [3393]P1(f328(f61(a875),f328(f298(a875,x33931),x33932))) % 154.70/154.55 [3394]P1(f328(f61(a1),f328(f298(a1,x33941),x33942))) % 154.70/154.55 [3397]E(f328(f283(f876(x33971),f876(x33971)),f154(x33971,x33972)),f154(x33971,f328(f283(x33971,x33971),x33972))) % 154.70/154.55 [3398]E(f328(f193(a871),f32(x33981,x33982)),f328(f328(f80(a875),f328(f193(a871),x33982)),f328(a116,f2(a875)))) % 154.70/154.55 [3400]E(f328(f298(a1,x34001),f328(f328(f80(a1),x34002),f78(a1))),f299(a1,x34001,x34002)) % 154.70/154.55 [3403]E(f328(f328(f38(a1),f328(f79(a1),x34031)),f328(f79(a1),x34032)),f328(f328(f38(a1),x34031),x34032)) % 154.70/154.55 [3411]E(f182(x34111,x34112,f328(f16(f879(x34112),x34111),f205(x34112))),f192(f882(x34111,a870))) % 154.70/154.55 [3412]E(f184(x34121,x34122,f328(f16(f879(x34122),x34121),f205(x34122))),f192(f882(x34122,a870))) % 154.70/154.55 [3413]E(f328(f328(f187(f881(x34131,x34131),a870),f78(a875)),x34132),x34132) % 154.70/154.55 [3415]E(f328(f328(f114(f882(x34151,a870)),x34152),f192(f882(x34151,a870))),x34152) % 154.70/154.55 [3416]E(f328(f328(f22(f882(x34161,a870)),x34162),f192(f882(x34161,a870))),x34162) % 154.70/154.55 [3417]E(f328(f328(f105(f882(x34171,a870)),x34172),f251(f882(x34171,a870))),x34172) % 154.70/154.55 [3418]E(f328(f262(a875,a875),f85(f881(a875,a875),f47(x34181,x34182))),f328(f328(f38(a875),x34181),x34182)) % 154.70/154.55 [3425]E(f310(x34251,f328(a20,x34252),f328(f79(a1),f328(a20,x34252))),f328(f328(f313(a1),x34251),x34252)) % 154.70/154.55 [3426]E(f299(a1,f328(f328(f80(a1),x34261),f78(a1)),x34262),f301(a1,x34261,x34262)) % 154.70/154.55 [3431]E(f328(f266(a875,a875),f85(f881(a875,a875),f47(x34311,x34312))),f44(a875,x34311,x34312)) % 154.70/154.55 [3439]E(f311(x34391,f328(a20,x34392),f328(f79(a1),f328(a20,x34392))),f312(a1,x34391,x34392)) % 154.70/154.55 [3442]P1(f328(f328(f330(x34421),x34422),f251(f882(x34421,a870)))) % 154.70/154.55 [3447]E(f328(f328(f22(a875),f328(a116,x34471)),x34472),f328(f37(a875),f299(a875,x34472,x34471))) % 154.70/154.55 [3474]E(f328(f328(f114(f882(x34741,a870)),x34742),f251(f882(x34741,a870))),f251(f882(x34741,a870))) % 154.70/154.55 [3475]E(f328(f328(f22(f882(x34751,a870)),x34752),f251(f882(x34751,a870))),f192(f882(x34751,a870))) % 154.70/154.55 [3476]E(f328(f328(f105(f882(x34761,a870)),x34762),f192(f882(x34761,a870))),f192(f882(x34761,a870))) % 154.70/154.55 [3491]E(f44(a1,f328(f104(a1),x34911),f328(f104(a1),x34912)),f328(f104(a1),f44(a875,x34911,x34912))) % 154.70/154.55 [3492]E(f44(a1,f328(f79(a1),x34921),f328(f79(a1),x34922)),f328(f79(a1),f44(a1,x34921,x34922))) % 154.70/154.55 [3503]E(f328(f193(f876(x35031)),f328(f169(x35031),x35032)),f328(f328(f22(a875),f328(f193(f876(x35031)),x35032)),f78(a875))) % 154.70/154.55 [3528]E(f328(f328(f38(a1),f44(a1,x35281,x35282)),x35282),f2(a1)) % 154.70/154.55 [3538]E(f328(a3,f44(a875,f328(a19,x35381),f328(a19,x35382))),f44(a103,x35381,x35382)) % 154.70/154.55 [3571]E(f328(a3,f328(f328(f22(a875),f328(a19,x35711)),f328(a19,x35712))),f328(f328(f22(a103),x35711),x35712)) % 154.70/154.55 [3572]E(f328(a3,f328(f328(f80(a875),f328(a19,x35721)),f328(a19,x35722))),f328(f328(f80(a103),x35721),x35722)) % 154.70/154.55 [3573]E(f328(a3,f328(f328(f81(a875),f328(a19,x35731)),f328(a19,x35732))),f328(f328(f81(a103),x35731),x35732)) % 154.70/154.55 [3574]E(f328(a3,f328(f328(f38(a875),f328(a19,x35741)),f328(a19,x35742))),f328(f328(f38(a103),x35741),x35742)) % 154.70/154.55 [3583]E(f328(f307(a875,a875,a116),f328(f298(a875,x35831),x35832)),f328(f298(a875,f328(a116,x35831)),f328(a116,x35832))) % 154.70/154.55 [3609]P1(f328(f47(x36091,x36092),f85(f881(a875,a875),f47(x36091,x36092)))) % 154.70/154.55 [3630]E(f328(f328(f80(a875),f328(f328(f80(a875),f31(x36301)),f31(x36302))),f328(a116,f2(a875))),f31(f33(x36301,x36302))) % 154.70/154.55 [3631]E(f44(a875,f328(a116,f44(a875,x36311,x36312)),x36312),f44(a875,f328(a116,x36311),x36312)) % 154.70/154.55 [3645]E(f328(f328(f41(f882(x36451,a870),f882(x36451,a870)),x36452),f5(f882(x36451,a870))),f39(f882(x36451,a870),x36452)) % 154.70/154.55 [3646]E(f328(f328(f42(f882(x36461,a870),f882(x36461,a870)),x36462),f5(f882(x36461,a870))),f40(f882(x36461,a870),x36462)) % 154.70/154.55 [3647]E(f328(f307(f876(x36471),f882(x36471,a870),f170(x36471)),f328(f170(f876(x36471)),f53(x36471,x36472))),f328(f305(x36471),f328(f170(x36471),x36472))) % 154.70/154.55 [3650]P1(f328(f328(f330(f882(x36501,a870)),x36502),f328(f305(x36501),x36502))) % 154.70/154.55 [3656]E(f44(a1,f328(f79(a1),f44(a1,x36561,x36562)),x36562),f44(a1,f328(f79(a1),x36561),x36562)) % 154.70/154.55 [3668]P1(f328(f328(f242(f882(x36681,a870)),x36682),f251(f882(x36681,a870)))) % 154.70/154.55 [3670]E(f328(f328(f285(x36701,x36701,x36701),f304(x36701,x36702)),f304(x36701,f304(x36701,x36702))),f304(x36701,x36702)) % 154.70/154.55 [3671]E(f328(f328(f114(f882(x36711,a870)),f328(f261(x36711,x36711),x36712)),f328(f259(x36711,x36711),x36712)),f328(f281(x36711),x36712)) % 154.70/154.55 [3692]E(f315(x36921,x36922,f251(f882(x36921,a870)),f251(f882(x36922,a870))),f251(f882(f880(x36921,x36922),a870))) % 154.70/154.55 [3743]P1(f328(f328(f242(a875),f44(a875,x37431,x37432)),x37431)) % 154.70/154.55 [3766]P1(f328(f328(f242(a1),f328(f79(a1),f328(f104(a1),x37661))),f328(f104(a1),x37662))) % 154.70/154.55 [3792]P1(f328(f328(f330(f882(x37921,a870)),f192(f882(x37921,a870))),f328(f305(x37921),x37922))) % 154.70/154.55 [3797]E(f304(x37971,f328(f328(f285(x37971,x37971,x37971),x37972),f304(x37971,x37972))),f304(x37971,x37972)) % 154.70/154.55 [3800]E(f328(f328(f285(x38001,x38001,x38001),f304(x38001,x38002)),x38002),f328(f328(f285(x38001,x38001,x38001),x38002),f304(x38001,x38002))) % 154.70/154.55 [3802]E(f328(a108,f328(f328(f80(a1),f328(f328(f22(a1),x38021),x38022)),f78(a1))),f328(f37(a1),f299(a1,x38022,x38021))) % 154.70/154.55 [3817]E(f328(f259(x38171,x38171),f328(f328(f285(x38171,x38171,x38171),x38172),f304(x38171,x38172))),f328(f259(x38171,x38171),x38172)) % 154.70/154.55 [3818]E(f328(f261(x38181,x38181),f328(f328(f285(x38181,x38181,x38181),x38182),f304(x38181,x38182))),f328(f261(x38181,x38181),x38182)) % 154.70/154.55 [3834]E(f328(f328(f80(a875),f328(f328(f80(a875),f328(f193(a871),x38341)),f328(f193(a871),x38342))),f328(a116,f2(a875))),f328(f193(a871),f33(x38341,x38342))) % 154.70/154.55 [3845]P27(a875,a875,f328(f328(f7(a875,a875,a875),f80(a875)),x38451),x38452) % 154.70/154.55 [3847]P16(a875,f328(f166(a875),f328(f328(f151(f876(x38471),a875),f193(f876(x38471))),f178(x38471,x38472)))) % 154.70/154.55 [3894]P1(f328(f328(f243(a1),f328(f79(a1),f328(f104(a1),f328(a116,x38941)))),f328(f104(a1),x38942))) % 154.70/154.55 [3940]E(f328(f139(f876(x39401),x39401,f328(f7(x39401,f876(x39401),f876(x39401)),f148(x39401)),f117(x39401)),x39402),f328(f166(x39401),x39402)) % 154.70/154.55 [3992]P1(f328(f328(f242(f882(f881(f876(x39921),f876(x39921)),a870)),f155(x39921,x39922)),f304(f876(x39921),f154(x39921,x39922)))) % 154.70/154.55 [4024]P1(f328(f47(x40241,x40242),f328(f328(f263(a875,a875),f328(f328(f38(a875),x40241),x40242)),f44(a875,x40241,x40242)))) % 154.70/154.55 [4035]P1(f328(f328(f242(f882(f881(f876(x40351),f876(x40351)),a870)),f154(x40351,f304(x40351,x40352))),f304(f876(x40351),f154(x40351,x40352)))) % 154.70/154.55 [4260]E(f328(f328(f269(f881(a103,a103),a103,f881(a103,a103),f881(x42601,f881(a103,a103))),f273(f328(f163(a103),f328(f328(f151(f881(a103,x42601),a103),f262(a103,x42601)),x42602)))),f328(f328(f8(x42601,f882(f881(a103,a103),f881(x42601,f881(a103,a103))),a103),f263(x42601,f881(a103,a103))),f274(x42601,x42602))),f272(x42601,x42602)) % 154.70/154.55 [4371]E(f328(f237(a875,f881(x43711,f877(x43711)),f2(a875),f328(f267(x43711,f877(x43711),a875),f328(f16(f882(f877(x43711),a875),x43711),f328(f328(f7(f877(x43711),a875,a875),f328(f328(f8(a875,f882(a875,a875),f877(x43711)),f80(a875)),f193(f877(x43711)))),f78(a875))))),f328(f132(x43711),x43712)),f328(f193(f877(x43711)),x43712)) % 154.70/154.55 [4448]E(f328(f267(f882(f881(x44481,x44481),a870),f882(f881(x44481,x44481),a870),f882(f882(x44482,x44481),f881(f882(f881(x44482,x44482),a870),f882(f881(x44482,x44482),a870)))),f328(f328(f7(f882(f881(x44481,x44481),a870),f882(f882(f881(x44481,x44481),a870),f882(f882(x44482,x44481),f882(f881(x44482,x44482),a870))),f882(f882(f881(x44481,x44481),a870),f882(f882(x44482,x44481),f881(f882(f881(x44482,x44482),a870),f882(f881(x44482,x44482),a870))))),f328(f328(f8(f882(f882(f882(x44482,x44481),f882(f881(x44482,x44482),a870)),f882(f882(x44482,x44481),f881(f882(f881(x44482,x44482),a870),f882(f881(x44482,x44482),a870)))),f882(f882(f882(f881(x44481,x44481),a870),f882(f882(x44482,x44481),f882(f881(x44482,x44482),a870))),f882(f882(f881(x44481,x44481),a870),f882(f882(x44482,x44481),f881(f882(f881(x44482,x44482),a870),f882(f881(x44482,x44482),a870))))),f882(f881(x44481,x44481),a870)),f8(f882(f882(x44482,x44481),f882(f881(x44482,x44482),a870)),f882(f882(x44482,x44481),f881(f882(f881(x44482,x44482),a870),f882(f881(x44482,x44482),a870))),f882(f881(x44481,x44481),a870))),f328(f328(f8(f882(f882(x44482,x44481),f882(f882(f881(x44482,x44482),a870),f881(f882(f881(x44482,x44482),a870),f882(f881(x44482,x44482),a870)))),f882(f882(f882(x44482,x44481),f882(f881(x44482,x44482),a870)),f882(f882(x44482,x44481),f881(f882(f881(x44482,x44482),a870),f882(f881(x44482,x44482),a870)))),f882(f881(x44481,x44481),a870)),f18(f882(x44482,x44481),f882(f881(x44482,x44482),a870),f881(f882(f881(x44482,x44482),a870),f882(f881(x44482,x44482),a870)))),f328(f328(f8(f882(f882(x44482,x44481),f882(f881(x44482,x44482),a870)),f882(f882(x44482,x44481),f882(f882(f881(x44482,x44482),a870),f881(f882(f881(x44482,x44482),a870),f882(f881(x44482,x44482),a870)))),f882(f881(x44481,x44481),a870)),f328(f8(f882(f881(x44482,x44482),a870),f882(f882(f881(x44482,x44482),a870),f881(f882(f881(x44482,x44482),a870),f882(f881(x44482,x44482),a870))),f882(x44482,x44481)),f263(f882(f881(x44482,x44482),a870),f882(f881(x44482,x44482),a870)))),f284(x44481,x44482))))),f284(x44481,x44482))),f74(x44481,x44482)) % 154.70/154.55 [4524]~E(f328(f305(x45241),x45242),f192(f882(f882(x45241,a870),a870))) % 154.70/154.55 [4538]~P1(f328(f328(f330(x45381),x45382),f192(f882(x45381,a870)))) % 154.70/154.55 [4548]~P1(f328(f328(f243(f882(x45481,a870)),x45482),f192(f882(x45481,a870)))) % 154.70/154.55 [3349]E(f328(f328(f22(a875),x33491),f328(f328(f80(a875),x33491),x33492)),f2(a875)) % 154.70/154.55 [3351]E(f328(f328(f114(f882(x33511,a870)),x33512),x33512),x33512) % 154.70/154.55 [3352]E(f328(f328(f105(f882(x33521,a870)),x33522),x33522),x33522) % 154.70/154.55 [3382]E(f328(f328(f22(f882(x33821,a870)),x33822),x33822),f192(f882(x33821,a870))) % 154.70/154.55 [3385]E(f328(f140(x33851,x33852),f2(a875)),f192(f882(f881(f876(x33851),f876(x33851)),a870))) % 154.70/154.55 [3386]E(f328(f328(f80(a875),x33861),f328(a116,x33862)),f328(a116,f328(f328(f80(a875),x33861),x33862))) % 154.70/154.55 [3399]E(f199(f328(f104(a1),x33991),f328(f104(a1),x33992)),f328(f104(a1),f328(f328(f22(a875),x33991),x33992))) % 154.70/154.55 [3402]E(f328(f328(f38(a1),f328(f79(a1),x34021)),x34022),f328(f328(f38(a1),x34021),f328(f79(a1),x34022))) % 154.70/154.55 [3406]E(f328(f37(a1),f328(f298(a1,x34061),x34062)),f328(a108,f328(f328(f22(a1),x34062),x34061))) % 154.70/154.55 [3409]E(f328(f328(f80(a875),f328(a116,x34091)),x34092),f328(a116,f328(f328(f80(a875),x34091),x34092))) % 154.70/154.55 [3414]E(f328(f79(f882(x34141,a870)),f328(f79(f882(x34141,a870)),x34142)),x34142) % 154.70/154.55 [3428]E(f178(x34281,f328(f328(f148(f876(x34281)),f117(x34281)),x34282)),f178(x34281,x34282)) % 154.70/154.55 [3432]E(f328(f328(f80(a875),x34321),f328(f328(f81(a875),x34321),x34322)),f328(f328(f81(a875),x34321),f328(a116,x34322))) % 154.70/154.55 [3440]E(f328(f328(a23,f328(a3,x34401)),f328(a3,x34402)),f328(a3,f328(f328(f22(a875),x34401),x34402))) % 154.70/154.55 [3454]E(f328(f328(f81(a1),f328(f79(a1),x34541)),x34542),f328(f79(a1),f328(f328(f81(a1),x34541),x34542))) % 154.70/154.55 [3456]E(f328(f328(f253(a1),f328(f104(a1),x34561)),x34562),f328(f104(a1),f328(f328(f253(a875),x34561),x34562))) % 154.70/154.55 [3457]E(f328(f328(f80(a103),f328(a3,x34571)),f328(a3,x34572)),f328(a3,f328(f328(f80(a875),x34571),x34572))) % 154.70/154.55 [3458]E(f328(f328(f81(a103),f328(a3,x34581)),f328(a3,x34582)),f328(a3,f328(f328(f81(a875),x34581),x34582))) % 154.70/154.55 [3459]E(f328(f328(f240(a875),f328(a116,x34591)),f328(a116,x34592)),f328(a116,f328(f328(f240(a875),x34591),x34592))) % 154.70/154.55 [3460]E(f328(f328(f241(a875),f328(a116,x34601)),f328(a116,x34602)),f328(a116,f328(f328(f241(a875),x34601),x34602))) % 154.70/154.55 [3466]E(f328(f170(a875),f136(a875,f328(f298(a875,x34661),x34662))),f328(f298(a875,x34661),x34662)) % 154.70/154.55 [3467]E(f309(x34671,f328(f328(f306(x34671),x34672),f192(f882(x34671,a870)))),x34672) % 154.70/154.55 [3472]E(f328(f259(x34721,x34722),f192(f882(f881(x34721,x34722),a870))),f192(f882(x34722,a870))) % 154.70/154.55 [3473]E(f328(f261(x34731,x34732),f192(f882(f881(x34731,x34732),a870))),f192(f882(x34731,a870))) % 154.70/154.55 [3477]E(f328(a108,f328(f328(f22(a1),x34771),x34772)),f328(f37(a1),f301(a1,x34772,x34771))) % 154.70/154.55 [3481]E(f328(f328(f80(a875),x34811),f328(f328(f81(a875),x34812),x34811)),f328(f328(f81(a875),f328(a116,x34812)),x34811)) % 154.70/154.55 [3483]E(f328(f328(f60(x34831),f192(f882(x34831,a870))),x34832),f192(f882(f882(x34831,a870),a870))) % 154.70/154.55 [3493]E(f328(f193(f876(a875)),f136(a875,f328(f298(a875,x34931),x34932))),f328(f328(f22(a875),x34932),x34931)) % 154.70/154.55 [3508]E(f328(f328(f114(f882(x35081,a870)),f192(f882(x35081,a870))),x35082),x35082) % 154.70/154.55 [3509]E(f328(f328(f105(f882(x35091,a870)),f251(f882(x35091,a870))),x35092),x35092) % 154.70/154.55 [3512]E(f328(f328(f80(a1),f328(f79(a1),x35121)),f328(f79(a1),x35122)),f328(f79(a1),f328(f328(f80(a1),x35121),x35122))) % 154.70/154.55 [3515]E(f328(f328(f80(a1),f328(f104(a1),x35151)),f328(f104(a1),x35152)),f328(f104(a1),f328(f328(f80(a875),x35151),x35152))) % 154.70/154.55 [3516]E(f328(f328(f80(a1),f328(f107(a1),x35161)),f328(f107(a1),x35162)),f328(f107(a1),f328(f328(f80(a1),x35161),x35162))) % 154.70/154.55 [3518]E(f328(f328(f81(a1),f328(f104(a1),x35181)),f328(f104(a1),x35182)),f328(f104(a1),f328(f328(f81(a875),x35181),x35182))) % 154.70/154.55 [3519]E(f328(f328(f81(a1),f328(f107(a1),x35191)),f328(f107(a1),x35192)),f328(f107(a1),f328(f328(f81(a1),x35191),x35192))) % 154.70/154.55 [3520]E(f328(f328(f38(a1),f328(f104(a1),x35201)),f328(f104(a1),x35202)),f328(f104(a1),f328(f328(f38(a875),x35201),x35202))) % 154.70/154.55 [3539]E(f328(f328(f6(x35391,a875),f328(f16(a875,x35391),f78(a875))),x35392),f328(f37(x35391),x35392)) % 154.70/154.55 [3546]E(f328(f79(a1),f44(a1,f328(f79(a1),x35461),x35462)),f44(a1,x35461,f328(f79(a1),x35462))) % 154.70/154.55 [3548]E(f328(f170(a1),f177(x35481,f328(f328(f22(a1),x35482),f78(a1)))),f328(f298(a1,x35481),x35482)) % 154.70/154.55 [3552]P1(f328(f328(f242(a875),x35521),f328(f328(f80(a875),x35522),x35521))) % 154.70/154.55 [3553]P1(f328(f328(f242(a875),x35531),f328(f328(f80(a875),x35531),x35532))) % 154.70/154.55 [3556]E(f328(f328(f114(f882(x35561,a870)),f251(f882(x35561,a870))),x35562),f251(f882(x35561,a870))) % 154.70/154.55 [3557]E(f328(f328(f22(f882(x35571,a870)),f192(f882(x35571,a870))),x35572),f192(f882(x35571,a870))) % 154.70/154.55 [3558]E(f328(f328(f105(f882(x35581,a870)),f192(f882(x35581,a870))),x35582),f192(f882(x35581,a870))) % 154.70/154.55 [3563]E(f328(f328(f263(a1,a1),x35631),f328(f79(a1),x35632)),f328(a50,f328(f328(f263(a1,a1),x35631),x35632))) % 154.70/154.55 [3564]E(f328(f298(a1,f328(f328(f80(a1),x35641),f78(a1))),x35642),f302(a1,x35641,x35642)) % 154.70/154.55 [3575]E(f328(f328(f81(a875),x35751),f328(f328(f38(a875),x35752),x35751)),f328(f328(f22(a875),x35752),f44(a875,x35752,x35751))) % 154.70/154.55 [3576]E(f328(f328(f81(a1),x35761),f328(f328(f38(a1),x35762),x35761)),f328(f328(f22(a1),x35762),f44(a1,x35762,x35761))) % 154.70/154.55 [3580]E(f328(f170(a1),f177(f328(f328(f80(a1),x35801),f78(a1)),x35802)),f301(a1,x35801,x35802)) % 154.70/154.55 [3584]P1(f328(f328(f242(f882(x35841,a870)),x35842),x35842)) % 154.70/154.55 [3587]E(f328(f328(f114(f882(x35871,a870)),x35872),f328(f79(f882(x35871,a870)),x35872)),f251(f882(x35871,a870))) % 154.70/154.55 [3588]E(f328(f328(f105(f882(x35881,a870)),x35882),f328(f79(f882(x35881,a870)),x35882)),f192(f882(x35881,a870))) % 154.70/154.55 [3596]E(f328(f328(f22(a875),f328(f328(f22(a875),x35961),f78(a875))),x35962),f328(f328(f22(a875),x35961),f328(a116,x35962))) % 154.70/154.55 [3601]E(f328(f328(f22(f882(x36011,a870)),f251(f882(x36011,a870))),x36012),f328(f79(f882(x36011,a870)),x36012)) % 154.70/154.55 [3602]E(f328(f328(f22(a1),f328(f107(a1),x36021)),f328(f107(a1),x36022)),f328(f107(a1),f328(f328(f80(a1),x36021),f328(f79(a1),x36022)))) % 154.70/154.55 [3614]E(f328(f170(a875),f136(a875,f328(f298(a875,x36141),f328(a116,x36142)))),f299(a875,x36141,x36142)) % 154.70/154.55 [3622]P1(f328(f328(f328(f328(a200,a24),x36221),x36222),x36221)) % 154.70/154.55 [3628]E(f328(f193(f876(f876(x36281))),f53(x36281,x36282)),f328(f328(f253(a875),f328(a116,f328(a116,f2(a875)))),f328(f193(f876(x36281)),x36282))) % 154.70/154.55 [3648]E(f328(f328(f187(f881(x36481,x36481),a870),f2(a875)),x36482),f304(x36481,f192(f882(f881(x36481,x36481),a870)))) % 154.70/154.55 [3652]P1(f328(f134(a875),f136(a875,f328(f298(a875,x36521),x36522)))) % 154.70/154.55 [3669]E(f328(f307(a1,a875,a108),f299(a1,f328(f104(a1),x36691),f328(f104(a1),x36692))),f299(a875,x36691,x36692)) % 154.70/154.55 [3679]E(f189(a875,f2(a875),f5(a875),f328(f328(f22(a875),x36791),x36792)),f328(f328(f22(a875),x36791),f328(a116,x36792))) % 154.70/154.55 [3680]E(f328(a108,f328(f328(f22(a1),x36801),f328(f328(f80(a1),x36802),f78(a1)))),f328(f37(a1),f302(a1,x36802,x36801))) % 154.70/154.55 [3716]E(f328(f328(f151(a875,a875),a116),f136(a875,f328(f298(a875,x37161),x37162))),f136(a875,f328(f298(a875,f328(a116,x37161)),f328(a116,x37162)))) % 154.70/154.55 [3723]E(f328(f170(a1),f177(f328(f328(f80(a1),x37231),f78(a1)),f328(f328(f22(a1),x37232),f78(a1)))),f302(a1,x37231,x37232)) % 154.70/154.55 [3734]P1(f328(f328(f242(f882(x37341,a870)),f192(f882(x37341,a870))),x37342)) % 154.70/154.55 [3739]E(f85(x37391,f328(f328(f7(x37391,x37391,a870),a325),x37392)),x37392) % 154.70/154.55 [3740]E(f90(x37401,f328(f328(f7(x37401,x37401,a870),a325),x37402)),x37402) % 154.70/154.55 [3744]E(f328(f170(a875),f136(a875,f328(f298(a875,f328(a116,x37441)),f328(a116,x37442)))),f301(a875,x37441,x37442)) % 154.70/154.55 [3769]E(f328(f328(f265(x37691,x37692),f251(f882(x37691,a870))),f328(f16(f882(x37692,a870),x37691),f251(f882(x37692,a870)))),f251(f882(f881(x37691,x37692),a870))) % 154.70/154.55 [3804]E(f328(f248(x38041),f328(f328(f8(a870,a870,x38041),a323),x38042)),f328(f79(f882(x38041,a870)),f328(f248(x38041),x38042))) % 154.70/154.55 [3807]E(f328(f248(x38071),f328(f328(f7(x38071,x38071,a870),a325),x38072)),f328(f328(f306(x38071),x38072),f192(f882(x38071,a870)))) % 154.70/154.55 [3814]E(f328(f328(f80(a1),f328(f328(f22(a1),x38141),x38142)),f328(f328(f22(a1),x38141),x38142)),f328(f328(f22(a1),f328(f328(f80(a1),x38141),x38141)),f328(f328(f80(a1),x38142),x38142))) % 154.70/154.55 [3815]E(f328(f328(f80(a1),f328(f328(f80(a1),x38151),x38151)),f328(f328(f80(a1),x38152),x38152)),f328(f328(f80(a1),f328(f328(f80(a1),x38151),x38152)),f328(f328(f80(a1),x38151),x38152))) % 154.70/154.55 [3831]P1(f328(f328(f242(a875),f328(f37(x38311),f328(f170(x38311),x38312))),f328(f193(f876(x38311)),x38312))) % 154.70/154.55 [3832]P1(f328(f328(f242(a875),f328(f193(f876(x38321)),f149(x38321,x38322))),f328(f193(f876(x38321)),x38322))) % 154.70/154.55 [3842]E(f328(f248(x38421),f328(f328(f7(x38421,f882(x38421,a870),a870),f330(x38421)),x38422)),x38422) % 154.70/154.55 [3858]E(f328(f328(f173(x38581),f328(f328(f22(a875),f328(f193(f876(x38581)),x38582)),f78(a875))),x38582),f118(x38581,x38582)) % 154.70/154.55 [3881]E(f189(a875,f2(a875),f328(f328(f8(a875,a875,a875),a116),f328(f240(a875),x38811)),x38812),f328(f328(f240(a875),f328(a116,x38811)),x38812)) % 154.70/154.55 [3885]E(f39(f882(x38851,a870),f328(f307(f882(f881(x38851,x38851),a870),f882(x38851,a870),f281(x38851)),x38852)),f328(f281(x38851),f39(f882(f881(x38851,x38851),a870),x38852))) % 154.70/154.55 [3886]E(f189(a875,f328(a116,x38861),f328(f328(f8(a875,a875,a875),a116),f328(f241(a875),x38861)),x38862),f328(f328(f241(a875),f328(a116,x38861)),x38862)) % 154.70/154.55 [3888]E(f328(f328(f263(a1,a1),f328(f328(f38(a1),f328(f75(a1),x38881)),f328(f75(a1),x38882))),f44(a1,f328(f75(a1),x38881),f328(f75(a1),x38882))),f52(x38881,x38882)) % 154.70/154.55 [3911]P1(f328(f328(f242(f882(f882(x39111,a870),a870)),x39112),f328(f305(x39111),f39(f882(x39111,a870),x39112)))) % 154.70/154.55 [3945]E(f328(f328(f41(x39451,f882(x39451,a870)),x39452),f328(f328(f7(x39451,f882(x39451,a870),f882(x39451,a870)),f306(x39451)),f192(f882(x39451,a870)))),x39452) % 154.70/154.55 [3946]E(f328(f328(f285(x39461,x39461,x39461),f328(f283(x39461,x39461),x39462)),f304(x39461,f328(f283(x39461,x39461),x39462))),f328(f283(x39461,x39461),f328(f328(f285(x39461,x39461,x39461),x39462),f304(x39461,x39462)))) % 154.70/154.55 [4015]E(f328(f170(x40151),f328(f139(f876(x40151),f876(x40151),f125(x40151),f117(x40151)),x40152)),f328(f328(f41(f876(x40151),f882(x40151,a870)),f328(f170(f876(x40151)),x40152)),f170(x40151))) % 154.70/154.55 [4047]E(f328(f328(f114(f882(f881(x40471,x40471),a870)),f304(x40471,f192(f882(f881(x40471,x40471),a870)))),f328(f328(f285(x40471,x40471,x40471),f304(x40471,x40472)),x40472)),f304(x40471,x40472)) % 154.70/154.55 [4081]E(f328(f328(f180(x40811,x40811),x40812),x40812),f328(f328(f151(x40811,f881(x40811,x40811)),f328(f328(f18(x40811,x40811,f881(x40811,x40811)),f263(x40811,x40811)),f5(x40811))),x40812)) % 154.70/154.55 [4197]E(f328(f139(a875,f876(x41971),f328(f7(f876(x41971),a875,a875),f328(f328(f8(a875,f882(a875,a875),f876(x41971)),f241(a875)),f193(f876(x41971)))),f2(a875)),f328(f166(f876(x41971)),x41972)),f328(f193(f876(f876(x41971))),f178(x41971,x41972))) % 154.70/154.55 [4275]E(f328(f328(f284(f881(a875,f876(x42751)),f876(x42751)),f320(a875,f876(x42751),a247,f142(x42751,x42752))),f328(f328(f18(f876(x42751),f876(x42751),f881(a875,f876(x42751))),f328(f328(f8(a875,f882(f876(x42751),f881(a875,f876(x42751))),f876(x42751)),f263(a875,f876(x42751))),f193(f876(x42751)))),f5(f876(x42751)))),f143(x42751,x42752)) % 154.70/154.55 [4405]E(f328(f248(x44051),f328(f328(f8(f882(f882(x44051,a870),a870),a870,x44051),f88(f882(x44051,a870))),f328(f328(f8(f882(f882(x44051,a870),a870),f882(f882(x44051,a870),a870),x44051),f328(f18(f882(x44051,a870),a870,a870),f328(f328(f8(a870,f882(a870,a870),f882(x44051,a870)),a331),f328(f328(f7(f882(x44051,a870),f882(f882(x44051,a870),a870),a870),f330(f882(x44051,a870))),x44052)))),f330(x44051)))),f40(f882(x44051,a870),x44052)) % 154.70/154.55 [4549]~P1(f328(f328(f243(a1),f328(f104(a1),x45491)),f328(f79(a1),f328(f104(a1),x45492)))) % 154.70/154.55 [4565]~P1(f328(f328(f91(a1),f328(f328(f22(a1),f328(f328(f80(a1),x45651),x45651)),a101)),f328(f328(f80(a1),x45652),x45652))) % 154.70/154.55 [3479]E(f328(f328(f22(a875),f328(f328(f80(a875),x34791),x34792)),x34792),x34791) % 154.70/154.55 [3480]E(f328(f328(f22(a875),f328(f328(f80(a875),x34801),x34802)),x34801),x34802) % 154.70/154.55 [3547]E(f328(f328(f80(a875),f328(f328(f22(a875),x35471),x35472)),x35472),f328(f328(f241(a875),x35471),x35472)) % 154.70/154.55 [3655]E(f328(f328(f81(a875),f328(f328(f38(a875),x36551),x36552)),x36552),f328(f328(f22(a875),x36551),f44(a875,x36551,x36552))) % 154.70/154.55 [3684]E(f328(f170(a875),f136(a875,f328(f298(a875,f328(a116,x36841)),x36842))),f302(a875,x36841,x36842)) % 154.70/154.55 [3691]E(f328(f104(a1),f223(f328(a108,f328(f75(a1),x36911)),f328(a108,f328(f75(a1),x36912)))),f328(f328(a224,x36911),x36912)) % 154.70/154.55 [3693]E(f328(f328(f114(f882(x36931,a870)),f328(f79(f882(x36931,a870)),x36932)),x36932),f251(f882(x36931,a870))) % 154.70/154.55 [3694]E(f328(f328(f105(f882(x36941,a870)),f328(f79(f882(x36941,a870)),x36942)),x36942),f192(f882(x36941,a870))) % 154.70/154.55 [3712]P1(f328(f328(f242(a875),f328(f328(f22(a875),x37121),x37122)),x37121)) % 154.70/154.55 [3713]P1(f328(f328(f242(a875),f328(f328(f38(a875),x37131),x37132)),x37131)) % 154.70/154.55 [3736]P1(f328(f328(f243(a875),x37361),f328(a116,f328(f328(f80(a875),x37362),x37361)))) % 154.70/154.55 [3737]P1(f328(f328(f243(a875),x37371),f328(a116,f328(f328(f80(a875),x37371),x37372)))) % 154.70/154.55 [3755]E(f328(f328(f81(a875),f328(a108,f328(f75(a1),x37551))),f328(a108,f328(f75(a1),x37552))),f328(a108,f328(f75(a1),f328(f328(f81(a1),x37551),x37552)))) % 154.70/154.55 [3765]P1(f328(f328(f242(a1),f2(a1)),f328(f328(f253(a1),f328(f75(a1),x37651)),x37652))) % 154.70/154.55 [3836]E(f328(f282(f876(x38361),f876(x38361),f155(x38361,x38362)),f328(f328(f306(f876(x38361)),f117(x38361)),f192(f882(f876(x38361),a870)))),f328(f328(f306(f876(x38361)),f117(x38361)),f192(f882(f876(x38361),a870)))) % 154.70/154.55 [3856]E(f328(f328(f114(f882(f881(x38561,x38561),a870)),f304(x38561,x38562)),f304(x38561,f192(f882(f881(x38561,x38561),a870)))),f304(x38561,x38562)) % 154.70/154.55 [3871]E(f328(f328(f38(a1),f328(f107(a1),f328(f328(f80(a1),x38711),x38711))),f328(f107(a1),f328(f328(f80(a1),x38712),x38712))),f328(f328(f38(a1),f328(f107(a1),x38711)),f328(f107(a1),x38712))) % 154.70/154.55 [3935]E(f328(f328(f253(a1),x39351),f328(f107(a875),f328(f328(f80(a1),x39352),x39352))),f328(f328(f86(a1,a1),f328(f328(f253(a1),x39351),f328(f107(a875),x39352))),f328(f328(f18(a1,a1,a1),f81(a1)),f5(a1)))) % 154.70/154.55 [3941]E(f328(f248(f882(x39411,a870)),f328(f328(f7(f882(x39411,a870),f882(x39411,a870),a870),f242(f882(x39411,a870))),x39412)),f328(f305(x39411),x39412)) % 154.70/154.55 [3956]E(f328(f328(f151(a1,a875),a108),f328(f328(f125(a1),f328(f328(f151(a875,a1),f104(a1)),x39561)),f328(f328(f151(a875,a1),f104(a1)),x39562))),f328(f328(f125(a875),x39561),x39562)) % 154.70/154.55 [3991]E(f328(f307(a1,a1,f328(f328(f7(a1,a1,a1),f80(a1)),x39911)),f328(f298(a1,f2(a1)),f328(f328(f22(a1),x39912),x39911))),f328(f298(a1,x39911),x39912)) % 154.70/154.55 [3993]P43(x39931,f328(f328(f22(f882(f881(x39931,x39931),a870)),x39932),f304(x39931,f192(f882(f881(x39931,x39931),a870))))) % 154.70/154.55 [4013]E(f328(f193(f876(x40131)),f328(f139(f876(x40131),f876(x40131),f125(x40131),f117(x40131)),x40132)),f328(f163(a875),f328(f328(f151(f876(x40131),a875),f193(f876(x40131))),x40132))) % 154.70/154.55 [4018]P41(x40181,f251(f882(x40181,a870)),f328(f328(f114(f882(f881(x40181,x40181),a870)),x40182),f304(x40181,f192(f882(f881(x40181,x40181),a870))))) % 154.70/154.55 [4061]E(f189(a875,f2(a875),f328(f328(f8(a875,a875,a875),a116),f328(f328(f7(a875,a875,a875),f240(a875)),x40611)),x40612),f328(f328(f240(a875),x40612),f328(a116,x40611))) % 154.70/154.55 [4064]E(f189(a875,f328(a116,x40641),f328(f328(f8(a875,a875,a875),a116),f328(f328(f7(a875,a875,a875),f241(a875)),x40641)),x40642),f328(f328(f241(a875),x40642),f328(a116,x40641))) % 154.70/154.55 [4067]E(f328(f307(x40671,f876(x40671),f328(f328(f7(x40671,f876(x40671),f876(x40671)),f148(x40671)),f117(x40671))),x40672),f172(x40671,x40672,f328(f328(f306(f876(x40671)),f117(x40671)),f192(f882(f876(x40671),a870))))) % 154.70/154.55 [4068]E(f328(f328(f114(f882(f881(x40681,x40681),a870)),f328(f328(f285(x40681,x40681,x40681),x40682),f304(x40681,x40682))),f304(x40681,f192(f882(f881(x40681,x40681),a870)))),f304(x40681,x40682)) % 154.70/154.55 [4076]P1(f328(f328(f242(f882(f881(x40761,x40761),a870)),f260(x40761,x40762)),f328(f328(f265(x40761,x40761),x40762),f328(f16(f882(x40761,a870),x40761),x40762)))) % 154.70/154.55 [4079]E(f328(f307(a1,a875,a108),f328(f328(f114(f882(a1,a870)),f328(f307(a875,a1,f104(a1)),x40791)),f328(f307(a875,a1,f104(a1)),x40792))),f328(f328(f114(f882(a875,a870)),x40791),x40792)) % 154.70/154.55 [4080]E(f328(f307(a1,a875,a108),f328(f328(f105(f882(a1,a870)),f328(f307(a875,a1,f104(a1)),x40801)),f328(f307(a875,a1,f104(a1)),x40802))),f328(f328(f105(f882(a875,a870)),x40801),x40802)) % 154.70/154.55 [4084]E(f328(f248(x40841),f328(f328(f8(a870,a870,x40841),a323),f328(f328(f7(x40841,f882(x40841,a870),a870),f330(x40841)),x40842))),f328(f79(f882(x40841,a870)),x40842)) % 154.70/154.55 [4111]E(f328(f139(f876(x41111),f876(x41111),f125(x41111),f117(x41111)),f328(f328(f151(f876(x41111),f876(x41111)),f166(x41111)),f328(f166(f876(x41111)),x41112))),f328(f166(x41111),f328(f139(f876(x41111),f876(x41111),f125(x41111),f117(x41111)),x41112))) % 154.70/154.55 [4140]E(f328(f328(f41(a875,f882(f881(x41401,x41401),a870)),f251(f882(a875,a870))),f328(f328(f7(a875,f882(f881(x41401,x41401),a870),f882(f881(x41401,x41401),a870)),f187(f881(x41401,x41401),a870)),x41402)),f304(x41401,x41402)) % 154.70/154.55 [4160]E(f85(x41601,f328(f328(f8(f882(x41601,a870),a870,x41601),f328(a325,x41602)),f328(f328(f7(x41601,f882(x41601,a870),f882(x41601,a870)),f306(x41601)),f192(f882(x41601,a870))))),f309(x41601,x41602)) % 154.70/154.55 [4168]E(f328(f193(f876(x41681)),f149(x41681,f328(f139(f876(x41681),f876(x41681),f125(x41681),f117(x41681)),x41682))),f328(f37(x41681),f328(f328(f41(f876(x41681),f882(x41681,a870)),f328(f170(f876(x41681)),x41682)),f170(x41681)))) % 154.70/154.55 [4184]E(f328(f328(f114(f882(f881(x41841,x41841),a870)),x41842),f328(f328(f285(x41841,x41841,x41841),f328(f328(f285(x41841,x41841,x41841),x41842),f304(x41841,x41842))),x41842)),f328(f328(f285(x41841,x41841,x41841),x41842),f304(x41841,x41842))) % 154.70/154.55 [4207]P1(f328(f328(f242(f882(f881(x42071,x42071),a870)),f328(f328(f285(x42071,x42071,x42071),x42072),f304(x42071,x42072))),f328(f328(f265(x42071,x42071),f328(f281(x42071),x42072)),f328(f16(f882(x42071,a870),x42071),f328(f281(x42071),x42072))))) % 154.70/154.55 [4250]E(f328(f248(f876(x42501)),f328(f328(f7(f876(x42501),f882(x42501,a870),a870),f328(f328(f8(f882(x42501,a870),f882(f882(x42501,a870),a870),f876(x42501)),f242(f882(x42501,a870))),f170(x42501))),x42502)),f158(x42501,x42502)) % 154.70/154.55 [4262]E(f328(f153(f876(x42621),x42621,f117(x42621),f328(f328(f8(f876(x42621),f882(f876(x42621),f876(x42621)),x42621),f328(f7(f876(x42621),f876(x42621),f876(x42621)),f125(x42621))),f328(f328(f7(x42621,f876(x42621),f876(x42621)),f148(x42621)),f117(x42621)))),x42622),f328(f165(x42621),x42622)) % 154.70/154.55 [4304]P27(f882(x43041,x43042),f882(f881(x43041,x43042),a870),f328(f328(f8(f882(f881(x43041,x43042),a870),f882(f881(x43041,x43042),a870),f882(x43041,x43042)),f248(f881(x43041,x43042))),f328(f328(f8(f882(x43041,f882(x43042,a870)),f882(f881(x43041,x43042),a870),f882(x43041,x43042)),f267(x43041,x43042,a870)),f328(f8(x43042,f882(x43042,a870),x43041),f328(f7(x43042,x43042,a870),a325)))),f251(f882(f882(x43041,x43042),a870))) % 154.70/154.55 [4309]E(f44(a1,f328(f107(a1),f328(f328(f80(a1),x43091),x43091)),f328(f107(a1),f328(f328(f80(a1),x43092),x43092))),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f44(a1,f328(f107(a1),x43091),f328(f107(a1),x43092)))) % 154.70/154.55 [4352]E(f328(f328(f41(x43521,f882(f881(x43521,x43521),a870)),x43522),f328(f328(f7(x43521,f882(f881(x43521,x43521),a870),f882(f881(x43521,x43521),a870)),f328(f328(f8(f881(x43521,x43521),f882(f882(f881(x43521,x43521),a870),f882(f881(x43521,x43521),a870)),x43521),f306(f881(x43521,x43521))),f328(f328(f18(x43521,x43521,f881(x43521,x43521)),f263(x43521,x43521)),f5(x43521)))),f192(f882(f881(x43521,x43521),a870)))),f260(x43521,x43522)) % 154.70/154.55 [4360]E(f210(x43601,f328(f328(f263(a1,a1),f328(f79(a1),f328(f328(f73(f881(a1,a1),a1,x43601,f262(a1,a1)),f219(x43601)),x43602))),f328(f328(f73(f881(a1,a1),a1,x43601,f266(a1,a1)),f219(x43601)),x43602))),f227(x43601,x43602)) % 154.70/154.55 [4443]E(f328(f248(f882(x44431,a870)),f328(f328(f8(f882(f882(x44431,a870),a870),a870,f882(x44431,a870)),f87(f882(x44431,a870))),f328(f328(f7(f882(x44431,a870),f882(f882(x44431,a870),a870),f882(f882(x44431,a870),a870)),f328(f328(f8(f882(f882(x44431,a870),f882(a870,a870)),f882(f882(f882(x44431,a870),a870),f882(f882(x44431,a870),a870)),f882(x44431,a870)),f18(f882(x44431,a870),a870,a870)),f328(f328(f8(f882(f882(x44431,a870),a870),f882(f882(x44431,a870),f882(a870,a870)),f882(x44431,a870)),f328(f8(a870,f882(a870,a870),f882(x44431,a870)),a326)),f328(f328(f7(f882(x44431,a870),f882(f882(x44431,a870),f882(x44431,a870)),f882(f882(x44431,a870),a870)),f328(f328(f8(f882(f882(x44431,a870),a870),f882(f882(f882(x44431,a870),f882(x44431,a870)),f882(f882(x44431,a870),a870)),f882(x44431,a870)),f8(f882(x44431,a870),a870,f882(x44431,a870))),a325)),f79(f882(x44431,a870)))))),f328(f328(f8(f882(f882(x44431,a870),a870),a870,f882(x44431,a870)),f328(f330(f882(x44431,a870)),x44432)),f305(x44431))))),f328(f305(x44431),f328(f79(f882(x44431,a870)),x44432))) % 154.70/154.55 [4546]~E(f328(f328(f80(a1),x45461),x45461),f328(f328(f22(a1),f328(f328(f80(a1),x45462),x45462)),a101)) % 154.70/154.55 [4552]~P1(f328(f328(f243(a875),f328(f328(f80(a875),x45521),x45522)),x45522)) % 154.70/154.55 [4553]~P1(f328(f328(f243(a875),f328(f328(f80(a875),x45531),x45532)),x45531)) % 154.70/154.55 [3770]E(f328(f328(f22(a875),x37701),f328(f328(f81(a875),f328(f328(f38(a875),x37701),x37702)),x37702)),f44(a875,x37701,x37702)) % 154.70/154.55 [3771]E(f328(f328(f22(a1),x37711),f328(f328(f81(a1),f328(f328(f38(a1),x37711),x37712)),x37712)),f44(a1,x37711,x37712)) % 154.70/154.55 [3805]E(f328(f328(f151(a875,x38051),f328(f162(x38051),x38052)),f136(a875,f328(f298(a875,f2(a875)),f328(f193(f876(x38051)),x38052)))),x38052) % 154.70/154.55 [3867]E(f328(f282(x38671,x38671,f304(x38671,f192(f882(f881(x38671,x38671),a870)))),x38672),x38672) % 154.70/154.55 [3996]E(f304(x39961,f328(f328(f114(f882(f881(x39961,x39961),a870)),x39962),f304(x39961,f192(f882(f881(x39961,x39961),a870))))),f304(x39961,x39962)) % 154.70/154.55 [3997]E(f304(x39971,f328(f328(f22(f882(f881(x39971,x39971),a870)),x39972),f304(x39971,f192(f882(f881(x39971,x39971),a870))))),f304(x39971,x39972)) % 154.70/154.55 [4050]E(f328(f328(f22(a1),f328(f328(f22(a1),f328(f328(f80(a1),x40501),x40501)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),x40502),x40502)),a101)),f328(f328(f80(a1),f328(f328(f22(a1),x40501),x40502)),f328(f328(f22(a1),x40501),x40502))) % 154.70/154.55 [4089]E(f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f80(a1),x40891),x40892)),f328(f328(f80(a1),x40891),x40892))),a101),f328(f328(f80(a1),f328(f328(f80(a1),x40891),x40891)),f328(f328(f22(a1),f328(f328(f80(a1),x40892),x40892)),a101))) % 154.70/154.55 [4115]E(f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),x41151),x41151)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),x41152),x41152)),a101)),f328(f328(f80(a1),f328(f328(f80(a1),x41151),f328(f328(f22(a1),x41152),a101))),f328(f328(f80(a1),x41151),f328(f328(f22(a1),x41152),a101)))) % 154.70/154.55 [4125]E(f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),x41251),x41252)),f328(f328(f22(a1),x41251),x41252))),a101),f328(f328(f22(a1),f328(f328(f22(a1),f328(f328(f80(a1),x41251),x41251)),a101)),f328(f328(f80(a1),x41252),x41252))) % 154.70/154.55 [4126]E(f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f80(a1),x41261),x41262)),f328(f328(f80(a1),x41261),x41262))),a101),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),x41261),x41261)),a101)),f328(f328(f80(a1),x41262),x41262))) % 154.70/154.55 [4181]E(f328(f104(a1),f328(f328(f38(a875),f328(f328(f81(a875),f328(a108,f328(f75(a1),x41811))),f328(a108,f328(f75(a1),x41812)))),f223(f328(a108,f328(f75(a1),x41811)),f328(a108,f328(f75(a1),x41812))))),f225(x41811,x41812)) % 154.70/154.55 [4227]E(f328(f328(f269(f881(a103,a103),a103,f881(a103,a103),f881(x42271,f881(a103,a103))),f273(f328(a3,f328(f193(f876(x42271)),x42272)))),f328(f328(f8(x42271,f882(f881(a103,a103),f881(x42271,f881(a103,a103))),a103),f263(x42271,f881(a103,a103))),f328(f328(f8(a875,x42271,a103),f328(f162(x42271),x42272)),a19))),f279(x42271,x42272)) % 154.70/154.55 [4310]E(f328(f139(a875,f876(x43101),f328(f7(f876(x43101),a875,a875),f328(f328(f8(a875,f882(a875,a875),f876(x43101)),f241(a875)),f193(f876(x43101)))),f2(a875)),f328(f166(f876(x43101)),f178(x43101,x43102))),f328(f193(f876(f876(x43101))),f328(f133(f876(x43101),f328(f328(f8(a870,a870,f876(x43101)),a323),f328(f328(f7(f876(x43101),f876(x43101),a870),a325),f117(x43101)))),x43102))) % 154.70/154.55 [4316]E(f328(f328(f41(a875,f882(x43161,a870)),f251(f882(a875,a870))),f328(f328(f7(a875,f882(a875,f882(x43161,a870)),f882(x43161,a870)),f328(f328(f8(f882(a875,a870),f882(f882(a875,f882(x43161,a870)),f882(x43161,a870)),a875),f41(a875,f882(x43161,a870))),f298(a875,f2(a875)))),x43162)),f328(f328(f41(a875,f882(x43161,a870)),f251(f882(a875,a870))),x43162)) % 154.70/154.55 [4336]P1(f328(f61(a875),f328(f248(a875),f328(f328(f18(a875,a870,a870),f328(f328(f8(a870,f882(a870,a870),a875),a326),x43361)),f328(f328(f7(a875,a875,a870),f243(a875)),x43362))))) % 154.70/154.55 [4454]E(f328(f248(f881(f876(x44541),f876(x44541))),f328(f267(f876(x44541),f876(x44541),a870),f328(f328(f18(f876(x44541),f882(f876(x44541),a870),f882(f876(x44541),a870)),f328(f328(f8(f882(f876(x44541),f882(a870,a870)),f882(f882(f876(x44541),a870),f882(f876(x44541),a870)),f876(x44541)),f18(f876(x44541),a870,a870)),f328(f328(f8(f882(f876(x44541),a870),f882(f876(x44541),f882(a870,a870)),f876(x44541)),f328(f8(a870,f882(a870,a870),f876(x44541)),a327)),f328(f328(f7(f876(x44541),f882(f876(x44541),a875),f882(f876(x44541),a870)),f328(f328(f8(f882(a875,a870),f882(f882(f876(x44541),a875),f882(f876(x44541),a870)),f876(x44541)),f8(a875,a870,f876(x44541))),f328(f328(f8(a875,f882(a875,a870),f876(x44541)),f243(a875)),f193(f876(x44541))))),f193(f876(x44541)))))),f328(f328(f18(f876(x44541),f882(f876(x44541),a870),f882(f876(x44541),a870)),f328(f328(f8(f882(f876(x44541),f882(a870,a870)),f882(f882(f876(x44541),a870),f882(f876(x44541),a870)),f876(x44541)),f18(f876(x44541),a870,a870)),f328(f328(f8(f882(f876(x44541),a870),f882(f876(x44541),f882(a870,a870)),f876(x44541)),f328(f8(a870,f882(a870,a870),f876(x44541)),a326)),f328(f328(f7(f876(x44541),f882(f876(x44541),a875),f882(f876(x44541),a870)),f328(f328(f8(f882(a875,a870),f882(f882(f876(x44541),a875),f882(f876(x44541),a870)),f876(x44541)),f8(a875,a870,f876(x44541))),f328(f328(f8(a875,f882(a875,a870),f876(x44541)),a325),f193(f876(x44541))))),f193(f876(x44541)))))),f328(f328(f7(f876(x44541),f882(f881(f876(x44541),f876(x44541)),a870),f882(f876(x44541),a870)),f328(f328(f8(f882(f876(x44541),f882(f882(f881(f876(x44541),f876(x44541)),a870),a870)),f882(f882(f881(f876(x44541),f876(x44541)),a870),f882(f876(x44541),a870)),f876(x44541)),f7(f876(x44541),f882(f881(f876(x44541),f876(x44541)),a870),a870)),f328(f328(f8(f882(f876(x44541),f881(f876(x44541),f876(x44541))),f882(f876(x44541),f882(f882(f881(f876(x44541),f876(x44541)),a870),a870)),f876(x44541)),f328(f8(f881(f876(x44541),f876(x44541)),f882(f882(f881(f876(x44541),f876(x44541)),a870),a870),f876(x44541)),f330(f881(f876(x44541),f876(x44541))))),f263(f876(x44541),f876(x44541))))),f142(x44541,x44542)))))),f143(x44541,x44542)) % 154.70/154.55 [4558]~P1(f328(f328(f91(a1),f328(f328(f80(a1),x45581),x45581)),f328(f328(f22(a1),f328(f328(f80(a1),x45582),x45582)),a101))) % 154.70/154.55 [4118]E(f328(f328(f80(a1),f328(f328(f80(a1),f328(f328(f81(a1),x41181),x41182)),f328(f328(f81(a1),x41181),x41182))),x41182),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f80(a1),x41181),x41181)),a101)),x41182)) % 154.70/154.55 [4225]E(f328(a108,f328(a89,f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),f328(f328(f263(a875,a875),x42251),x42252)),f192(f882(f881(a875,a875),a870)))))),f328(f328(f22(a875),x42251),x42252)) % 154.70/154.55 [4230]E(f328(f328(f285(x42301,x42301,x42301),f328(f328(f114(f882(f881(x42301,x42301),a870)),x42302),f304(x42301,f192(f882(f881(x42301,x42301),a870))))),f304(x42301,f328(f328(f114(f882(f881(x42301,x42301),a870)),x42302),f304(x42301,f192(f882(f881(x42301,x42301),a870)))))),f304(x42301,x42302)) % 154.70/154.55 [4268]E(f274(x42681,f328(f133(f881(a103,x42681),f328(f267(a103,x42681,a870),f328(f328(f8(a870,f882(x42681,a870),a103),f16(a870,x42681)),f328(f243(a103),f2(a103))))),x42682)),f274(x42681,x42682)) % 154.70/154.55 [4269]E(f272(x42691,f328(f133(f881(a103,x42691),f328(f267(a103,x42691,a870),f328(f328(f8(a870,f882(x42691,a870),a103),f16(a870,x42691)),f328(f243(a103),f2(a103))))),x42692)),f272(x42691,x42692)) % 154.70/154.55 [4271]E(f328(f79(a1),f328(a89,f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),f328(f328(f263(a875,a875),x42711),x42712)),f192(f882(f881(a875,a875),a870)))))),f328(a89,f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),f328(f328(f263(a875,a875),x42712),x42711)),f192(f882(f881(a875,a875),a870)))))) % 154.70/154.55 [4328]E(f328(f328(f284(f876(a875),x43281),f142(a875,a247)),f328(f328(f7(x43281,f876(f882(x43281,a875)),f876(a875)),f328(f328(f8(f882(f882(x43281,a875),a875),f882(f876(f882(x43281,a875)),f876(a875)),x43281),f151(f882(x43281,a875),a875)),f328(f7(f882(x43281,a875),x43281,a875),f5(f882(x43281,a875))))),x43282)),f150(x43281,x43282)) % 154.70/154.55 [4349]E(f328(f328(f86(a1,a875),f328(f107(a1),f328(f328(f80(a1),x43491),a101))),f328(f328(f18(a1,a875,a875),f328(f328(f7(a1,a875,f882(a875,a875)),f328(f328(f8(a870,f882(a875,f882(a875,a875)),a1),f100(a875)),a197)),f2(a875))),f328(f328(f8(a875,a875,a1),a116),f328(f328(f8(a875,a875,a1),f328(f240(a875),x43492)),a108)))),f328(f328(f240(a875),f328(a116,x43492)),f328(f107(a875),x43491))) % 154.70/154.55 [4350]E(f328(f328(f86(a1,a875),f328(f107(a1),f328(f328(f80(a1),x43501),a101))),f328(f328(f18(a1,a875,a875),f328(f328(f7(a1,a875,f882(a875,a875)),f328(f328(f8(a870,f882(a875,f882(a875,a875)),a1),f100(a875)),a197)),f328(a116,x43502))),f328(f328(f8(a875,a875,a1),a116),f328(f328(f8(a875,a875,a1),f328(f241(a875),x43502)),a108)))),f328(f328(f241(a875),f328(a116,x43502)),f328(f107(a875),x43501))) % 154.70/154.55 [4370]E(f328(f139(f876(x43701),f876(x43701),f125(x43701),f117(x43701)),f328(f328(f151(f876(x43701),f876(x43701)),f153(f876(x43701),x43701,f117(x43701),f328(f328(f8(f876(x43701),f882(f876(x43701),f876(x43701)),x43701),f16(f876(x43701),f876(x43701))),f328(f328(f7(x43701,f876(x43701),f876(x43701)),f148(x43701)),f117(x43701))))),x43702)),f328(f328(f151(f876(x43701),x43701),f138(x43701)),f328(f133(f876(x43701),f328(f328(f8(a870,a870,f876(x43701)),a323),f328(f328(f7(f876(x43701),f876(x43701),a870),a325),f117(x43701)))),x43702))) % 154.70/154.55 [4435]E(f328(f267(a1,a1,a870),f328(f328(f7(a1,f882(a1,a870),f882(a1,a870)),f328(f328(f8(f882(a1,f882(a870,a870)),f882(f882(a1,a870),f882(a1,a870)),a1),f18(a1,a870,a870)),f328(f328(f8(f882(a1,a870),f882(a1,f882(a870,a870)),a1),f328(f8(a870,f882(a870,a870),a1),a326)),f328(f328(f8(f882(a1,a1),f882(a1,a870),a1),f328(f8(a1,a870,a1),f328(a325,x44351))),f328(f328(f8(a1,f882(a1,a1),a1),f80(a1)),f328(f81(a1),x44352)))))),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a326),f328(f328(f8(a870,a870,a1),f328(a331,f328(f328(f243(a1),f2(a1)),x44352))),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a326),f328(f242(a1),f2(a1)))),f328(f328(f7(a1,a1,a870),f243(a1)),x44352))))),f328(f328(f8(a870,a870,a1),f328(a331,f328(a323,f328(f328(f243(a1),f2(a1)),x44352)))),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a326),f328(f243(a1),x44352))),f328(f328(f7(a1,a1,a870),f242(a1)),f2(a1))))))),f48(x44351,x44352)) % 154.70/154.55 [4437]E(f328(f248(x44371),f328(f328(f8(f882(a875,a870),a870,x44371),f87(a875)),f328(f328(f7(x44371,f882(a875,a870),f882(a875,a870)),f328(f328(f8(f882(a875,f882(a870,a870)),f882(f882(a875,a870),f882(a875,a870)),x44371),f18(a875,a870,a870)),f328(f328(f8(f882(a875,a870),f882(a875,f882(a870,a870)),x44371),f328(f8(a870,f882(a870,a870),a875),a326)),f328(f328(f7(x44371,f882(a875,x44371),f882(a875,a870)),f328(f328(f8(f882(x44371,a870),f882(f882(a875,x44371),f882(a875,a870)),x44371),f8(x44371,a870,a875)),a325)),f328(f162(x44371),x44372))))),f328(f328(f7(a875,a875,a870),f243(a875)),f328(f193(f876(x44371)),x44372))))),f328(f170(x44371),x44372)) % 154.70/154.55 [4240]E(f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),x42401),a101)),x42402)),f328(f328(f22(a1),f328(f328(f80(a1),x42401),a101)),x42402))),a101),f328(f328(f22(a1),f328(f328(f80(a1),x42401),x42401)),f328(f328(f22(a1),f328(f328(f80(a1),x42402),x42402)),a101))) % 154.70/154.55 [4365]E(f328(f139(f876(f876(x43651)),f876(f876(x43651)),f125(f876(x43651)),f117(f876(x43651))),f328(f328(f151(f876(x43651),f876(f876(x43651))),f153(f876(f876(x43651)),x43651,f117(f876(x43651)),f328(f16(f882(f876(x43651),f876(f876(x43651))),x43651),f328(f328(f7(f876(x43651),f876(f876(x43651)),f876(f876(x43651))),f148(f876(x43651))),f117(f876(x43651)))))),x43652)),f328(f328(f151(f876(x43651),f876(x43651)),f169(x43651)),f328(f133(f876(x43651),f328(f328(f8(a870,a870,f876(x43651)),a323),f328(f328(f7(f876(x43651),f876(x43651),a870),a325),f117(x43651)))),x43652))) % 154.70/154.55 [4376]E(f328(f328(f86(a1,a875),f328(f107(a1),f328(f328(f80(a1),x43761),a101))),f328(f328(f18(a1,a875,a875),f328(f328(f7(a1,a875,f882(a875,a875)),f328(f328(f8(a870,f882(a875,f882(a875,a875)),a1),f100(a875)),a197)),f2(a875))),f328(f328(f8(a875,a875,a1),a116),f328(f328(f7(a1,a875,a875),f328(f328(f8(a875,f882(a875,a875),a1),f240(a875)),a108)),x43762)))),f328(f328(f240(a875),f328(f107(a875),x43761)),f328(a116,x43762))) % 154.70/154.55 [4377]E(f328(f328(f86(a1,a875),f328(f107(a1),f328(f328(f80(a1),x43771),a101))),f328(f328(f18(a1,a875,a875),f328(f328(f7(a1,a875,f882(a875,a875)),f328(f328(f8(a870,f882(a875,f882(a875,a875)),a1),f100(a875)),a197)),f328(a116,x43772))),f328(f328(f8(a875,a875,a1),a116),f328(f328(f7(a1,a875,a875),f328(f328(f8(a875,f882(a875,a875),a1),f241(a875)),a108)),x43772)))),f328(f328(f241(a875),f328(f107(a875),x43771)),f328(a116,x43772))) % 154.70/154.55 [4364]E(f328(f267(x43641,x43641,a870),f328(f328(f18(x43641,a870,f882(x43641,a870)),f328(f328(f8(f882(x43641,f882(a870,a870)),f882(a870,f882(x43641,a870)),x43641),f7(x43641,a870,a870)),f328(f328(f8(f882(x43641,a870),f882(x43641,f882(a870,a870)),x43641),f328(f8(a870,f882(a870,a870),x43641),a326)),a325))),x43642)),f260(x43641,x43642)) % 154.70/154.55 [4411]E(f328(f328(f38(a875),x44111),f328(f328(f80(a875),f328(f107(a875),f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),a101))),x44112)),f328(f328(f38(a875),x44111),f328(a116,f328(a116,f328(a116,x44112))))) % 154.70/154.55 [4412]E(f44(a875,x44121,f328(f328(f80(a875),f328(f107(a875),f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),a101))),x44122)),f44(a875,x44121,f328(a116,f328(a116,f328(a116,x44122))))) % 154.70/154.55 [4413]E(f44(a875,f328(f328(f80(a875),f328(f107(a875),f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),a101))),x44131),x44132),f44(a875,f328(a116,f328(a116,f328(a116,x44131))),x44132)) % 154.70/154.55 [4428]E(f124(f328(x44281,f328(f328(f81(a103),f328(f107(a103),f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),a101))),x44282))),f328(f208(x44281),x44282)) % 154.70/154.55 [4429]E(f328(f328(f38(a875),f328(f328(f80(a875),f328(f107(a875),f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),a101))),x44291)),x44292),f328(f328(f38(a875),f328(a116,f328(a116,f328(a116,x44291)))),x44292)) % 154.70/154.55 [4478]~E(f33(x44781,x44782),f328(a26,x44783)) % 154.70/154.55 [4479]~E(f32(x44791,x44792),f328(a26,x44793)) % 154.70/154.55 [4480]~E(f328(a26,x44801),f33(x44802,x44803)) % 154.70/154.55 [4481]~E(f328(a26,x44811),f32(x44812,x44813)) % 154.70/154.55 [4494]~E(f30(x44941,x44942,x44943),a24) % 154.70/154.55 [4495]~E(f29(x44951,x44952,x44953),a24) % 154.70/154.55 [3193]E(f328(f196(x31931,x31932),x31933),f122(x31931,x31932)) % 154.70/154.55 [3214]E(f328(f207(x32141,x32142),x32143),f328(f126(x32141),x32142)) % 154.70/154.55 [3292]E(f328(f328(f151(x32921,x32922),x32923),f117(x32921)),f117(x32922)) % 154.70/154.55 [3293]E(f328(f328(f206(x32931,x32932),x32933),f205(x32931)),f205(x32932)) % 154.70/154.55 [3333]E(f328(f188(x33331,x33332,x33333),f2(a875)),x33332) % 154.70/154.55 [3335]E(f328(f328(f180(x33351,x33352),x33353),f117(x33352)),f117(f881(x33351,x33352))) % 154.70/154.55 [3369]E(f85(x33691,f62(x33691,x33692,x33693)),f328(f63(x33691,x33692),x33693)) % 154.70/154.55 [3375]E(f252(x33751,x33752,f252(x33752,x33751,x33753)),x33753) % 154.70/154.55 [3395]E(f328(f166(x33951),f168(x33951,x33952,x33953)),f168(x33951,x33952,x33953)) % 154.70/154.55 [3424]E(f137(x34241,x34242,f149(x34241,x34243)),f149(x34241,f137(x34241,x34242,x34243))) % 154.70/154.55 [3443]E(f328(f262(f876(x34431),f876(x34431)),f164(x34431,x34432,x34433)),f328(f133(x34431,x34432),x34433)) % 154.70/154.55 [3489]E(f328(f328(f148(x34891),x34892),f168(x34891,x34893,x34892)),f168(x34891,f328(a116,x34893),x34892)) % 154.70/154.55 [3521]E(f189(x35211,x35212,x35213,f2(a875)),x35212) % 154.70/154.55 [3522]E(f17(x35221,x35222,x35223,f2(a103)),x35222) % 154.70/154.55 [3529]E(f160(x35291,x35292,x35293,f117(x35291)),f117(x35292)) % 154.70/154.55 [3530]E(f161(x35301,x35302,x35303,f117(x35301)),f117(x35302)) % 154.70/154.55 [3537]E(f328(f328(f162(x35371),f328(f328(f148(x35371),x35372),x35373)),f2(a875)),x35372) % 154.70/154.55 [3565]E(f59(x35651,x35652,f117(x35651),x35653),f117(f881(x35651,x35652))) % 154.70/154.55 [3586]P27(x35861,x35862,x35863,f192(f882(x35861,a870))) % 154.70/154.55 [3745]E(f328(f73(x37451,x37452,x37451,x37453),f34(x37451)),x37453) % 154.70/154.55 [3926]P1(f328(f328(f330(f881(x39261,x39261)),f328(f328(f263(x39261,x39261),x39262),x39262)),f304(x39261,x39263))) % 154.70/154.55 [4559]~P1(f328(f328(f330(f881(f876(x45591),f876(x45591))),f328(f328(f263(f876(x45591),f876(x45591)),x45592),f117(x45591))),f142(x45591,x45593))) % 154.70/154.55 [4560]~P1(f328(f328(f330(f881(f876(x45601),f876(x45601))),f328(f328(f263(f876(x45601),f876(x45601)),x45602),f117(x45601))),f144(x45601,x45603))) % 154.70/154.55 [4561]~P1(f328(f328(f330(f881(f876(x45611),f876(x45611))),f328(f328(f263(f876(x45611),f876(x45611)),x45612),f117(x45611))),f154(x45611,x45613))) % 154.70/154.55 [4562]~P1(f328(f328(f330(f881(f876(x45621),f876(x45621))),f328(f328(f263(f876(x45621),f876(x45621)),f117(x45621)),x45622)),f142(x45621,x45623))) % 154.70/154.55 [4563]~P1(f328(f328(f330(f881(f876(x45631),f876(x45631))),f328(f328(f263(f876(x45631),f876(x45631)),f117(x45631)),x45632)),f154(x45631,x45633))) % 154.70/154.55 [3267]E(f328(f328(f209(x32671),x32672),x32673),f210(x32671,f222(x32672,x32673))) % 154.70/154.55 [3322]E(f328(f283(x33221,x33222),f328(f283(x33222,x33221),x33223)),x33223) % 154.70/154.55 [3345]E(f328(f328(f180(x33451,x33452),f117(x33451)),x33453),f117(f881(x33451,x33452))) % 154.70/154.55 [3348]E(f174(x33481,x33482,f328(f249(a875),x33483)),f328(f328(f173(x33481),x33483),x33482)) % 154.70/154.55 [3366]E(f149(x33661,f328(f133(x33661,x33662),x33663)),f328(f133(x33661,x33662),f149(x33661,x33663))) % 154.70/154.55 [3367]E(f328(f259(x33671,x33672),f328(f283(x33672,x33671),x33673)),f328(f261(x33672,x33671),x33673)) % 154.70/154.55 [3368]E(f328(f261(x33681,x33682),f328(f283(x33682,x33681),x33683)),f328(f259(x33682,x33681),x33683)) % 154.70/154.55 [3387]E(f328(f133(x33871,x33872),f328(f166(x33871),x33873)),f328(f166(x33871),f328(f133(x33871,x33872),x33873))) % 154.70/154.55 [3401]E(f328(f328(f135(x34011),x34012),f328(f169(x34011),x34013)),f328(f328(f135(x34011),f328(a116,x34012)),x34013)) % 154.70/154.55 [3419]E(f31(f29(x34191,x34192,x34193)),f328(f328(f80(a875),f31(x34193)),f328(a116,f2(a875)))) % 154.70/154.55 [3420]E(f328(f307(x34201,x34202,x34203),f192(f882(x34201,a870))),f192(f882(x34202,a870))) % 154.70/154.55 [3421]E(f328(f308(x34211,x34212,x34213),f192(f882(x34212,a870))),f192(f882(x34211,a870))) % 154.70/154.55 [3422]E(f328(f308(x34221,x34222,x34223),f251(f882(x34222,a870))),f251(f882(x34221,a870))) % 154.70/154.55 [3423]E(f328(f282(x34231,x34232,x34233),f192(f882(x34231,a870))),f192(f882(x34232,a870))) % 154.70/154.55 [3452]E(f328(f328(f306(x34521),x34522),f328(f170(x34521),x34523)),f328(f170(x34521),f137(x34521,x34522,x34523))) % 154.70/154.55 [3464]E(f236(x34641,x34642,f328(f235(x34641),x34643)),f328(f328(f80(a875),f328(x34642,x34643)),f328(a116,f2(a875)))) % 154.70/154.55 [3541]E(f328(f193(a871),f29(x35411,x35412,x35413)),f328(f328(f80(a875),f328(f193(a871),x35413)),f328(a116,f2(a875)))) % 154.70/154.55 [3542]E(f328(f307(f881(x35421,x35422),x35422,f266(x35421,x35422)),x35423),f328(f259(x35421,x35422),x35423)) % 154.70/154.55 [3543]E(f328(f307(f881(x35431,x35432),x35431,f262(x35431,x35432)),x35433),f328(f261(x35431,x35432),x35433)) % 154.70/154.55 [3613]E(f328(f328(f263(x36131,x36132),f328(f262(x36131,x36132),x36133)),f328(f266(x36131,x36132),x36133)),x36133) % 154.70/154.55 [3620]E(f328(f193(f877(x36201)),f127(x36201,x36202,x36203)),f328(f328(f80(a875),f328(f193(f877(x36201)),x36203)),f328(a116,f2(a875)))) % 154.70/154.55 [3623]E(f328(f328(f267(x36231,x36232,x36231),f16(x36231,x36232)),x36233),f328(f262(x36231,x36232),x36233)) % 154.70/154.55 [3643]E(f183(x36431,x36432,x36433,f328(f16(f879(x36432),x36431),f205(x36432))),x36433) % 154.70/154.55 [3644]E(f183(x36441,x36442,f328(f16(f879(x36442),x36441),f205(x36442)),x36443),x36443) % 154.70/154.55 [3700]E(f31(f30(x37001,x37002,x37003)),f328(f328(f80(a875),f328(f328(f80(a875),f31(x37002)),f31(x37003))),f328(a116,f2(a875)))) % 154.70/154.55 [3750]E(f328(f73(x37501,x37501,x37502,f34(x37501)),x37503),x37503) % 154.70/154.55 [3859]E(f328(f193(a871),f30(x38591,x38592,x38593)),f328(f328(f80(a875),f328(f328(f80(a875),f328(f193(a871),x38592)),f328(f193(a871),x38593))),f328(a116,f2(a875)))) % 154.70/154.55 [3936]P1(f328(f328(f242(f882(x39361,a870)),f328(f170(x39361),f328(f133(x39361,x39362),x39363))),f328(f170(x39361),x39363))) % 154.70/154.55 [3981]P1(f328(f328(f242(f882(x39811,a870)),f328(f170(x39811),f328(f328(f173(x39811),x39812),x39813))),f328(f170(x39811),x39813))) % 154.70/154.55 [3982]P1(f328(f328(f242(f882(x39821,a870)),f328(f170(x39821),f328(f328(f135(x39821),x39822),x39823))),f328(f170(x39821),x39823))) % 154.70/154.55 [3987]P1(f328(f328(f242(f882(x39871,a870)),f328(f170(x39871),f174(x39871,x39872,x39873))),f328(f170(x39871),x39872))) % 154.70/154.55 [3988]P1(f328(f328(f242(f882(x39881,a870)),f328(f170(x39881),f167(x39881,x39882,x39883))),f328(f170(x39881),x39883))) % 154.70/154.55 [4011]P27(f881(x40111,x40112),f881(x40112,x40111),f328(f267(x40111,x40112,f881(x40112,x40111)),f328(f7(x40112,x40111,f881(x40112,x40111)),f263(x40112,x40111))),x40113) % 154.70/154.55 [4023]E(f328(f328(f328(f187(f876(x40231),f876(x40231)),f44(a875,x40232,f328(f193(f876(x40231)),x40233))),f165(x40231)),x40233),f328(f328(f328(f187(f876(x40231),f876(x40231)),x40232),f165(x40231)),x40233)) % 154.70/154.55 [4065]P1(f328(f328(f330(f881(f876(x40651),f876(x40651))),f328(f328(f263(f876(x40651),f876(x40651)),x40652),x40652)),f155(x40651,f304(x40651,x40653)))) % 154.70/154.55 [4210]E(f85(f881(x42101,x42102),f328(f328(f18(f881(x42101,x42102),x42102,a870),f328(f328(f8(x42101,f882(x42102,a870),f881(x42101,x42102)),x42103),f262(x42101,x42102))),f266(x42101,x42102))),f85(f881(x42101,x42102),f328(f267(x42101,x42102,a870),x42103))) % 154.70/154.55 [4211]E(f90(f881(x42111,x42112),f328(f328(f18(f881(x42111,x42112),x42112,a870),f328(f328(f8(x42111,f882(x42112,a870),f881(x42111,x42112)),x42113),f262(x42111,x42112))),f266(x42111,x42112))),f90(f881(x42111,x42112),f328(f267(x42111,x42112,a870),x42113))) % 154.70/154.55 [4247]E(f328(f328(f284(f881(a875,x42471),x42471),f320(a875,x42471,a247,x42472)),f328(f328(f18(x42471,x42471,f881(a875,x42471)),f328(f328(f8(a875,f882(x42471,f881(a875,x42471)),x42471),f263(a875,x42471)),x42473)),f5(x42471))),f322(x42471,x42473,x42472)) % 154.70/154.55 [4312]E(f328(f268(x43121,x43121,x43122,x43122,f5(x43121),f5(x43122)),x43123),x43123) % 154.70/154.55 [4387]E(f328(f139(f876(f876(x43871)),f876(f876(x43871)),f125(f876(x43871)),f117(f876(x43871))),f328(f328(f151(f876(x43871),f876(f876(x43871))),f328(f328(f7(f876(x43871),f876(x43871),f876(f876(x43871))),f328(f328(f8(f882(x43871,f876(x43871)),f882(f876(x43871),f876(f876(x43871))),f876(x43871)),f151(x43871,f876(x43871))),f328(f7(x43871,f876(x43871),f876(x43871)),f148(x43871)))),x43872)),f54(x43871,x43873,x43872))),f54(x43871,f328(a116,x43873),x43872)) % 154.70/154.55 [4450]E(f328(f237(a875,f881(x44501,f877(x44501)),f2(a875),f328(f267(x44501,f877(x44501),a875),f328(f328(f7(x44501,a875,f882(f877(x44501),a875)),f328(f328(f8(f882(f877(x44501),f882(a875,a875)),f882(a875,f882(f877(x44501),a875)),x44501),f7(f877(x44501),a875,a875)),f328(f328(f8(f882(f877(x44501),a875),f882(f877(x44501),f882(a875,a875)),x44501),f328(f8(a875,f882(a875,a875),f877(x44501)),f80(a875))),f328(f328(f7(x44501,f882(f877(x44501),a875),f882(f877(x44501),a875)),f328(f328(f8(f882(a875,a875),f882(f882(f877(x44501),a875),f882(f877(x44501),a875)),x44501),f8(a875,a875,f877(x44501))),f328(f328(f8(a875,f882(a875,a875),x44501),f80(a875)),x44502))),f129(x44501,x44502))))),f78(a875)))),f328(f132(x44501),x44503)),f328(f129(x44501,x44502),x44503)) % 154.70/154.55 [4453]E(f328(f328(f86(a1,x44531),f225(f328(f328(f73(f881(a1,a1),a1,x44531,f266(a1,a1)),f219(x44531)),x44532),f328(f328(f73(f881(a1,a1),a1,x44531,f266(a1,a1)),f219(x44531)),x44533))),f328(f328(f18(a1,a1,x44531),f328(f328(f8(a1,f882(a1,x44531),a1),f209(x44531)),f328(f328(f18(a1,a1,a1),f328(f328(f8(a1,f882(a1,a1),a1),f80(a1)),f328(f328(f8(a1,a1,a1),f328(f81(a1),f328(f328(f73(f881(a1,a1),a1,x44531,f262(a1,a1)),f219(x44531)),x44532))),f328(f328(f7(a1,a1,a1),f38(a1)),f328(f328(f73(f881(a1,a1),a1,x44531,f266(a1,a1)),f219(x44531)),x44532))))),f328(f328(f8(a1,a1,a1),f328(f81(a1),f328(f328(f73(f881(a1,a1),a1,x44531,f262(a1,a1)),f219(x44531)),x44533))),f328(f328(f7(a1,a1,a1),f38(a1)),f328(f328(f73(f881(a1,a1),a1,x44531,f266(a1,a1)),f219(x44531)),x44533)))))),f5(a1))),f230(x44531,x44532,x44533)) % 154.70/154.55 [4490]~E(f328(f328(f148(x44901),x44902),x44903),x44903) % 154.70/154.55 [4497]~E(f328(f328(f148(x44971),x44972),x44973),f117(x44971)) % 154.70/154.55 [4513]~E(f328(f328(f306(x45131),x45132),x45133),f192(f882(x45131,a870))) % 154.70/154.55 [4536]~E(f328(f307(x45361,f882(x45361,a870),x45362),x45363),f328(f305(x45361),x45363)) % 154.70/154.55 [3327]E(f328(f328(f156(x33271,f117(x33271)),x33272),x33273),f117(x33271)) % 154.70/154.55 [3328]E(f328(f138(x33281),f328(f328(f148(x33281),x33282),x33283)),x33282) % 154.70/154.55 [3329]E(f328(f169(x33291),f328(f328(f148(x33291),x33292),x33293)),x33293) % 154.70/154.55 [3374]E(f328(f328(f135(x33741),f78(a875)),f328(f328(f148(x33741),x33742),x33743)),x33743) % 154.70/154.55 [3408]E(f118(x34081,f328(f328(f135(x34081),x34082),x34083)),f328(f328(f135(x34081),x34082),f118(x34081,x34083))) % 154.70/154.55 [3410]E(f328(f328(f156(x34101,x34102),x34103),f328(f328(f162(x34101),x34102),x34103)),x34102) % 154.70/154.55 [3434]E(f328(f328(f306(x34341),x34342),f328(f328(f306(x34341),x34342),x34343)),f328(f328(f306(x34341),x34342),x34343)) % 154.70/154.55 [3445]E(f328(f328(f176(x34451,x34452),f117(f881(x34451,x34452))),x34453),f205(x34452)) % 154.70/154.55 [3448]E(f328(f328(f306(x34481),x34482),f328(f170(x34481),x34483)),f328(f170(x34481),f328(f328(f148(x34481),x34482),x34483))) % 154.70/154.55 [3450]E(f328(f328(f135(x34501),x34502),f328(f169(x34501),x34503)),f328(f169(x34501),f328(f328(f135(x34501),x34502),x34503))) % 154.70/154.55 [3461]E(f328(f328(f173(x34611),f78(a875)),f328(f328(f148(x34611),x34612),x34613)),f328(f328(f148(x34611),x34612),f117(x34611))) % 154.70/154.55 [3506]E(f328(f63(x35061,x35062),f328(f328(f306(x35061),x35063),f192(f882(x35061,a870)))),x35063) % 154.70/154.55 [3549]E(f328(f328(f80(a875),x35491),f328(f328(f80(a875),x35492),x35493)),f328(f328(f80(a875),x35492),f328(f328(f80(a875),x35491),x35493))) % 154.70/154.55 [3550]E(f328(f328(f80(a1),x35501),f328(f328(f80(a1),x35502),x35503)),f328(f328(f80(a1),x35502),f328(f328(f80(a1),x35501),x35503))) % 154.70/154.55 [3555]E(f328(f328(f265(x35551,x35552),f192(f882(x35551,a870))),x35553),f192(f882(f881(x35551,x35552),a870))) % 154.70/154.55 [3578]E(f328(f328(f114(f882(x35781,a870)),x35782),x35783),f328(f328(f114(f882(x35781,a870)),x35783),x35782)) % 154.70/154.55 [3579]E(f328(f328(f105(f882(x35791,a870)),x35792),x35793),f328(f328(f105(f882(x35791,a870)),x35793),x35792)) % 154.70/154.55 [3581]E(f328(f328(f125(x35811),x35812),f328(f328(f148(x35811),x35813),f117(x35811))),f328(f165(x35811),f328(f328(f148(x35811),x35813),x35812))) % 154.70/154.55 [3582]E(f328(f328(f125(x35821),f328(f166(x35821),x35822)),f328(f166(x35821),x35823)),f328(f166(x35821),f328(f328(f125(x35821),x35823),x35822))) % 154.70/154.55 [3592]E(f328(f169(x35921),f328(f328(f173(x35921),f328(a116,x35922)),x35923)),f328(f328(f173(x35921),x35922),f328(f169(x35921),x35923))) % 154.70/154.55 [3599]P1(f328(f328(f330(x35991),x35992),f328(f328(f306(x35991),x35992),x35993))) % 154.70/154.55 [3603]E(f328(f328(f42(x36031,f882(x36032,a870)),f192(f882(x36031,a870))),x36033),f251(f882(x36032,a870))) % 154.70/154.55 [3606]E(f328(f282(x36061,x36061,f260(x36061,x36062)),x36063),f328(f328(f105(f882(x36061,a870)),x36062),x36063)) % 154.70/154.55 [3619]E(f328(f193(f876(x36191)),f328(f328(f148(x36191),x36192),x36193)),f328(f328(f80(a875),f328(f193(f876(x36191)),x36193)),f328(a116,f2(a875)))) % 154.70/154.55 [3625]E(f118(x36251,f328(f328(f125(x36251),x36252),f328(f328(f148(x36251),x36253),f117(x36251)))),x36252) % 154.70/154.55 [3626]E(f141(x36261,f328(f328(f125(x36261),x36262),f328(f328(f148(x36261),x36263),f117(x36261)))),x36263) % 154.70/154.55 [3632]E(f328(f328(f125(x36321),f328(f328(f173(x36321),x36322),x36323)),f328(f328(f135(x36321),x36322),x36323)),x36323) % 154.70/154.55 [3641]E(f328(f328(f22(a875),f328(f328(f80(a875),x36411),x36412)),f328(f328(f80(a875),x36413),x36412)),f328(f328(f22(a875),x36411),x36413)) % 154.70/154.55 [3642]E(f328(f328(f22(a875),f328(f328(f80(a875),x36421),x36422)),f328(f328(f80(a875),x36421),x36423)),f328(f328(f22(a875),x36422),x36423)) % 154.70/154.55 [3649]E(f328(f328(f125(x36491),f328(f166(x36491),x36492)),f328(f328(f148(x36491),x36493),f117(x36491))),f328(f166(x36491),f328(f328(f148(x36491),x36493),x36492))) % 154.70/154.55 [3651]E(f328(f328(f80(a875),f328(f193(f876(x36511)),x36512)),f328(f193(f876(x36511)),x36513)),f328(f193(f876(x36511)),f328(f328(f125(x36511),x36512),x36513))) % 154.70/154.55 [3654]E(f328(f328(f80(a875),f328(f193(f876(x36541)),x36542)),f328(f193(f876(x36541)),x36543)),f328(f193(f876(x36541)),f171(x36541,x36542,x36543))) % 154.70/154.55 [3662]E(f328(f328(f114(f882(x36621,a870)),f328(f170(x36621),x36622)),f328(f170(x36621),x36623)),f328(f170(x36621),f328(f328(f125(x36621),x36622),x36623))) % 154.70/154.55 [3663]E(f44(a875,f328(f328(f81(a875),x36631),x36632),f328(f328(f81(a875),x36631),x36633)),f328(f328(f81(a875),x36631),f44(a875,x36632,x36633))) % 154.70/154.55 [3676]E(f328(f328(f173(x36761),f328(f328(f22(a875),x36762),f78(a875))),f328(f169(x36761),x36763)),f328(f169(x36761),f328(f328(f173(x36761),x36762),x36763))) % 154.70/154.55 [3681]E(f328(f328(f105(f882(x36811,a870)),x36812),f328(f79(f882(x36811,a870)),x36813)),f328(f328(f22(f882(x36811,a870)),x36812),x36813)) % 154.70/154.55 [3682]E(f328(f328(f22(f882(x36821,a870)),x36822),f328(f79(f882(x36821,a870)),x36823)),f328(f328(f105(f882(x36821,a870)),x36822),x36823)) % 154.70/154.55 [3704]E(f328(f328(f265(x37041,x37042),x37043),f328(f16(f882(x37042,a870),x37041),f192(f882(x37042,a870)))),f192(f882(f881(x37041,x37042),a870))) % 154.70/154.55 [3706]E(f328(f328(f22(a875),f328(f328(f81(a875),x37061),x37062)),f328(f328(f81(a875),x37061),x37063)),f328(f328(f81(a875),x37061),f328(f328(f22(a875),x37062),x37063))) % 154.70/154.55 [3707]E(f328(f328(f80(a875),f328(f328(f81(a875),x37071),x37072)),f328(f328(f81(a875),x37071),x37073)),f328(f328(f81(a875),x37071),f328(f328(f80(a875),x37072),x37073))) % 154.70/154.55 [3708]E(f328(f328(f22(a1),f328(f328(f81(a1),x37081),x37082)),f328(f328(f81(a1),x37081),x37083)),f328(f328(f81(a1),x37081),f328(f328(f22(a1),x37082),x37083))) % 154.70/154.55 [3709]E(f328(f328(f80(a1),f328(f328(f81(a1),x37091),x37092)),f328(f328(f81(a1),x37091),x37093)),f328(f328(f81(a1),x37091),f328(f328(f80(a1),x37092),x37093))) % 154.70/154.55 [3710]E(f328(f328(f81(a1),f328(f328(f253(a1),x37101),x37102)),f328(f328(f253(a1),x37101),x37103)),f328(f328(f253(a1),x37101),f328(f328(f80(a875),x37102),x37103))) % 154.70/154.55 [3724]E(f328(f328(f41(x37241,f882(x37242,a870)),x37243),f328(f16(f882(x37242,a870),x37241),f192(f882(x37242,a870)))),f192(f882(x37242,a870))) % 154.70/154.55 [3726]E(f44(a875,f328(f328(f81(a875),x37261),x37262),f328(f328(f81(a875),x37263),x37262)),f328(f328(f81(a875),f44(a875,x37261,x37263)),x37262)) % 154.70/154.55 [3730]E(f44(a1,f328(f328(f22(a1),x37301),f44(a1,x37302,x37303)),x37303),f44(a1,f328(f328(f22(a1),x37301),x37302),x37303)) % 154.70/154.55 [3731]E(f44(a1,f328(f328(f81(a1),x37311),f44(a1,x37312,x37313)),x37313),f44(a1,f328(f328(f81(a1),x37311),x37312),x37313)) % 154.70/154.55 [3732]P1(f328(f328(f242(f882(x37321,a870)),x37322),f328(f328(f306(x37321),x37323),x37322))) % 154.70/154.55 [3735]E(f328(f307(f881(x37351,x37352),x37351,f262(x37351,x37352)),f328(f170(f881(x37351,x37352)),x37353)),f182(x37351,x37352,f328(f176(x37351,x37352),x37353))) % 154.70/154.55 [3784]P1(f328(f61(x37841),f182(x37841,x37842,f328(f176(x37841,x37842),x37843)))) % 154.70/154.55 [3809]E(f328(f328(f42(f882(x38091,a870),f882(x38091,a870)),x38092),f328(f114(f882(x38091,a870)),x38093)),f328(f328(f114(f882(x38091,a870)),x38093),f40(f882(x38091,a870),x38092))) % 154.70/154.55 [3810]E(f328(f328(f41(f882(x38101,a870),f882(x38101,a870)),x38102),f328(f105(f882(x38101,a870)),x38103)),f328(f328(f105(f882(x38101,a870)),x38103),f39(f882(x38101,a870),x38102))) % 154.70/154.55 [3821]E(f328(f170(x38211),f328(f328(f328(f187(f876(x38211),f876(x38211)),x38212),f165(x38211)),x38213)),f328(f170(x38211),x38213)) % 154.70/154.55 [3825]E(f328(f328(f173(x38251),f328(f193(f876(x38251)),f175(x38251,x38252,x38253))),x38253),f175(x38251,x38252,x38253)) % 154.70/154.55 [3826]E(f182(x38261,x38262,f328(f328(f8(x38262,f879(x38262),x38261),f235(x38262)),x38263)),f251(f882(x38261,a870))) % 154.70/154.55 [3830]E(f328(f193(f876(x38301)),f328(f328(f328(f187(f876(x38301),f876(x38301)),x38302),f165(x38301)),x38303)),f328(f193(f876(x38301)),x38303)) % 154.70/154.55 [3833]E(f328(f328(f267(x38331,x38332,x38332),f328(f16(f882(x38332,x38332),x38331),f5(x38332))),x38333),f328(f266(x38331,x38332),x38333)) % 154.70/154.55 [3839]E(f44(a1,f328(f328(f22(a1),f44(a1,x38391,x38392)),x38393),x38392),f44(a1,f328(f328(f22(a1),x38391),x38393),x38392)) % 154.70/154.55 [3840]E(f44(a1,f328(f328(f253(a1),f44(a1,x38401,x38402)),x38403),x38402),f44(a1,f328(f328(f253(a1),x38401),x38403),x38402)) % 154.70/154.55 [3843]E(f328(f328(f41(f882(f881(x38431,x38432),a870),f882(x38432,a870)),x38433),f259(x38431,x38432)),f328(f259(x38431,x38432),f39(f882(f881(x38431,x38432),a870),x38433))) % 154.70/154.55 [3844]E(f328(f328(f41(f882(f881(x38441,x38442),a870),f882(x38441,a870)),x38443),f261(x38441,x38442)),f328(f261(x38441,x38442),f39(f882(f881(x38441,x38442),a870),x38443))) % 154.70/154.55 [3872]E(f328(f73(x38721,x38721,x38721,x38722),f328(f328(f187(x38721,x38721),x38723),x38722)),f328(f328(f187(x38721,x38721),f328(a116,x38723)),x38722)) % 154.70/154.55 [3882]E(f237(f879(x38821),x38822,f205(x38821),f328(f328(f8(x38821,f879(x38821),x38822),f235(x38821)),x38823)),f328(f206(x38822,x38821),x38823)) % 154.70/154.55 [3889]E(f328(f328(f135(x38891),f328(f328(f22(a875),f328(f193(f876(x38891)),x38892)),x38893)),f328(f166(x38891),x38892)),f328(f166(x38891),f328(f328(f173(x38891),x38893),x38892))) % 154.70/154.55 [3890]E(f328(f328(f173(x38901),f328(f328(f22(a875),f328(f193(f876(x38901)),x38902)),x38903)),f328(f166(x38901),x38902)),f328(f166(x38901),f328(f328(f135(x38901),x38903),x38902))) % 154.70/154.55 [3893]E(f328(f328(f80(a875),f328(f163(a875),f328(f328(f151(x38931,a875),x38932),x38933))),f328(f193(f876(x38931)),x38933)),f152(x38931,x38932,x38933)) % 154.70/154.55 [3912]E(f328(f165(x39121),f328(f328(f328(f187(f876(x39121),f876(x39121)),x39122),f165(x39121)),x39123)),f328(f328(f328(f187(f876(x39121),f876(x39121)),f328(a116,x39122)),f165(x39121)),x39123)) % 154.70/154.55 [3927]P1(f328(f328(f242(a875),f328(f193(f876(x39271)),f328(f133(x39271,x39272),x39273))),f328(f193(f876(x39271)),x39273))) % 154.70/154.55 [3944]E(f328(f328(f114(f882(f882(x39441,a870),a870)),f328(f305(x39441),x39442)),f328(f307(f882(x39441,a870),f882(x39441,a870),f328(f306(x39441),x39443)),f328(f305(x39441),x39442))),f328(f305(x39441),f328(f328(f306(x39441),x39443),x39442))) % 154.70/154.55 [3963]P26(x39631,x39632,f328(f328(f306(f874(x39631)),f328(f328(f328(f92(x39631),x39633),a24),x39633)),f192(f882(f874(x39631),a870)))) % 154.70/154.55 [3978]P1(f328(f328(f242(a875),f328(f193(f876(x39781)),f175(x39781,x39782,x39783))),f328(f193(f876(x39781)),x39783))) % 154.70/154.55 [3986]E(f328(f261(x39861,x39862),f328(f248(f881(x39861,x39862)),f328(f267(x39861,x39862,a870),x39863))),f328(f248(x39861),f328(f328(f8(f882(x39862,a870),a870,x39861),f87(x39862)),x39863))) % 154.70/154.55 [3998]E(f328(f307(a875,a875,f328(f328(f7(a875,a875,a875),f80(a875)),x39981)),f299(a875,x39982,x39983)),f299(a875,f328(f328(f80(a875),x39982),x39981),f328(f328(f80(a875),x39983),x39981))) % 154.70/154.55 [4001]P1(f328(f61(f879(x40011)),f328(f307(x40012,f879(x40011),f328(f176(x40012,x40011),x40013)),f251(f882(x40012,a870))))) % 154.70/154.55 [4014]E(f328(f307(a875,a875,f328(f328(f7(a875,a875,a875),f80(a875)),x40141)),f328(f298(a875,x40142),x40143)),f328(f298(a875,f328(f328(f80(a875),x40142),x40141)),f328(f328(f80(a875),x40143),x40141))) % 154.70/154.55 [4032]E(f328(f328(f180(x40321,x40322),f328(f328(f151(f881(x40321,x40322),x40321),f262(x40321,x40322)),x40323)),f328(f328(f151(f881(x40321,x40322),x40322),f266(x40321,x40322)),x40323)),x40323) % 154.70/154.55 [4037]E(f328(f328(f80(a875),f328(f328(f81(a875),x40371),f44(a875,f328(f328(f38(a875),x40372),x40371),x40373))),f44(a875,x40372,x40371)),f44(a875,x40372,f328(f328(f81(a875),x40371),x40373))) % 154.70/154.55 [4051]E(f328(f328(f125(x40511),x40512),f328(f139(f876(x40511),f876(x40511),f125(x40511),f117(x40511)),x40513)),f328(f139(f876(x40511),f876(x40511),f125(x40511),x40512),x40513)) % 154.70/154.55 [4069]P1(f328(f328(f330(f881(x40691,x40691)),f328(f328(f263(x40691,x40691),x40692),x40692)),f328(f328(f187(f881(x40691,x40691),a870),f2(a875)),x40693))) % 154.70/154.55 [4075]E(f328(f248(x40751),f328(f328(f8(f882(x40752,a870),a870,x40751),f87(x40752)),f328(f7(x40752,x40751,a870),x40753))),f328(f259(x40752,x40751),f328(f248(f881(x40752,x40751)),f328(f267(x40752,x40751,a870),x40753)))) % 154.70/154.55 [4093]E(f328(f328(f114(f882(x40931,a870)),f328(f328(f41(a875,f882(x40931,a870)),f299(a875,f78(a875),x40932)),x40933)),f328(x40933,f2(a875))),f328(f328(f41(a875,f882(x40931,a870)),f328(f297(a875),x40932)),x40933)) % 154.70/154.55 [4108]E(f328(f139(f876(x41081),f876(x41081),f125(x41081),f117(x41081)),f328(f328(f151(f876(x41081),f876(x41081)),f133(x41081,x41082)),x41083)),f328(f133(x41081,x41082),f328(f139(f876(x41081),f876(x41081),f125(x41081),f117(x41081)),x41083))) % 154.70/154.55 [4113]E(f328(f266(f876(x41131),f876(x41131)),f164(x41131,x41132,x41133)),f328(f133(x41131,f328(f73(a870,a870,x41131,a323),x41132)),x41133)) % 154.70/154.55 [4131]E(f328(f328(f42(x41311,f882(x41312,a870)),f251(f882(x41311,a870))),f328(f328(f8(f882(x41312,a870),f882(x41312,a870),x41311),f248(x41312)),f328(f7(x41312,x41311,a870),x41313))),f328(f248(x41312),f328(f328(f8(f882(x41311,a870),a870,x41312),f88(x41311)),x41313))) % 154.70/154.55 [4162]E(f328(f328(f80(a1),f328(f328(f80(a1),f328(f328(f81(a1),x41621),f328(f328(f38(a1),x41622),x41621))),f44(a1,x41622,x41621))),x41623),f328(f328(f80(a1),x41622),x41623)) % 154.70/154.55 [4199]E(f328(f328(f80(a1),f328(f328(f80(a1),f328(f328(f81(a1),f328(f328(f38(a1),x41991),x41992)),x41992)),f44(a1,x41991,x41992))),x41993),f328(f328(f80(a1),x41991),x41993)) % 154.70/154.55 [4228]E(f85(f881(x42281,x42282),f328(f267(x42281,x42282,a870),f328(f328(f8(f882(x42282,f881(x42281,x42282)),f882(x42282,a870),x42281),f328(f8(f881(x42281,x42282),a870,x42282),x42283)),f263(x42281,x42282)))),f85(f881(x42281,x42282),x42283)) % 154.70/154.55 [4229]E(f90(f881(x42291,x42292),f328(f267(x42291,x42292,a870),f328(f328(f8(f882(x42292,f881(x42291,x42292)),f882(x42292,a870),x42291),f328(f8(f881(x42291,x42292),a870,x42292),x42293)),f263(x42291,x42292)))),f90(f881(x42291,x42292),x42293)) % 154.70/154.55 [4257]P1(f328(f328(f242(f882(x42571,a870)),f39(f882(x42571,a870),f328(f328(f105(f882(f882(x42571,a870),a870)),x42572),x42573))),f328(f328(f105(f882(x42571,a870)),f39(f882(x42571,a870),x42572)),f39(f882(x42571,a870),x42573)))) % 154.70/154.55 [4258]E(f328(f166(x42581),f328(f328(f328(f187(f876(x42581),f876(x42581)),f328(f328(f22(a875),f328(f193(f876(x42581)),x42582)),f44(a875,x42583,f328(f193(f876(x42581)),x42582)))),f165(x42581)),x42582)),f328(f328(f328(f187(f876(x42581),f876(x42581)),x42583),f165(x42581)),f328(f166(x42581),x42582))) % 154.70/154.55 [4272]E(f328(f248(x42721),f328(f328(f8(a870,a870,x42721),a323),f328(f328(f7(x42721,f879(x42722),a870),f328(f328(f8(f879(x42722),f882(f879(x42722),a870),x42721),a325),x42723)),f205(x42722)))),f182(x42721,x42722,x42723)) % 154.70/154.55 [4297]P1(f328(f328(f242(a875),f328(f193(f876(x42971)),f328(f328(f135(x42971),f328(f193(f876(x42971)),f175(x42971,x42972,x42973))),x42973))),f328(f193(f876(x42971)),x42973))) % 154.70/154.55 [4338]E(f328(f248(x43381),f328(f328(f8(f882(x43382,a870),a870,x43381),f87(x43382)),f328(f328(f8(f879(x43381),f882(x43382,a870),x43381),f328(f7(x43382,f879(x43381),a870),f328(f328(f8(f879(x43381),f882(f879(x43381),a870),x43382),a325),x43383))),f235(x43381)))),f184(x43382,x43381,x43383)) % 154.70/154.55 [4550]~P1(f328(f62(x45501,x45502,f192(f882(x45501,a870))),x45503)) % 154.70/154.55 [4557]~P1(f328(f328(f330(f881(x45571,x45571)),f328(f328(f263(x45571,x45571),x45572),x45573)),f150(x45571,f117(f882(x45571,a875))))) % 154.70/154.55 [3593]E(f328(f193(f876(x35931)),f328(f328(f173(x35931),x35932),x35933)),f328(f328(f240(a875),f328(f193(f876(x35931)),x35933)),x35932)) % 154.70/154.55 [3594]E(f328(f193(f876(x35941)),f328(f328(f135(x35941),x35942),x35943)),f328(f328(f22(a875),f328(f193(f876(x35941)),x35943)),x35942)) % 154.70/154.55 [3618]E(f328(f193(f876(f876(x36181))),f54(x36181,x36182,x36183)),f328(f328(f253(a875),f328(f193(f876(x36181)),x36183)),x36182)) % 154.70/154.55 [3634]E(f328(f328(f38(a875),f328(f328(f38(a875),x36341),x36342)),x36343),f328(f328(f38(a875),x36341),f328(f328(f81(a875),x36342),x36343))) % 154.70/154.55 [3635]E(f328(f328(f22(a875),f328(f328(f22(a875),x36351),x36352)),x36353),f328(f328(f22(a875),x36351),f328(f328(f80(a875),x36352),x36353))) % 154.70/154.55 [3636]E(f328(f328(f80(a875),f328(f328(f80(a875),x36361),x36362)),x36363),f328(f328(f80(a875),x36361),f328(f328(f80(a875),x36362),x36363))) % 154.70/154.55 [3637]E(f328(f328(f80(a1),f328(f328(f80(a1),x36371),x36372)),x36373),f328(f328(f80(a1),x36371),f328(f328(f80(a1),x36372),x36373))) % 154.70/154.55 [3638]E(f328(f328(f81(a875),f328(f328(f81(a875),x36381),x36382)),x36383),f328(f328(f81(a875),x36381),f328(f328(f81(a875),x36382),x36383))) % 154.70/154.55 [3639]E(f328(f328(f81(a1),f328(f328(f81(a1),x36391),x36392)),x36393),f328(f328(f81(a1),x36391),f328(f328(f81(a1),x36392),x36393))) % 154.70/154.55 [3640]E(f328(f328(f253(a1),f328(f328(f253(a1),x36401),x36402)),x36403),f328(f328(f253(a1),x36401),f328(f328(f81(a875),x36402),x36403))) % 154.70/154.55 [3660]E(f159(x36601,f328(f328(f148(f882(x36601,a870)),x36602),x36603)),f172(x36601,x36602,f159(x36601,x36603))) % 154.70/154.55 [3705]E(f328(f328(f22(a875),f328(f328(f22(a875),x37051),x37052)),x37053),f328(f328(f22(a875),f328(f328(f22(a875),x37051),x37053)),x37052)) % 154.70/154.55 [3711]E(f328(f235(f881(x37111,f877(x37111))),f328(f328(f263(x37111,f877(x37111)),x37112),x37113)),f328(f132(x37111),f127(x37111,x37112,x37113))) % 154.70/154.55 [3714]E(f328(f328(f105(f882(x37141,a870)),x37142),f328(f328(f22(f882(x37141,a870)),x37143),x37142)),f192(f882(x37141,a870))) % 154.70/154.55 [3756]E(f39(f882(x37561,a870),f328(f328(f306(f882(x37561,a870)),x37562),x37563)),f328(f328(f114(f882(x37561,a870)),x37562),f39(f882(x37561,a870),x37563))) % 154.70/154.55 [3757]E(f40(f882(x37571,a870),f328(f328(f306(f882(x37571,a870)),x37572),x37573)),f328(f328(f105(f882(x37571,a870)),x37572),f40(f882(x37571,a870),x37573))) % 154.70/154.55 [3759]E(f328(f328(f22(a875),f328(f328(f81(a875),x37591),x37592)),f328(f328(f81(a875),x37593),x37592)),f328(f328(f81(a875),f328(f328(f22(a875),x37591),x37593)),x37592)) % 154.70/154.55 [3760]E(f328(f328(f80(a875),f328(f328(f81(a875),x37601),x37602)),f328(f328(f81(a875),x37603),x37602)),f328(f328(f81(a875),f328(f328(f80(a875),x37601),x37603)),x37602)) % 154.70/154.55 [3761]E(f328(f328(f22(a1),f328(f328(f81(a1),x37611),x37612)),f328(f328(f81(a1),x37613),x37612)),f328(f328(f81(a1),f328(f328(f22(a1),x37611),x37613)),x37612)) % 154.70/154.55 [3762]E(f328(f328(f80(a1),f328(f328(f81(a1),x37621),x37622)),f328(f328(f81(a1),x37623),x37622)),f328(f328(f81(a1),f328(f328(f80(a1),x37621),x37623)),x37622)) % 154.70/154.55 [3764]E(f328(f328(f240(a875),f328(f328(f22(a875),x37641),x37642)),f328(f328(f22(a875),x37643),x37642)),f328(f328(f22(a875),f328(f328(f240(a875),x37641),x37643)),x37642)) % 154.70/154.55 [3787]E(f328(f328(f105(f882(f876(x37871),a870)),f157(x37871,x37872)),f157(x37871,x37873)),f157(x37871,f328(f328(f105(f882(x37871,a870)),x37872),x37873))) % 154.70/154.55 [3789]E(f328(f328(f114(f882(x37891,a870)),x37892),f328(f328(f114(f882(x37891,a870)),x37892),x37893)),f328(f328(f114(f882(x37891,a870)),x37892),x37893)) % 154.70/154.55 [3790]E(f328(f328(f114(f882(x37901,a870)),x37902),f328(f328(f22(f882(x37901,a870)),x37903),x37902)),f328(f328(f114(f882(x37901,a870)),x37902),x37903)) % 154.70/154.55 [3791]E(f328(f328(f105(f882(x37911,a870)),x37912),f328(f328(f105(f882(x37911,a870)),x37912),x37913)),f328(f328(f105(f882(x37911,a870)),x37912),x37913)) % 154.70/154.55 [3803]E(f328(f328(f285(x38031,x38032,x38032),x38033),f304(x38032,f192(f882(f881(x38032,x38032),a870)))),x38033) % 154.70/154.55 [3806]E(f328(f328(f114(f882(x38061,a870)),f328(f328(f306(x38061),x38062),f192(f882(x38061,a870)))),x38063),f328(f328(f306(x38061),x38062),x38063)) % 154.70/154.55 [3824]E(f328(f328(f22(a875),f328(f328(f22(a875),f328(a116,x38241)),x38242)),f328(a116,x38243)),f328(f328(f22(a875),f328(f328(f22(a875),x38241),x38242)),x38243)) % 154.70/154.55 [3853]E(f328(f328(f105(f882(f882(x38531,a870),a870)),f328(f305(x38531),x38532)),f328(f305(x38531),x38533)),f328(f305(x38531),f328(f328(f105(f882(x38531,a870)),x38532),x38533))) % 154.70/154.55 [3857]E(f328(f328(f114(f882(x38571,a870)),f328(f79(f882(x38571,a870)),x38572)),x38573),f328(f79(f882(x38571,a870)),f328(f328(f22(f882(x38571,a870)),x38572),x38573))) % 154.70/154.55 [3869]E(f328(f328(f306(x38691),x38692),f328(f328(f22(f882(x38691,a870)),x38693),f328(f328(f306(x38691),x38692),f192(f882(x38691,a870))))),f328(f328(f306(x38691),x38692),x38693)) % 154.70/154.55 [3879]P1(f328(f328(f242(f882(x38791,a870)),x38792),f328(f328(f114(f882(x38791,a870)),x38793),x38792))) % 154.70/154.55 [3880]P1(f328(f328(f242(f882(x38801,a870)),x38802),f328(f328(f114(f882(x38801,a870)),x38802),x38803))) % 154.70/154.55 [3883]E(f328(f328(f105(f882(x38831,a870)),f328(f79(f882(x38831,a870)),x38832)),f328(f79(f882(x38831,a870)),x38833)),f328(f79(f882(x38831,a870)),f328(f328(f114(f882(x38831,a870)),x38832),x38833))) % 154.70/154.55 [3884]E(f328(f328(f114(f882(x38841,a870)),f328(f79(f882(x38841,a870)),x38842)),f328(f79(f882(x38841,a870)),x38843)),f328(f79(f882(x38841,a870)),f328(f328(f105(f882(x38841,a870)),x38842),x38843))) % 154.70/154.55 [3898]P1(f328(f328(f242(f882(x38981,a870)),f328(f170(x38981),x38982)),f328(f170(x38981),f328(f328(f148(x38981),x38983),x38982)))) % 154.70/154.55 [3909]E(f328(f328(f114(f882(x39091,a870)),f328(f328(f22(f882(x39091,a870)),x39092),x39093)),f328(f328(f105(f882(x39091,a870)),x39092),x39093)),x39092) % 154.70/154.55 [3965]E(f328(f328(f6(x39651,a1),f328(f328(f8(a875,a1,x39651),f104(a1)),x39652)),x39653),f328(f104(a1),f328(f328(f6(x39651,a875),x39652),x39653))) % 154.70/154.55 [3966]E(f328(f328(f9(x39661,a1),f328(f328(f8(a875,a1,x39661),f104(a1)),x39662)),x39663),f328(f104(a1),f328(f328(f9(x39661,a875),x39662),x39663))) % 154.70/154.55 [4016]E(f328(f328(f125(x40161),f175(x40161,x40162,x40163)),f328(f328(f135(x40161),f328(f193(f876(x40161)),f175(x40161,x40162,x40163))),x40163)),x40163) % 154.70/154.55 [4021]E(f328(f79(f882(f881(x40211,x40212),a870)),f328(f328(f265(x40211,x40212),x40213),f328(f16(f882(x40212,a870),x40211),f251(f882(x40212,a870))))),f328(f328(f265(x40211,x40212),f328(f79(f882(x40211,a870)),x40213)),f328(f16(f882(x40212,a870),x40211),f251(f882(x40212,a870))))) % 154.70/154.55 [4022]E(f328(f79(f882(f881(x40221,x40222),a870)),f328(f328(f265(x40221,x40222),f251(f882(x40221,a870))),f328(f16(f882(x40222,a870),x40221),x40223))),f328(f328(f265(x40221,x40222),f251(f882(x40221,a870))),f328(f16(f882(x40222,a870),x40221),f328(f79(f882(x40222,a870)),x40223)))) % 154.70/154.55 [4070]E(f328(f328(f41(f882(x40701,a870),f882(x40701,a870)),x40702),f328(f328(f7(f882(x40701,a870),f882(x40701,a870),f882(x40701,a870)),f105(f882(x40701,a870))),x40703)),f328(f328(f105(f882(x40701,a870)),f39(f882(x40701,a870),x40702)),x40703)) % 154.70/154.55 [4077]E(f328(f139(f876(x40771),f876(x40771),f125(x40771),f117(x40771)),f328(f328(f148(f876(x40771)),x40772),x40773)),f328(f328(f125(x40771),x40772),f328(f139(f876(x40771),f876(x40771),f125(x40771),f117(x40771)),x40773))) % 154.70/154.55 [4099]E(f328(f328(f306(f882(x40991,a870)),f328(f282(x40991,x40991,x40992),f328(f328(f306(x40991),x40993),f192(f882(x40991,a870))))),f192(f882(f882(x40991,a870),a870))),f328(f328(f60(x40991),f328(f328(f306(x40991),x40993),f192(f882(x40991,a870)))),x40992)) % 154.70/154.55 [4109]E(f328(f328(f80(a875),f328(f328(f81(a875),x41091),f328(f328(f38(a875),x41092),x41093))),f328(f328(f38(a875),f328(f328(f81(a875),x41091),f44(a875,x41092,x41093))),x41093)),f328(f328(f38(a875),f328(f328(f81(a875),x41091),x41092)),x41093)) % 154.70/154.55 [4110]E(f328(f328(f80(a1),f328(f328(f81(a1),x41101),f328(f328(f38(a1),x41102),x41103))),f328(f328(f38(a1),f328(f328(f81(a1),x41101),f44(a1,x41102,x41103))),x41103)),f328(f328(f38(a1),f328(f328(f81(a1),x41101),x41102)),x41103)) % 154.70/154.55 [4147]E(f328(f328(f22(f882(x41471,a870)),f328(f170(x41471),x41472)),f328(f328(f306(x41471),x41473),f192(f882(x41471,a870)))),f328(f170(x41471),f328(f133(x41471,f328(f328(f8(a870,a870,x41471),a323),f328(a325,x41473))),x41472))) % 154.70/154.55 [4196]E(f328(f328(f125(x41961),f328(f139(f876(x41961),f876(x41961),f125(x41961),f117(x41961)),x41962)),f328(f139(f876(x41961),f876(x41961),f125(x41961),f117(x41961)),x41963)),f328(f139(f876(x41961),f876(x41961),f125(x41961),f117(x41961)),f328(f328(f125(f876(x41961)),x41962),x41963))) % 154.70/154.55 [4201]E(f328(f328(f263(f876(x42011),f876(x42011)),f328(f133(x42011,x42012),x42013)),f328(f133(x42011,f328(f73(a870,a870,x42011,a323),x42012)),x42013)),f164(x42011,x42012,x42013)) % 154.70/154.55 [4204]E(f328(f328(f80(a875),f328(f328(f80(a875),f328(f328(f38(a875),x42041),x42042)),f328(f328(f38(a875),x42043),x42042))),f328(f328(f38(a875),f328(f328(f80(a875),f44(a875,x42041,x42042)),f44(a875,x42043,x42042))),x42042)),f328(f328(f38(a875),f328(f328(f80(a875),x42041),x42043)),x42042)) % 154.70/154.55 [4205]E(f328(f328(f80(a1),f328(f328(f80(a1),f328(f328(f38(a1),x42051),x42052)),f328(f328(f38(a1),x42053),x42052))),f328(f328(f38(a1),f328(f328(f80(a1),f44(a1,x42051,x42052)),f44(a1,x42053,x42052))),x42052)),f328(f328(f38(a1),f328(f328(f80(a1),x42051),x42053)),x42052)) % 154.70/154.55 [4261]E(f328(f328(f105(f882(f876(x42611),a870)),f328(f328(f7(f876(x42611),f882(f876(x42611),a870),a870),f330(f876(x42611))),f158(x42611,x42612))),f328(f328(f7(f876(x42611),f882(f876(x42611),a870),a870),f330(f876(x42611))),f158(x42611,x42613))),f157(x42611,f328(f328(f105(f882(x42611,a870)),f328(f328(f7(x42611,f882(x42611,a870),a870),f330(x42611)),x42612)),f328(f328(f7(x42611,f882(x42611,a870),a870),f330(x42611)),x42613)))) % 154.70/154.55 [4274]E(f328(f248(x42741),f328(f328(f18(x42741,a870,a870),f328(f328(f8(a870,f882(a870,a870),x42741),a327),f328(f328(f7(x42741,x42741,a870),a325),x42742))),f328(f328(f7(x42741,f882(x42741,a870),a870),f330(x42741)),x42743))),f328(f328(f306(x42741),x42742),x42743)) % 154.70/154.55 [4294]E(f328(f328(f86(f876(f876(x42941)),f876(f876(x42941))),f53(x42941,x42942)),f328(f328(f18(f876(f876(x42941)),f876(f876(x42941)),f876(f876(x42941))),f328(f328(f8(f876(f876(x42941)),f882(f876(f876(x42941)),f876(f876(x42941))),f876(f876(x42941))),f125(f876(x42941))),f328(f151(f876(x42941),f876(x42941)),f328(f148(x42941),x42943)))),f5(f876(f876(x42941))))),f53(x42941,f328(f328(f148(x42941),x42943),x42942))) % 154.70/154.55 [4298]E(f328(f248(x42981),f328(f328(f18(x42981,a870,a870),f328(f328(f8(a870,f882(a870,a870),x42981),a327),f328(f328(f7(x42981,f882(x42981,a870),a870),f330(x42981)),x42982))),f328(f328(f7(x42981,f882(x42981,a870),a870),f330(x42981)),x42983))),f328(f328(f114(f882(x42981,a870)),x42982),x42983)) % 154.70/154.55 [4299]E(f328(f248(x42991),f328(f328(f18(x42991,a870,a870),f328(f328(f8(a870,f882(a870,a870),x42991),a326),f328(f328(f7(x42991,f882(x42991,a870),a870),f330(x42991)),x42992))),f328(f328(f7(x42991,f882(x42991,a870),a870),f330(x42991)),x42993))),f328(f328(f105(f882(x42991,a870)),x42992),x42993)) % 154.70/154.55 [4390]E(f328(f328(f41(x43901,f882(f882(x43901,a870),a870)),x43902),f328(f328(f7(x43901,f882(f882(x43901,a870),a870),f882(f882(x43901,a870),a870)),f328(f328(f8(f882(x43901,a870),f882(f882(f882(x43901,a870),a870),f882(f882(x43901,a870),a870)),x43901),f306(f882(x43901,a870))),f328(f328(f8(f882(x43901,a870),f882(x43901,a870),x43901),f282(x43901,x43901,x43903)),f328(f328(f7(x43901,f882(x43901,a870),f882(x43901,a870)),f306(x43901)),f192(f882(x43901,a870)))))),f192(f882(f882(x43901,a870),a870)))),f328(f328(f60(x43901),x43902),x43903)) % 154.70/154.55 [4392]E(f328(f328(f209(x43921),f328(f328(f81(a1),f328(f328(f73(f881(a1,a1),a1,x43921,f262(a1,a1)),f219(x43921)),x43922)),f328(f328(f73(f881(a1,a1),a1,x43921,f262(a1,a1)),f219(x43921)),x43923))),f328(f328(f81(a1),f328(f328(f73(f881(a1,a1),a1,x43921,f266(a1,a1)),f219(x43921)),x43922)),f328(f328(f73(f881(a1,a1),a1,x43921,f266(a1,a1)),f219(x43921)),x43923))),f228(x43921,x43922,x43923)) % 154.70/154.55 [4395]E(f328(f248(f876(x43951)),f328(f328(f18(f876(x43951),a870,a870),f328(f328(f8(a870,f882(a870,a870),f876(x43951)),a326),f328(f328(f7(f876(x43951),a875,a870),f328(f328(f8(a875,f882(a875,a870),f876(x43951)),a325),f193(f876(x43951)))),x43952))),f328(f328(f7(f876(x43951),f882(x43951,a870),a870),f328(f328(f8(f882(x43951,a870),f882(f882(x43951,a870),a870),f876(x43951)),f242(f882(x43951,a870))),f170(x43951))),f328(f170(x43951),x43953)))),f328(f170(f876(x43951)),f54(x43951,x43952,x43953))) % 154.70/154.55 [3777]E(f44(a875,f328(f328(f80(a875),f328(f328(f81(a875),x37771),x37772)),x37773),x37772),f44(a875,x37773,x37772)) % 154.70/154.55 [3823]E(f136(a875,f328(f298(a875,f328(f328(f80(a875),x38231),x38232)),x38233)),f328(f328(f135(a875),x38232),f136(a875,f328(f298(a875,x38231),x38233)))) % 154.70/154.55 [3868]E(f328(f328(f80(a1),f328(f104(a1),x38681)),f328(f328(f80(a1),f328(f104(a1),x38682)),x38683)),f328(f328(f80(a1),f328(f104(a1),f328(f328(f80(a875),x38681),x38682))),x38683)) % 154.70/154.55 [3875]E(f328(f328(f114(f882(x38751,a870)),f328(f328(f22(f882(x38751,a870)),x38752),x38753)),x38753),f328(f328(f114(f882(x38751,a870)),x38752),x38753)) % 154.70/154.55 [3876]E(f328(f328(f22(f882(x38761,a870)),f328(f328(f22(f882(x38761,a870)),x38762),x38763)),x38763),f328(f328(f22(f882(x38761,a870)),x38762),x38763)) % 154.70/154.55 [3899]E(f328(f328(f285(x38991,x38991,x38992),f304(x38991,f192(f882(f881(x38991,x38991),a870)))),x38993),x38993) % 154.70/154.55 [3906]E(f328(f328(f114(f882(x39061,a870)),f328(f281(x39061),x39062)),f328(f281(x39061),x39063)),f328(f281(x39061),f328(f328(f114(f882(f881(x39061,x39061),a870)),x39062),x39063))) % 154.70/154.55 [3917]E(f272(x39171,f328(f328(f148(f881(a103,x39171)),f328(f328(f263(a103,x39171),f2(a103)),x39172)),x39173)),f272(x39171,x39173)) % 154.70/154.55 [3920]E(f328(f328(f114(f882(x39201,a870)),f39(f882(x39201,a870),x39202)),f39(f882(x39201,a870),x39203)),f39(f882(x39201,a870),f328(f328(f114(f882(f882(x39201,a870),a870)),x39202),x39203))) % 154.70/154.55 [3921]E(f328(f328(f105(f882(x39211,a870)),f40(f882(x39211,a870),x39212)),f40(f882(x39211,a870),x39213)),f40(f882(x39211,a870),f328(f328(f114(f882(f882(x39211,a870),a870)),x39212),x39213))) % 154.70/154.55 [3957]E(f328(f328(f285(x39571,x39571,x39571),f328(f328(f187(f881(x39571,x39571),a870),x39572),x39573)),x39573),f328(f328(f187(f881(x39571,x39571),a870),f328(a116,x39572)),x39573)) % 154.70/154.55 [4007]P1(f328(f328(f242(f882(x40071,a870)),f328(f328(f22(f882(x40071,a870)),x40072),x40073)),x40072)) % 154.70/154.55 [4008]P1(f328(f328(f242(f882(x40081,a870)),f328(f328(f105(f882(x40081,a870)),x40082),x40083)),x40083)) % 154.70/154.55 [4009]P1(f328(f328(f242(f882(x40091,a870)),f328(f328(f105(f882(x40091,a870)),x40092),x40093)),x40092)) % 154.70/154.55 [4034]E(f304(x40341,f328(f328(f114(f882(f881(x40341,x40341),a870)),f304(x40341,x40342)),f304(x40341,x40343))),f304(x40341,f328(f328(f114(f882(f881(x40341,x40341),a870)),x40342),x40343))) % 154.70/154.55 [4038]E(f39(f882(x40381,a870),f328(f328(f306(f882(x40381,a870)),x40382),f328(f328(f306(f882(x40381,a870)),x40383),f192(f882(f882(x40381,a870),a870))))),f328(f328(f114(f882(x40381,a870)),x40382),x40383)) % 154.70/154.55 [4039]E(f40(f882(x40391,a870),f328(f328(f306(f882(x40391,a870)),x40392),f328(f328(f306(f882(x40391,a870)),x40393),f192(f882(f882(x40391,a870),a870))))),f328(f328(f105(f882(x40391,a870)),x40392),x40393)) % 154.70/154.55 [4045]E(f328(f328(f285(x40451,x40451,x40451),f328(f328(f187(f881(x40451,x40451),a870),x40452),x40453)),x40453),f328(f328(f285(x40451,x40451,x40451),x40453),f328(f328(f187(f881(x40451,x40451),a870),x40452),x40453))) % 154.70/154.55 [4114]E(f328(f328(f114(f882(x41141,a870)),f328(f248(x41141),f328(f328(f7(x41141,x41141,a870),a325),x41142))),x41143),f328(f328(f306(x41141),x41142),x41143)) % 154.70/154.55 [4116]E(f328(a108,f328(f328(f6(x41161,a1),f328(f328(f8(a875,a1,x41161),f104(a1)),x41162)),x41163)),f328(f328(f6(x41161,a875),x41162),x41163)) % 154.70/154.55 [4117]E(f328(a108,f328(f328(f9(x41171,a1),f328(f328(f8(a875,a1,x41171),f104(a1)),x41172)),x41173)),f328(f328(f9(x41171,a875),x41172),x41173)) % 154.70/154.55 [4193]E(f328(f153(f876(x41931),x41931,f328(f169(x41931),x41932),f328(f16(f882(f876(x41931),f876(x41931)),x41931),f328(f328(f7(f876(x41931),f876(x41931),f876(x41931)),f125(x41931)),x41932))),x41933),f328(f169(x41931),f328(f328(f125(x41931),x41933),x41932))) % 154.70/154.55 [4224]P1(f328(f328(f242(f882(f882(x42241,a870),a870)),f328(f328(f114(f882(f882(x42241,a870),a870)),f328(f305(x42241),x42242)),f328(f305(x42241),x42243))),f328(f305(x42241),f328(f328(f114(f882(x42241,a870)),x42242),x42243)))) % 154.70/154.55 [4317]E(f328(f248(x43171),f328(f328(f18(x43171,a870,a870),f328(f328(f8(a870,f882(a870,a870),x43171),a326),f328(f328(f7(x43171,f882(x43171,a870),a870),f330(x43171)),x43172))),f328(f328(f8(a870,a870,x43171),a323),f328(f328(f7(x43171,f882(x43171,a870),a870),f330(x43171)),x43173)))),f328(f328(f22(f882(x43171,a870)),x43172),x43173)) % 154.70/154.55 [4339]E(f328(f37(a875),f328(f248(a875),f328(f328(f18(a875,a870,a870),f328(f328(f8(a870,f882(a870,a870),a875),a326),f328(f328(f7(a875,a875,a870),f243(a875)),f328(f193(f876(x43391)),x43392)))),f328(f328(f8(x43391,a870,a875),x43393),f328(f162(x43391),x43392))))),f328(f193(f876(x43391)),f328(f133(x43391,x43393),x43392))) % 154.70/154.55 [4341]E(f328(f193(f876(x43411)),f174(x43411,x43412,x43413)),f328(f37(a875),f328(f248(a875),f328(f328(f18(a875,a870,a870),f328(f328(f8(a870,f882(a870,a870),a875),a326),f328(f328(f7(a875,a875,a870),f243(a875)),f328(f193(f876(x43411)),x43412)))),f328(f328(f7(a875,f882(a875,a870),a870),f330(a875)),x43413))))) % 154.70/154.55 [4440]E(f328(f328(f105(f882(f881(f876(x44401),f876(x44401)),a870)),f328(f307(f881(f881(x44401,f876(x44401)),f881(x44401,f876(x44401))),f881(f876(x44401),f876(x44401)),f268(f881(x44401,f876(x44401)),f876(x44401),f881(x44401,f876(x44401)),f876(x44401),f328(f267(x44401,f876(x44401),f876(x44401)),f148(x44401)),f328(f267(x44401,f876(x44401),f876(x44401)),f148(x44401)))),f320(x44401,f876(x44401),x44402,f328(f140(x44401,x44402),x44403)))),f328(f248(f881(f876(x44401),f876(x44401))),f328(f267(f876(x44401),f876(x44401),a870),f328(f328(f7(f876(x44401),f882(f876(x44401),a870),f882(f876(x44401),a870)),f328(f328(f8(f882(a870,a870),f882(f882(f876(x44401),a870),f882(f876(x44401),a870)),f876(x44401)),f8(a870,a870,f876(x44401))),f328(f328(f8(a870,f882(a870,a870),f876(x44401)),a326),f328(f328(f7(f876(x44401),a875,a870),f328(f328(f8(a875,f882(a875,a870),f876(x44401)),a325),f193(f876(x44401)))),f328(a116,x44403))))),f328(f328(f7(f876(x44401),a875,a870),f328(f328(f8(a875,f882(a875,a870),f876(x44401)),a325),f193(f876(x44401)))),f328(a116,x44403)))))),f328(f140(x44401,x44402),f328(a116,x44403))) % 154.70/154.55 [3922]E(f44(a875,f328(a116,f328(f328(f80(a875),f328(f328(f81(a875),x39221),x39222)),x39223)),x39222),f44(a875,f328(a116,x39223),x39222)) % 154.70/154.55 [4182]E(f328(f248(x41821),f328(f328(f18(x41821,a870,a870),f328(f328(f8(a870,f882(a870,a870),x41821),a326),x41822)),x41823)),f328(f328(f105(f882(x41821,a870)),f328(f248(x41821),x41822)),f328(f248(x41821),x41823))) % 154.70/154.55 [4183]E(f328(f248(x41831),f328(f328(f18(x41831,a870,a870),f328(f328(f8(a870,f882(a870,a870),x41831),a327),x41832)),x41833)),f328(f328(f114(f882(x41831,a870)),f328(f248(x41831),x41832)),f328(f248(x41831),x41833))) % 154.70/154.55 [4185]E(f328(f328(f125(x41851),f328(f328(f135(x41851),f44(a875,x41852,f328(f193(f876(x41851)),x41853))),x41853)),f328(f328(f173(x41851),f44(a875,x41852,f328(f193(f876(x41851)),x41853))),x41853)),f328(f328(f328(f187(f876(x41851),f876(x41851)),x41852),f165(x41851)),x41853)) % 154.70/154.55 [4190]E(f328(f248(x41901),f328(f328(f18(x41901,a870,a870),f328(f328(f8(a870,f882(a870,a870),x41901),a331),x41902)),x41903)),f328(f328(f114(f882(x41901,a870)),f328(f79(f882(x41901,a870)),f328(f248(x41901),x41902))),f328(f248(x41901),x41903))) % 154.70/154.55 [4206]E(f328(f328(f80(a875),f328(f193(f876(x42061)),f328(f133(x42061,x42062),x42063))),f328(f193(f876(x42061)),f328(f133(x42061,f328(f328(f8(a870,a870,x42061),a323),x42062)),x42063))),f328(f193(f876(x42061)),x42063)) % 154.70/154.55 [4231]P1(f328(f328(f242(f882(x42311,a870)),f328(f328(f114(f882(x42311,a870)),f40(f882(x42311,a870),x42312)),f40(f882(x42311,a870),x42313))),f40(f882(x42311,a870),f328(f328(f105(f882(f882(x42311,a870),a870)),x42312),x42313)))) % 154.70/154.55 [4245]E(f328(f170(x42451),f328(f133(x42451,f328(f328(f8(a870,a870,x42451),a323),f328(f328(f7(x42451,x42451,a870),a325),x42452))),x42453)),f328(f328(f22(f882(x42451,a870)),f328(f170(x42451),x42453)),f328(f328(f306(x42451),x42452),f192(f882(x42451,a870))))) % 154.70/154.55 [4254]P1(f328(f328(f242(f882(f881(x42541,x42541),a870)),f328(f328(f114(f882(f881(x42541,x42541),a870)),f304(x42541,x42542)),f304(x42541,x42543))),f304(x42541,f328(f328(f114(f882(f881(x42541,x42541),a870)),x42542),x42543)))) % 154.70/154.55 [4279]E(f328(f328(f81(a875),f328(a116,f328(a116,f2(a875)))),f328(f328(f6(a875,a875),f328(f328(f8(a875,a875,a875),f328(f80(a875),x42791)),f328(f328(f7(a875,a875,a875),f81(a875)),x42792))),f328(f249(a875),x42793))),f328(f328(f81(a875),x42793),f328(f328(f80(a875),x42791),f328(f328(f80(a875),x42791),f328(f328(f81(a875),f328(f328(f22(a875),x42793),f78(a875))),x42792))))) % 154.70/154.55 [4289]E(f328(f248(x42891),f328(f328(f18(x42891,a870,a870),f328(f328(f8(a870,f882(a870,a870),x42891),a326),f328(f328(f7(x42891,f882(x42891,a870),a870),f330(x42891)),f328(f170(x42891),x42892)))),x42893)),f328(f170(x42891),f328(f133(x42891,x42893),x42892))) % 154.70/154.55 [4439]E(f328(f248(x44391),f328(f328(f8(f882(a875,a870),a870,x44391),f87(a875)),f328(f328(f7(x44391,f882(a875,a870),f882(a875,a870)),f328(f328(f8(f882(a875,f882(a870,a870)),f882(f882(a875,a870),f882(a875,a870)),x44391),f18(a875,a870,a870)),f328(f328(f8(f882(a875,a870),f882(a875,f882(a870,a870)),x44391),f328(f8(a870,f882(a870,a870),a875),a326)),f328(f328(f7(x44391,f882(a875,x44391),f882(a875,a870)),f328(f328(f8(f882(x44391,a870),f882(f882(a875,x44391),f882(a875,a870)),x44391),f8(x44391,a870,a875)),a325)),f328(f162(x44391),x44392))))),f328(f328(f18(a875,a870,a870),f328(f328(f8(a870,f882(a870,a870),a875),a326),f328(f328(f7(a875,a875,a870),f243(a875)),f328(f193(f876(x44391)),x44392)))),f328(f328(f7(a875,f882(a875,a870),a870),f330(a875)),x44393))))),f328(f170(x44391),f174(x44391,x44392,x44393))) % 154.70/154.55 [4329]E(f328(f248(x43291),f328(f328(f18(x43291,a870,a870),f328(f328(f8(a870,f882(a870,a870),x43291),a331),f328(f328(f8(a870,a870,x43291),a323),f328(f328(f7(x43291,x43291,a870),a325),x43292)))),x43293)),f328(f328(f306(x43291),x43292),f328(f248(x43291),x43293))) % 154.70/154.55 [4361]E(f328(f328(f151(f881(x43611,a875),x43611),f262(x43611,a875)),f328(f133(f881(x43611,a875),f328(f328(f7(f881(x43611,a875),f882(a875,a870),a870),f328(f328(f8(a875,f882(f882(a875,a870),a870),f881(x43611,a875)),f330(a875)),f266(x43611,a875))),x43612)),f328(f328(f180(x43611,a875),x43613),f136(a875,f328(f298(a875,f2(a875)),f328(f193(f876(x43611)),x43613)))))),f174(x43611,x43613,x43612)) % 154.70/154.55 [4391]E(f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(f328(f6(a875,a1),f328(f328(f8(a1,a1,a875),f328(f80(a1),x43911)),f328(f328(f7(a875,a1,a1),f328(f328(f8(a1,f882(a1,a1),a875),f81(a1)),f104(a1))),x43912))),f328(f249(a875),x43913))),f328(f328(f81(a1),f328(f104(a1),x43913)),f328(f328(f80(a1),x43911),f328(f328(f80(a1),x43911),f328(f328(f81(a1),f328(f104(a1),f328(f328(f22(a875),x43913),f78(a875)))),x43912))))) % 154.70/154.55 [4433]E(f328(f248(f881(x44331,x44332)),f328(f267(x44331,x44332,a870),f328(f328(f7(x44331,f882(f881(x44332,x44331),a870),f882(x44332,a870)),f328(f328(f8(f882(x44332,f882(f882(f881(x44332,x44331),a870),a870)),f882(f882(f881(x44332,x44331),a870),f882(x44332,a870)),x44331),f7(x44332,f882(f881(x44332,x44331),a870),a870)),f328(f328(f8(f882(x44332,f881(x44332,x44331)),f882(x44332,f882(f882(f881(x44332,x44331),a870),a870)),x44331),f328(f8(f881(x44332,x44331),f882(f882(f881(x44332,x44331),a870),a870),x44332),f330(f881(x44332,x44331)))),f328(f7(x44332,x44331,f881(x44332,x44331)),f263(x44332,x44331))))),x44333))),f328(f283(x44332,x44331),x44333)) % 154.70/154.55 [4455]E(f328(f248(f876(x44551)),f328(f328(f8(f882(x44551,a870),a870,f876(x44551)),f87(x44551)),f328(f328(f8(f882(x44551,f882(f876(x44551),a870)),f882(x44551,a870),f876(x44551)),f328(f8(f882(f876(x44551),a870),a870,x44551),f87(f876(x44551)))),f328(f328(f7(f876(x44551),f882(x44551,f882(f876(x44551),a870)),f882(x44551,f882(f876(x44551),a870))),f328(f328(f8(f882(x44551,f882(f882(f876(x44551),a870),f882(f876(x44551),a870))),f882(f882(x44551,f882(f876(x44551),a870)),f882(x44551,f882(f876(x44551),a870))),f876(x44551)),f18(x44551,f882(f876(x44551),a870),f882(f876(x44551),a870))),f328(f328(f8(f882(x44551,f882(f876(x44551),f882(a870,a870))),f882(x44551,f882(f882(f876(x44551),a870),f882(f876(x44551),a870))),f876(x44551)),f328(f8(f882(f876(x44551),f882(a870,a870)),f882(f882(f876(x44551),a870),f882(f876(x44551),a870)),x44551),f18(f876(x44551),a870,a870))),f328(f328(f8(f882(x44551,f882(f876(x44551),a870)),f882(x44551,f882(f876(x44551),f882(a870,a870))),f876(x44551)),f328(f8(f882(f876(x44551),a870),f882(f876(x44551),f882(a870,a870)),x44551),f328(f8(a870,f882(a870,a870),f876(x44551)),a326))),f328(f328(f7(f876(x44551),f882(x44551,f882(f876(x44551),f876(x44551))),f882(x44551,f882(f876(x44551),a870))),f328(f328(f8(f882(f882(f876(x44551),f876(x44551)),f882(f876(x44551),a870)),f882(f882(x44551,f882(f876(x44551),f876(x44551))),f882(x44551,f882(f876(x44551),a870))),f876(x44551)),f8(f882(f876(x44551),f876(x44551)),f882(f876(x44551),a870),x44551)),f328(f328(f8(f882(f876(x44551),a870),f882(f882(f876(x44551),f876(x44551)),f882(f876(x44551),a870)),f876(x44551)),f8(f876(x44551),a870,f876(x44551))),a325))),f148(x44551)))))),f328(f328(f7(x44551,f882(f876(x44551),a870),f882(f876(x44551),a870)),f328(f328(f8(f882(a870,a870),f882(f882(f876(x44551),a870),f882(f876(x44551),a870)),x44551),f8(a870,a870,f876(x44551))),f328(f328(f8(a870,f882(a870,a870),x44551),a326),f328(f328(f7(x44551,f882(x44551,a870),a870),f330(x44551)),x44552)))),f328(f328(f7(f876(x44551),f882(f876(x44551),a870),a870),f330(f876(x44551))),x44553)))))),f172(x44551,x44552,x44553)) % 154.70/154.55 [4452]E(f328(f328(f86(a1,f881(a1,a1)),f328(f328(f22(a1),x44521),x44522)),f328(f328(f7(a1,f881(a1,a1),f881(a1,a1)),f328(f328(f18(a1,f881(a1,a1),f882(f881(a1,a1),f881(a1,a1))),f328(f328(f8(a870,f882(f881(a1,a1),f882(f881(a1,a1),f881(a1,a1))),a1),f100(f881(a1,a1))),f328(f242(a1),f2(a1)))),f328(f263(a1,a1),f328(f328(f80(a1),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x44523)),f78(a1))))),f328(f328(f263(a1,a1),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x44523)),x44521))),f328(f43(x44522),f328(f328(f263(a1,a1),x44523),x44521))) % 154.70/154.55 [4483]~E(f32(x44831,x44832),f33(x44833,x44834)) % 154.70/154.55 [4500]~E(f328(a26,x45001),f30(x45002,x45003,x45004)) % 154.70/154.55 [4501]~E(f328(a26,x45011),f29(x45012,x45013,x45014)) % 154.70/154.55 [4502]~E(f30(x45021,x45022,x45023),f328(a26,x45024)) % 154.70/154.55 [4503]~E(f29(x45031,x45032,x45033),f328(a26,x45034)) % 154.70/154.55 [3471]E(f328(f328(f328(f72(x34711,x34712),x34713),x34714),f328(x34713,x34714)),x34713) % 154.70/154.55 [3531]E(f328(f328(f254(x35311,x35312,x35313),x35314),f2(a875)),x35312) % 154.70/154.55 [3570]E(f189(x35701,x35702,x35703,f328(a116,x35704)),f328(x35703,x35704)) % 154.70/154.55 [3611]E(f167(x36111,x36112,f167(x36111,x36113,x36114)),f167(x36111,x36113,f167(x36111,x36112,x36114))) % 154.70/154.55 [3746]E(f328(f153(x37461,x37462,x37463,x37464),f117(x37462)),x37463) % 154.70/154.55 [3747]E(f328(f237(x37471,x37472,x37473,x37474),f205(x37472)),x37473) % 154.70/154.55 [3748]E(f328(f139(x37481,x37482,x37483,x37484),f117(x37482)),x37484) % 154.70/154.55 [3852]E(f328(f328(f125(x38521),f168(x38521,x38522,x38523)),f168(x38521,x38524,x38523)),f328(f328(f125(x38521),f168(x38521,x38524,x38523)),f168(x38521,x38522,x38523))) % 154.70/154.55 [3865]E(f328(f237(f879(x38651),x38652,f205(x38651),f328(f16(f879(x38651),x38652),f205(x38651))),f328(x38653,x38654)),f205(x38651)) % 154.70/154.55 [3910]E(f328(f328(f114(f882(x39101,a870)),f182(x39101,x39102,x39103)),f182(x39101,x39102,x39104)),f182(x39101,x39102,f183(x39101,x39102,x39104,x39103))) % 154.70/154.55 [3942]E(f328(f328(f269(x39421,x39422,x39423,f881(x39422,x39423)),x39424),f263(x39422,x39423)),x39424) % 154.70/154.55 [3951]E(f185(x39511,x39512,x39513,x39514,f117(x39512)),x39513) % 154.70/154.55 [3952]E(f238(x39521,x39522,x39523,x39524,f205(x39522)),x39523) % 154.70/154.55 [3953]E(f185(x39531,x39532,x39533,f117(x39531),x39534),x39533) % 154.70/154.55 [4238]P44(x42381,x42382,x42383,x42384,f192(f882(x42381,a870)),x42384) % 154.70/154.55 [3273]E(f328(f328(f16(x32731,x32732),x32733),x32734),x32733) % 154.70/154.55 [3388]E(f328(f328(f206(x33881,x33882),x33883),f328(f235(x33881),x33884)),f328(f235(x33882),f328(x33883,x33884))) % 154.70/154.55 [3561]E(f167(x35611,x35612,f328(f133(x35611,x35613),x35614)),f328(f133(x35611,x35613),f167(x35611,x35612,x35614))) % 154.70/154.55 [3595]E(f328(f328(f64(x35951,x35952,x35953),x35954),f192(f882(x35951,a870))),x35954) % 154.70/154.55 [3617]E(f328(f328(f162(x36171),f328(f328(f148(x36171),x36172),x36173)),f328(a116,x36174)),f328(f328(f162(x36171),x36173),x36174)) % 154.70/154.55 [3661]P29(x36611,f2(a875),f328(f328(f328(f92(x36611),x36612),f328(a26,x36613)),x36614)) % 154.70/154.55 [3686]E(f328(f328(x36861,x36862),f328(f188(x36863,x36864,x36861),x36862)),f328(f188(x36863,x36864,x36861),f328(a116,x36862))) % 154.70/154.55 [3782]E(f328(f328(f156(x37821,f328(f328(f148(x37821),x37822),x37823)),f2(a875)),x37824),f328(f328(f148(x37821),x37824),x37823)) % 154.70/154.55 [3793]E(f328(f328(f41(f882(x37931,a870),f882(x37932,a870)),x37933),f307(x37931,x37932,x37934)),f328(f307(x37931,x37932,x37934),f39(f882(x37931,a870),x37933))) % 154.70/154.55 [3794]E(f328(f328(f41(f882(x37941,a870),f882(x37942,a870)),x37943),f308(x37942,x37941,x37944)),f328(f308(x37942,x37941,x37944),f39(f882(x37941,a870),x37943))) % 154.70/154.55 [3892]E(f182(x38921,x38922,f186(x38921,x38922,x38923,x38924)),f328(f328(f105(f882(x38921,a870)),f182(x38921,x38922,x38923)),x38924)) % 154.70/154.55 [3896]E(f328(f129(x38961,x38962),f127(x38961,x38963,x38964)),f328(f328(f80(a875),f328(f328(f80(a875),f328(x38962,x38963)),f328(f129(x38961,x38962),x38964))),f328(a116,f2(a875)))) % 154.70/154.55 [3916]E(f328(f139(x39161,x39162,f328(f7(x39162,x39161,x39161),x39163),x39164),f328(f166(x39162),f117(x39162))),x39164) % 154.70/154.55 [3964]E(f76(x39641,x39642,x39643,x39644,f192(f882(x39641,a870))),x39643) % 154.70/154.55 [4010]E(f328(f328(f328(f328(f72(x40101,f879(x40102)),f328(f16(f879(x40102),x40101),f205(x40102))),x40103),f205(x40102)),x40104),f205(x40102)) % 154.70/154.55 [4165]E(f328(f267(x41651,x41652,x41653),f328(f328(f8(f882(x41652,f881(x41651,x41652)),f882(x41652,x41653),x41651),f328(f8(f881(x41651,x41652),x41653,x41652),x41654)),f263(x41651,x41652))),x41654) % 154.70/154.55 [3469]E(f328(f266(x34691,x34692),f328(f328(f263(x34691,x34692),x34693),x34694)),x34694) % 154.70/154.55 [3470]E(f328(f262(x34701,x34702),f328(f328(f263(x34701,x34702),x34703),x34704)),x34703) % 154.70/154.55 [3504]E(f328(f193(f876(x35041)),f328(f328(f156(x35041,x35042),x35043),x35044)),f328(f193(f876(x35041)),x35042)) % 154.70/154.55 [3505]E(f328(f193(f876(x35051)),f328(f328(f151(x35052,x35051),x35053),x35054)),f328(f193(f876(x35052)),x35054)) % 154.70/154.55 [3525]E(f328(f328(f135(x35251),f328(a116,x35252)),f328(f328(f148(x35251),x35253),x35254)),f328(f328(f135(x35251),x35252),x35254)) % 154.70/154.55 [3590]E(f328(f328(f173(x35901),x35902),f168(x35901,x35903,x35904)),f168(x35901,f328(f328(f240(a875),x35902),x35903),x35904)) % 154.70/154.55 [3591]E(f328(f328(f135(x35911),x35912),f168(x35911,x35913,x35914)),f168(x35911,f328(f328(f22(a875),x35913),x35912),x35914)) % 154.70/154.55 [3597]E(f328(f328(f306(x35971),x35972),f328(f328(f306(x35971),x35973),x35974)),f328(f328(f306(x35971),x35973),f328(f328(f306(x35971),x35972),x35974))) % 154.70/154.55 [3600]E(f328(f328(f151(x36001,x36002),x36003),f118(x36001,x36004)),f118(x36002,f328(f328(f151(x36001,x36002),x36003),x36004))) % 154.70/154.55 [3615]E(f328(f166(x36151),f328(f328(f151(x36152,x36151),x36153),x36154)),f328(f328(f151(x36152,x36151),x36153),f328(f166(x36152),x36154))) % 154.70/154.55 [3616]E(f328(f328(f151(x36161,x36162),x36163),f328(f169(x36161),x36164)),f328(f169(x36162),f328(f328(f151(x36161,x36162),x36163),x36164))) % 154.70/154.55 [3629]E(f328(f328(f173(x36291),f328(a116,x36292)),f328(f328(f148(x36291),x36293),x36294)),f328(f328(f148(x36291),x36293),f328(f328(f173(x36291),x36292),x36294))) % 154.70/154.55 [3633]E(f328(f170(x36331),f328(f328(f151(x36332,x36331),x36333),x36334)),f328(f307(x36332,x36331,x36333),f328(f170(x36332),x36334))) % 154.70/154.55 [3685]E(f17(x36851,x36852,x36853,f328(a3,f328(a116,f328(a19,x36854)))),f328(x36853,x36854)) % 154.70/154.55 [3688]E(f328(f328(f125(x36881),f328(f133(x36881,x36882),x36883)),f328(f133(x36881,x36882),x36884)),f328(f133(x36881,x36882),f328(f328(f125(x36881),x36883),x36884))) % 154.70/154.55 [3701]E(f149(x37011,f328(f328(f151(x37012,x37011),x37013),f149(x37012,x37014))),f149(x37011,f328(f328(f151(x37012,x37011),x37013),x37014))) % 154.70/154.55 [3717]E(f328(f283(x37171,x37171),f328(f328(f284(x37172,x37171),x37173),x37174)),f328(f328(f284(x37172,x37171),f328(f283(x37172,x37172),x37173)),x37174)) % 154.70/154.55 [3727]E(f328(f328(f285(x37271,x37272,x37273),x37274),f192(f882(f881(x37272,x37273),a870))),f192(f882(f881(x37271,x37273),a870))) % 154.70/154.55 [3728]E(f328(f328(f173(x37281),f328(f328(f22(a875),x37282),x37283)),f328(f328(f135(x37281),x37283),x37284)),f328(f328(f135(x37281),x37283),f328(f328(f173(x37281),x37282),x37284))) % 154.70/154.55 [3749]E(f328(f328(f125(x37491),f168(x37491,x37492,x37493)),f168(x37491,x37494,x37493)),f168(x37491,f328(f328(f80(a875),x37492),x37494),x37493)) % 154.70/154.55 [3774]E(f39(f882(x37741,a870),f328(f307(x37742,f882(x37741,a870),x37743),x37744)),f328(f328(f41(x37742,f882(x37741,a870)),x37744),x37743)) % 154.70/154.55 [3775]E(f40(f882(x37751,a870),f328(f307(x37752,f882(x37751,a870),x37753),x37754)),f328(f328(f42(x37752,f882(x37751,a870)),x37754),x37753)) % 154.70/154.55 [3776]E(f328(f193(f876(f881(x37761,x37762))),f328(f328(f180(x37761,x37762),x37763),x37764)),f328(f328(f240(a875),f328(f193(f876(x37761)),x37763)),f328(f193(f876(x37762)),x37764))) % 154.70/154.55 [3778]E(f328(f308(x37781,x37782,x37783),f328(f79(f882(x37782,a870)),x37784)),f328(f79(f882(x37781,a870)),f328(f308(x37781,x37782,x37783),x37784))) % 154.70/154.55 [3808]E(f328(f186(x38081,x38082,x38083,f192(f882(x38081,a870))),x38084),f205(x38082)) % 154.70/154.55 [3829]E(f328(f308(x38291,x38292,x38293),f328(f248(x38292),x38294)),f328(f248(x38291),f328(f328(f8(x38292,a870,x38291),x38294),x38293))) % 154.70/154.55 [3846]E(f328(f328(f162(x38461),f328(f328(f125(x38461),x38462),f328(f328(f148(x38461),x38463),x38464))),f328(f193(f876(x38461)),x38462)),x38463) % 154.70/154.55 [3851]E(f328(f186(x38511,x38512,f328(f16(f879(x38512),x38511),f205(x38512)),x38513),x38514),f205(x38512)) % 154.70/154.55 [3873]E(f328(f307(x38731,x38732,x38733),f328(f308(x38731,x38732,x38733),x38734)),f328(f328(f105(f882(x38732,a870)),x38734),f328(f307(x38731,x38732,x38733),f251(f882(x38731,a870))))) % 154.70/154.55 [3891]P1(f328(f328(f330(x38911),f328(x38912,x38913)),f328(f307(x38914,x38911,x38912),f251(f882(x38914,a870))))) % 154.70/154.55 [3903]E(f328(f328(f125(x39031),f168(x39031,x39032,x39033)),f328(f328(f148(x39031),x39033),x39034)),f328(f328(f148(x39031),x39033),f328(f328(f125(x39031),f168(x39031,x39032,x39033)),x39034))) % 154.70/154.55 [3905]E(f328(f328(f265(x39051,x39052),f328(f170(x39051),x39053)),f328(f16(f882(x39052,a870),x39051),f328(f170(x39052),x39054))),f328(f170(f881(x39051,x39052)),f59(x39051,x39052,x39053,x39054))) % 154.70/154.55 [3919]E(f152(x39191,x39192,f328(f328(f148(x39191),x39193),x39194)),f328(f328(f80(a875),f328(f328(f80(a875),f328(x39192,x39193)),f152(x39191,x39192,x39194))),f328(a116,f2(a875)))) % 154.70/154.55 [3933]E(f189(f876(x39331),f328(f328(f148(x39331),x39332),x39333),f328(f328(f7(a875,f876(x39331),f876(x39331)),f135(x39331)),x39333),x39334),f328(f328(f135(x39331),x39334),f328(f328(f148(x39331),x39332),x39333))) % 154.70/154.55 [3934]P27(x39341,f881(x39342,x39341),f332(x39343,x39344,x39342,x39341),f328(f328(f41(x39342,f882(x39341,a870)),x39344),x39343)) % 154.70/154.55 [3943]E(f328(f328(f22(f882(x39431,a870)),f328(f328(f22(f882(x39431,a870)),x39432),x39433)),f328(f328(f306(x39431),x39434),f192(f882(x39431,a870)))),f328(f328(f22(f882(x39431,a870)),x39432),f328(f328(f306(x39431),x39434),x39433))) % 154.70/154.55 [3955]E(f328(f328(f187(f882(x39551,x39552),f882(x39551,x39552)),x39553),f73(x39552,x39552,x39551,x39554)),f73(x39552,x39552,x39551,f328(f328(f187(x39552,x39552),x39553),x39554))) % 154.70/154.55 [4033]E(f328(f328(f328(f187(f876(x40331),f876(x40331)),x40332),f165(x40331)),f328(f328(f328(f187(f876(x40331),f876(x40331)),x40333),f165(x40331)),x40334)),f328(f328(f328(f187(f876(x40331),f876(x40331)),f328(f328(f80(a875),x40332),x40333)),f165(x40331)),x40334)) % 154.70/154.55 [4119]P1(f328(f328(f242(f882(x41191,a870)),f328(f170(x41191),f328(f328(f156(x41191,x41192),x41193),x41194))),f328(f328(f306(x41191),x41194),f328(f170(x41191),x41192)))) % 154.70/154.55 [4155]E(f328(f328(f41(f882(x41551,a870),f882(f881(x41551,x41552),a870)),x41553),f328(f328(f7(f882(x41551,a870),f882(x41551,f882(x41552,a870)),f882(f881(x41551,x41552),a870)),f265(x41551,x41552)),x41554)),f328(f328(f265(x41551,x41552),f39(f882(x41551,a870),x41553)),x41554)) % 154.70/154.55 [4192]E(f216(x41921,x41922,x41923,f328(f73(x41922,f882(a103,f882(a103,f882(f881(a103,a103),f882(a103,f877(x41922))))),x41921,f215(x41922)),x41924)),f217(x41921,x41922,x41924,x41923)) % 154.70/154.55 [4209]E(f212(x42091,x42092,x42093,f328(f73(x42092,f882(a103,f882(a103,f882(f881(a103,a103),f882(a103,f877(f879(x42092)))))),x42091,f211(x42092)),x42094)),f213(x42091,x42092,x42094,x42093)) % 154.70/154.55 [4214]P1(f328(f66(x42141,x42142,x42143,x42144,f192(f882(x42141,a870))),x42144)) % 154.70/154.55 [4256]E(f328(f328(f41(x42561,f882(x42562,a870)),x42563),f328(f328(f7(x42561,f882(x42562,a870),f882(x42562,a870)),f328(f328(f8(x42562,f882(f882(x42562,a870),f882(x42562,a870)),x42561),f306(x42562)),x42564)),f192(f882(x42562,a870)))),f328(f307(x42561,x42562,x42564),x42563)) % 154.70/154.55 [4263]P1(f328(f328(f242(f882(x42631,a870)),f328(f259(x42632,x42631),f328(f328(f105(f882(f881(x42632,x42631),a870)),x42633),x42634))),f328(f328(f105(f882(x42631,a870)),f328(f259(x42632,x42631),x42633)),f328(f259(x42632,x42631),x42634)))) % 154.70/154.55 [4264]P1(f328(f328(f242(f882(x42641,a870)),f328(f261(x42641,x42642),f328(f328(f105(f882(f881(x42641,x42642),a870)),x42643),x42644))),f328(f328(f105(f882(x42641,a870)),f328(f261(x42641,x42642),x42643)),f328(f261(x42641,x42642),x42644)))) % 154.70/154.55 [4326]P1(f328(f328(f242(f882(f881(x43261,x43262),a870)),f328(f307(x43262,f881(x43261,x43262),f332(x43263,x43264,x43261,x43262)),f328(f328(f41(x43261,f882(x43262,a870)),x43264),x43263))),f328(f328(f265(x43261,x43262),x43264),x43263))) % 154.70/154.55 [4327]E(f328(f120(x43271,f881(x43271,x43272),x43273),f328(f328(f8(f882(x43272,f877(f881(x43271,x43272))),f877(f881(x43271,x43272)),x43271),f120(x43272,f881(x43271,x43272),x43274)),f328(f328(f8(f882(x43272,f881(x43271,x43272)),f882(x43272,f877(f881(x43271,x43272))),x43271),f328(f8(f881(x43271,x43272),f877(f881(x43271,x43272)),x43272),f126(f881(x43271,x43272)))),f263(x43271,x43272)))),f131(x43271,x43272,x43273,x43274)) % 154.70/154.55 [4367]E(f85(f881(x43671,x43672),f328(f267(x43671,x43672,a870),f328(f328(f7(x43671,f882(x43672,a870),f882(x43672,a870)),f328(f328(f8(f882(a870,a870),f882(f882(x43672,a870),f882(x43672,a870)),x43671),f8(a870,a870,x43672)),f328(f328(f8(a870,f882(a870,a870),x43671),a326),f328(a325,x43673)))),f328(a325,x43674)))),f328(f328(f263(x43671,x43672),x43673),x43674)) % 154.70/154.55 [4368]E(f90(f881(x43681,x43682),f328(f267(x43681,x43682,a870),f328(f328(f7(x43681,f882(x43682,a870),f882(x43682,a870)),f328(f328(f8(f882(a870,a870),f882(f882(x43682,a870),f882(x43682,a870)),x43681),f8(a870,a870,x43682)),f328(f328(f8(a870,f882(a870,a870),x43681),a326),f328(a325,x43683)))),f328(a325,x43684)))),f328(f328(f263(x43681,x43682),x43683),x43684)) % 154.70/154.55 [4441]E(f328(f328(f267(f876(x44411),f876(x44411),f881(f876(x44411),f876(x44411))),f328(f328(f18(f876(x44411),f882(f876(x44411),f881(f876(x44411),f876(x44411))),f882(f876(x44411),f881(f876(x44411),f876(x44411)))),f328(f328(f8(f882(f876(x44411),f882(f881(f876(x44411),f876(x44411)),f881(f876(x44411),f876(x44411)))),f882(f882(f876(x44411),f881(f876(x44411),f876(x44411))),f882(f876(x44411),f881(f876(x44411),f876(x44411)))),f876(x44411)),f18(f876(x44411),f881(f876(x44411),f876(x44411)),f881(f876(x44411),f876(x44411)))),f328(f328(f8(f882(f876(x44411),f881(f876(x44411),f876(x44411))),f882(f876(x44411),f882(f881(f876(x44411),f876(x44411)),f881(f876(x44411),f876(x44411)))),f876(x44411)),f328(f8(f881(f876(x44411),f876(x44411)),f882(f881(f876(x44411),f876(x44411)),f881(f876(x44411),f876(x44411))),f876(x44411)),f328(f100(f881(f876(x44411),f876(x44411))),f328(x44412,x44413)))),f328(f328(f8(f876(x44411),f882(f876(x44411),f881(f876(x44411),f876(x44411))),f876(x44411)),f263(f876(x44411),f876(x44411))),f328(f148(x44411),x44413))))),f328(f328(f7(f876(x44411),f882(f876(x44411),f876(x44411)),f882(f876(x44411),f881(f876(x44411),f876(x44411)))),f328(f328(f8(f882(f876(x44411),f881(f876(x44411),f876(x44411))),f882(f882(f876(x44411),f876(x44411)),f882(f876(x44411),f881(f876(x44411),f876(x44411)))),f876(x44411)),f8(f876(x44411),f881(f876(x44411),f876(x44411)),f876(x44411))),f263(f876(x44411),f876(x44411)))),f328(f148(x44411),x44413)))),f164(x44411,x44412,x44414)),f164(x44411,x44412,f328(f328(f148(x44411),x44413),x44414))) % 154.70/154.55 [4447]E(f328(f139(f882(x44471,f879(x44472)),f881(x44471,x44472),f328(f7(f881(x44471,x44472),f882(x44471,f879(x44472)),f882(x44471,f879(x44472))),f328(f267(x44471,x44472,f882(f882(x44471,f879(x44472)),f882(x44471,f879(x44472)))),f328(f328(f7(x44471,f882(x44472,f879(x44472)),f882(x44472,f882(f882(x44471,f879(x44472)),f882(x44471,f879(x44472))))),f328(f328(f8(f882(f879(x44472),f882(f882(x44471,f879(x44472)),f882(x44471,f879(x44472)))),f882(f882(x44472,f879(x44472)),f882(x44472,f882(f882(x44471,f879(x44472)),f882(x44471,f879(x44472))))),x44471),f8(f879(x44472),f882(f882(x44471,f879(x44472)),f882(x44471,f879(x44472))),x44472)),f328(f328(f8(f882(f882(x44471,f879(x44472)),f882(f879(x44472),f882(x44471,f879(x44472)))),f882(f879(x44472),f882(f882(x44471,f879(x44472)),f882(x44471,f879(x44472)))),x44471),f7(f882(x44471,f879(x44472)),f879(x44472),f882(x44471,f879(x44472)))),f328(f7(f882(x44471,f879(x44472)),x44471,f882(f879(x44472),f882(x44471,f879(x44472)))),f72(x44471,f879(x44472)))))),f235(x44472)))),x44473),f328(f166(f881(x44471,x44472)),x44474)),f183(x44471,x44472,x44473,f328(f176(x44471,x44472),x44474))) % 154.70/154.55 [3544]E(f328(f193(f874(x35441)),f328(f328(f328(f92(x35441),x35442),x35443),x35444)),f2(a875)) % 154.70/154.55 [3664]E(f328(f328(f173(x36641),x36642),f328(f328(f173(x36641),x36643),x36644)),f328(f328(f173(x36641),f328(f328(f240(a875),x36642),x36643)),x36644)) % 154.70/154.55 [3665]E(f328(f328(f135(x36651),x36652),f328(f328(f135(x36651),x36653),x36654)),f328(f328(f135(x36651),f328(f328(f80(a875),x36652),x36653)),x36654)) % 154.70/154.55 [3677]E(f328(f328(f125(x36771),f328(f328(f148(x36771),x36772),x36773)),x36774),f328(f328(f148(x36771),x36772),f328(f328(f125(x36771),x36773),x36774))) % 154.70/154.55 [3678]E(f328(f328(f125(x36781),f328(f328(f125(x36781),x36782),x36783)),x36784),f328(f328(f125(x36781),x36782),f328(f328(f125(x36781),x36783),x36784))) % 154.70/154.55 [3758]E(f328(f328(f162(x37581),f328(f328(f148(x37581),x37582),x37583)),x37584),f189(x37581,x37582,f328(f162(x37581),x37583),x37584)) % 154.70/154.55 [3767]E(f328(f328(f187(x37671,x37671),x37672),f328(f328(f187(x37671,x37671),x37673),x37674)),f328(f328(f187(x37671,x37671),f328(f328(f81(a875),x37673),x37672)),x37674)) % 154.70/154.55 [3796]E(f328(f328(f114(f882(x37961,a870)),x37962),f328(f328(f306(x37961),x37963),x37964)),f328(f328(f306(x37961),x37963),f328(f328(f114(f882(x37961,a870)),x37962),x37964))) % 154.70/154.55 [3811]E(f328(f328(f328(f187(x38111,x38111),x38112),x38113),f328(x38113,x38114)),f328(x38113,f328(f328(f328(f187(x38111,x38111),x38112),x38113),x38114))) % 154.70/154.55 [3819]E(f328(f328(f285(x38191,x38192,x38193),f192(f882(f881(x38191,x38192),a870))),x38194),f192(f882(f881(x38191,x38193),a870))) % 154.70/154.55 [3835]E(f328(f328(f114(f882(x38351,a870)),f328(f328(f306(x38351),x38352),x38353)),x38354),f328(f328(f306(x38351),x38352),f328(f328(f114(f882(x38351,a870)),x38353),x38354))) % 154.70/154.55 [3854]E(f183(x38541,x38542,f328(f176(x38541,x38542),x38543),f328(f176(x38541,x38542),x38544)),f328(f176(x38541,x38542),f328(f328(f125(f881(x38541,x38542)),x38544),x38543))) % 154.70/154.55 [3855]E(f328(f37(f881(x38551,x38552)),f328(f328(f265(x38551,x38552),x38553),f328(f16(f882(x38552,a870),x38551),x38554))),f328(f328(f81(a875),f328(f37(x38551),x38553)),f328(f37(x38552),x38554))) % 154.70/154.55 [3862]E(f328(f328(f105(f882(x38621,a870)),f328(f328(f306(x38621),x38622),x38623)),f328(f328(f306(x38621),x38622),x38624)),f328(f328(f306(x38621),x38622),f328(f328(f105(f882(x38621,a870)),x38623),x38624))) % 154.70/154.55 [3877]E(f328(f328(f114(f882(x38771,a870)),x38772),f328(f328(f114(f882(x38771,a870)),x38773),x38774)),f328(f328(f114(f882(x38771,a870)),x38773),f328(f328(f114(f882(x38771,a870)),x38772),x38774))) % 154.70/154.55 [3878]E(f328(f328(f105(f882(x38781,a870)),x38782),f328(f328(f105(f882(x38781,a870)),x38783),x38784)),f328(f328(f105(f882(x38781,a870)),x38783),f328(f328(f105(f882(x38781,a870)),x38782),x38784))) % 154.70/154.55 [3887]E(f64(x38871,x38872,f328(f328(f8(x38872,f882(x38872,x38872),x38871),x38873),x38874)),f328(f65(x38872,x38871,x38873),x38874)) % 154.70/154.55 [3897]E(f178(x38971,f328(f328(f151(f876(x38972),f876(x38971)),f328(f151(x38972,x38971),x38973)),x38974)),f328(f328(f151(f876(x38972),f876(x38971)),f328(f151(x38972,x38971),x38973)),f178(x38972,x38974))) % 154.70/154.55 [3915]E(f328(f139(f876(x39151),f876(x39151),f125(x39151),f117(x39151)),f328(f328(f151(x39152,f876(x39151)),x39153),x39154)),f161(x39152,x39151,x39153,x39154)) % 154.70/154.55 [3918]E(f186(x39181,x39182,x39183,f328(f79(f882(x39181,a870)),f328(f328(f306(x39181),x39184),f192(f882(x39181,a870))))),f328(f328(f328(f72(x39181,f879(x39182)),x39183),x39184),f205(x39182))) % 154.70/154.55 [3960]E(f328(f328(f328(f72(x39601,f879(x39602)),f328(f176(x39601,x39602),x39603)),f328(f262(x39601,x39602),x39604)),f328(f235(x39602),f328(f266(x39601,x39602),x39604))),f328(f176(x39601,x39602),f328(f328(f148(f881(x39601,x39602)),x39604),x39603))) % 154.70/154.55 [3977]E(f328(f73(x39771,x39771,x39771,f328(f328(f187(x39771,x39771),x39772),x39773)),f328(f328(f187(x39771,x39771),x39774),x39773)),f328(f328(f187(x39771,x39771),f328(f328(f80(a875),x39772),x39774)),x39773)) % 154.70/154.55 [4002]E(f328(f328(f105(f882(x40021,a870)),f328(f328(f114(f882(x40021,a870)),x40022),x40023)),f328(f328(f114(f882(x40021,a870)),x40022),x40024)),f328(f328(f114(f882(x40021,a870)),x40022),f328(f328(f105(f882(x40021,a870)),x40023),x40024))) % 154.70/154.55 [4003]E(f328(f328(f105(f882(x40031,a870)),f328(f328(f22(f882(x40031,a870)),x40032),x40033)),f328(f328(f22(f882(x40031,a870)),x40032),x40034)),f328(f328(f22(f882(x40031,a870)),x40032),f328(f328(f114(f882(x40031,a870)),x40033),x40034))) % 154.70/154.55 [4004]E(f328(f328(f114(f882(x40041,a870)),f328(f328(f22(f882(x40041,a870)),x40042),x40043)),f328(f328(f22(f882(x40041,a870)),x40042),x40044)),f328(f328(f22(f882(x40041,a870)),x40042),f328(f328(f105(f882(x40041,a870)),x40043),x40044))) % 154.70/154.55 [4005]E(f328(f328(f114(f882(x40051,a870)),f328(f328(f105(f882(x40051,a870)),x40052),x40053)),f328(f328(f105(f882(x40051,a870)),x40052),x40054)),f328(f328(f105(f882(x40051,a870)),x40052),f328(f328(f114(f882(x40051,a870)),x40053),x40054))) % 154.70/154.55 [4006]E(f328(f328(f22(f882(x40061,a870)),f328(f328(f105(f882(x40061,a870)),x40062),x40063)),f328(f328(f105(f882(x40061,a870)),x40062),x40064)),f328(f328(f105(f882(x40061,a870)),x40062),f328(f328(f22(f882(x40061,a870)),x40063),x40064))) % 154.70/154.55 [4012]E(f328(f37(f881(x40121,x40122)),f328(f328(f265(x40121,x40122),f328(f328(f306(x40121),x40123),f192(f882(x40121,a870)))),f328(f16(f882(x40122,a870),x40121),x40124))),f328(f37(x40122),x40124)) % 154.70/154.55 [4048]E(f328(f328(f42(x40481,f882(x40482,a870)),x40483),f328(f328(f8(f882(x40482,a870),f882(x40482,a870),x40481),f79(f882(x40482,a870))),x40484)),f328(f79(f882(x40482,a870)),f328(f328(f41(x40481,f882(x40482,a870)),x40483),x40484))) % 154.70/154.55 [4049]E(f328(f328(f41(x40491,f882(x40492,a870)),x40493),f328(f328(f8(f882(x40492,a870),f882(x40492,a870),x40491),f79(f882(x40492,a870))),x40494)),f328(f79(f882(x40492,a870)),f328(f328(f42(x40491,f882(x40492,a870)),x40493),x40494))) % 154.70/154.55 [4063]E(f328(f328(f285(x40631,x40631,x40631),f328(f328(f187(f881(x40631,x40631),a870),x40632),x40633)),f328(f328(f187(f881(x40631,x40631),a870),x40634),x40633)),f328(f328(f187(f881(x40631,x40631),a870),f328(f328(f80(a875),x40632),x40634)),x40633)) % 154.70/154.55 [4094]E(f328(f328(f42(x40941,f882(f882(x40942,a870),a870)),x40943),f328(f328(f8(f882(x40942,a870),f882(f882(x40942,a870),a870),x40941),f305(x40942)),x40944)),f328(f305(x40942),f328(f328(f42(x40941,f882(x40942,a870)),x40943),x40944))) % 154.70/154.55 [4123]E(f328(f328(f41(f882(x41231,a870),f882(x41232,a870)),x41233),f328(f328(f7(f882(x41231,a870),f882(x41231,f882(x41232,a870)),f882(x41232,a870)),f41(x41231,f882(x41232,a870))),x41234)),f328(f328(f41(x41231,f882(x41232,a870)),f39(f882(x41231,a870),x41233)),x41234)) % 154.70/154.55 [4124]E(f328(f328(f42(f882(x41241,a870),f882(x41242,a870)),x41243),f328(f328(f7(f882(x41241,a870),f882(x41241,f882(x41242,a870)),f882(x41242,a870)),f42(x41241,f882(x41242,a870))),x41244)),f328(f328(f42(x41241,f882(x41242,a870)),f39(f882(x41241,a870),x41243)),x41244)) % 154.70/154.55 [4129]E(f328(f328(f151(x41291,x41292),x41293),f328(f139(f876(x41291),f876(x41291),f125(x41291),f117(x41291)),x41294)),f328(f139(f876(x41292),f876(x41292),f125(x41292),f117(x41292)),f328(f328(f151(f876(x41291),f876(x41292)),f328(f151(x41291,x41292),x41293)),x41294))) % 154.70/154.55 [4133]E(f189(f876(x41331),f117(x41331),f328(f328(f8(f876(x41331),f876(x41331),a875),f328(f148(x41331),x41332)),f328(f328(f7(a875,f876(x41331),f876(x41331)),f173(x41331)),x41333)),x41334),f328(f328(f173(x41331),x41334),f328(f328(f148(x41331),x41332),x41333))) % 154.70/154.55 [4175]P1(f328(f328(f242(f882(x41751,a870)),f328(f307(x41752,x41751,x41753),f328(f308(x41752,x41751,x41753),x41754))),x41754)) % 154.70/154.55 [4178]E(f328(f307(f881(x41781,x41782),f881(x41782,x41781),f328(f267(x41781,x41782,f881(x41782,x41781)),f328(f7(x41782,x41781,f881(x41782,x41781)),f263(x41782,x41781)))),f328(f328(f265(x41781,x41782),x41783),f328(f16(f882(x41782,a870),x41781),x41784))),f328(f328(f265(x41782,x41781),x41784),f328(f16(f882(x41781,a870),x41782),x41783))) % 154.70/154.55 [4187]E(f328(f328(f41(x41871,f882(x41872,a870)),x41873),f328(f328(f8(f882(x41871,a870),f882(x41872,a870),x41871),f308(x41872,x41871,x41874)),f328(f328(f7(x41871,f882(x41871,a870),f882(x41871,a870)),f306(x41871)),f192(f882(x41871,a870))))),f328(f308(x41872,x41871,x41874),x41873)) % 154.70/154.55 [4188]E(f328(f328(f41(x41881,f882(x41882,a870)),x41883),f328(f328(f8(f882(x41881,a870),f882(x41882,a870),x41881),f282(x41881,x41882,x41884)),f328(f328(f7(x41881,f882(x41881,a870),f882(x41881,a870)),f306(x41881)),f192(f882(x41881,a870))))),f328(f282(x41881,x41882,x41884),x41883)) % 154.70/154.55 [4278]E(f328(f328(f114(f882(x42781,a870)),f328(f328(f114(f882(x42781,a870)),f328(f328(f105(f882(x42781,a870)),x42782),x42783)),f328(f328(f105(f882(x42781,a870)),x42783),x42784))),f328(f328(f105(f882(x42781,a870)),x42784),x42782)),f328(f328(f105(f882(x42781,a870)),f328(f328(f105(f882(x42781,a870)),f328(f328(f114(f882(x42781,a870)),x42782),x42783)),f328(f328(f114(f882(x42781,a870)),x42783),x42784))),f328(f328(f114(f882(x42781,a870)),x42784),x42782))) % 154.70/154.55 [4340]E(f328(f139(f876(x43401),f876(x43401),f125(x43401),f117(x43401)),f328(f328(f151(x43402,f876(x43401)),f328(f328(f7(x43402,f876(x43401),f876(x43401)),f328(f328(f8(x43401,f882(f876(x43401),f876(x43401)),x43402),f148(x43401)),x43403)),f117(x43401))),x43404)),f328(f328(f151(x43402,x43401),x43403),x43404)) % 154.70/154.55 [4351]E(f328(f328(f86(a1,x43511),f328(f107(a1),f328(f328(f80(a1),x43512),a101))),f328(f328(f18(a1,x43511,x43511),f328(f328(f7(a1,x43511,f882(x43511,x43511)),f328(f328(f8(a870,f882(x43511,f882(x43511,x43511)),a1),f100(x43511)),a197)),x43513)),f328(f328(f8(a875,x43511,a1),x43514),a108))),f189(x43511,x43513,x43514,f328(f107(a875),x43512))) % 154.70/154.55 [4555]~P1(f328(f328(f192(f882(x45551,f882(x45552,a870))),x45553),x45554)) % 154.70/154.55 [3822]E(f328(f328(f162(x38221),f328(f328(f125(x38221),x38222),x38223)),f328(f328(f80(a875),f328(f193(f876(x38221)),x38222)),x38224)),f328(f328(f162(x38221),x38223),x38224)) % 154.70/154.55 [3828]E(f328(f328(f135(x38281),x38282),f328(f328(f173(x38281),f328(f328(f80(a875),x38283),x38282)),x38284)),f328(f328(f173(x38281),x38283),f328(f328(f135(x38281),x38282),x38284))) % 154.70/154.55 [3931]E(f328(f328(f114(f882(x39311,a870)),f328(f259(x39312,x39311),x39313)),f328(f259(x39312,x39311),x39314)),f328(f259(x39312,x39311),f328(f328(f114(f882(f881(x39312,x39311),a870)),x39313),x39314))) % 154.70/154.55 [3932]E(f328(f328(f114(f882(x39321,a870)),f328(f261(x39321,x39322),x39323)),f328(f261(x39321,x39322),x39324)),f328(f261(x39321,x39322),f328(f328(f114(f882(f881(x39321,x39322),a870)),x39323),x39324))) % 154.70/154.55 [3937]E(f328(f328(f114(f882(x39371,a870)),f328(f328(f114(f882(x39371,a870)),x39372),x39373)),x39374),f328(f328(f114(f882(x39371,a870)),x39372),f328(f328(f114(f882(x39371,a870)),x39373),x39374))) % 154.70/154.55 [3938]E(f328(f328(f22(f882(x39381,a870)),f328(f328(f105(f882(x39381,a870)),x39382),x39383)),x39384),f328(f328(f105(f882(x39381,a870)),x39382),f328(f328(f22(f882(x39381,a870)),x39383),x39384))) % 154.70/154.55 [3939]E(f328(f328(f105(f882(x39391,a870)),f328(f328(f105(f882(x39391,a870)),x39392),x39393)),x39394),f328(f328(f105(f882(x39391,a870)),x39392),f328(f328(f105(f882(x39391,a870)),x39393),x39394))) % 154.70/154.55 [3979]E(f328(f328(f114(f882(f881(x39791,x39792),a870)),f328(f283(x39792,x39791),x39793)),f328(f283(x39792,x39791),x39794)),f328(f283(x39792,x39791),f328(f328(f114(f882(f881(x39792,x39791),a870)),x39793),x39794))) % 154.70/154.55 [3980]E(f328(f328(f105(f882(f881(x39801,x39802),a870)),f328(f283(x39802,x39801),x39803)),f328(f283(x39802,x39801),x39804)),f328(f283(x39802,x39801),f328(f328(f105(f882(f881(x39802,x39801),a870)),x39803),x39804))) % 154.70/154.55 [3994]E(f328(f328(f114(f882(x39941,f882(x39942,a870))),f252(x39942,x39941,x39943)),f252(x39942,x39941,x39944)),f252(x39942,x39941,f328(f328(f114(f882(x39942,f882(x39941,a870))),x39943),x39944))) % 154.70/154.55 [3995]E(f328(f328(f105(f882(x39951,f882(x39952,a870))),f252(x39952,x39951,x39953)),f252(x39952,x39951,x39954)),f252(x39952,x39951,f328(f328(f105(f882(x39952,f882(x39951,a870))),x39953),x39954))) % 154.70/154.55 [4052]E(f328(f328(f105(f882(x40521,a870)),f328(f328(f114(f882(x40521,a870)),x40522),x40523)),f328(f328(f114(f882(x40521,a870)),x40524),x40523)),f328(f328(f114(f882(x40521,a870)),f328(f328(f105(f882(x40521,a870)),x40522),x40524)),x40523)) % 154.70/154.55 [4053]E(f328(f328(f114(f882(x40531,a870)),f328(f328(f22(f882(x40531,a870)),x40532),x40533)),f328(f328(f22(f882(x40531,a870)),x40534),x40533)),f328(f328(f22(f882(x40531,a870)),f328(f328(f114(f882(x40531,a870)),x40532),x40534)),x40533)) % 154.70/154.55 [4054]E(f328(f328(f114(f882(x40541,a870)),f328(f328(f105(f882(x40541,a870)),x40542),x40543)),f328(f328(f105(f882(x40541,a870)),x40544),x40543)),f328(f328(f105(f882(x40541,a870)),f328(f328(f114(f882(x40541,a870)),x40542),x40544)),x40543)) % 154.70/154.55 [4055]E(f328(f328(f22(f882(x40551,a870)),f328(f328(f105(f882(x40551,a870)),x40552),x40553)),f328(f328(f105(f882(x40551,a870)),x40554),x40553)),f328(f328(f105(f882(x40551,a870)),f328(f328(f22(f882(x40551,a870)),x40552),x40554)),x40553)) % 154.70/154.55 [4056]E(f328(f328(f22(f882(x40561,a870)),f328(f328(f105(f882(x40561,a870)),x40562),x40563)),f328(f328(f105(f882(x40561,a870)),x40564),x40563)),f328(f328(f22(f882(x40561,a870)),f328(f328(f105(f882(x40561,a870)),x40562),x40563)),x40564)) % 154.70/154.55 [4066]E(f328(f328(f22(f882(x40661,a870)),f328(f328(f22(f882(x40661,a870)),x40662),f328(f328(f306(x40661),x40663),f192(f882(x40661,a870))))),x40664),f328(f328(f22(f882(x40661,a870)),x40662),f328(f328(f306(x40661),x40663),x40664))) % 154.70/154.55 [4120]E(f328(f328(f114(f882(x41201,a870)),f328(f328(f306(x41201),x41202),f328(f328(f306(x41201),x41203),f192(f882(x41201,a870))))),f328(f281(x41201),x41204)),f328(f281(x41201),f328(f328(f306(f881(x41201,x41201)),f328(f328(f263(x41201,x41201),x41202),x41203)),x41204))) % 154.70/154.55 [4150]E(f328(f328(f41(a875,f882(x41501,a870)),f328(f297(a875),x41502)),f328(f328(f8(a875,f882(x41501,a870),a875),x41503),f328(f328(f7(a875,a875,a875),f80(a875)),x41504))),f328(f328(f41(a875,f882(x41501,a870)),f299(a875,x41504,f328(f328(f80(a875),x41502),x41504))),x41503)) % 154.70/154.55 [4151]E(f172(x41511,f328(f282(x41511,x41511,x41512),f328(f328(f306(x41511),x41513),f192(f882(x41511,a870)))),f328(f282(f876(x41511),f876(x41511),f155(x41511,x41512)),f328(f328(f306(f876(x41511)),x41514),f192(f882(f876(x41511),a870))))),f328(f282(f876(x41511),f876(x41511),f155(x41511,x41512)),f328(f328(f306(f876(x41511)),f328(f328(f148(x41511),x41513),x41514)),f192(f882(f876(x41511),a870))))) % 154.70/154.55 [4212]E(f328(f176(x42121,x42122),f328(f328(f151(x42121,f881(x42121,x42122)),f328(f328(f18(x42121,x42122,f881(x42121,x42122)),f263(x42121,x42122)),x42123)),x42124)),f186(x42121,x42122,f328(f73(x42122,f879(x42122),x42121,f235(x42122)),x42123),f328(f170(x42121),x42124))) % 154.70/154.55 [4217]E(f328(f248(x42171),f328(f328(f7(x42171,f882(x42172,a870),a870),f328(f328(f8(x42172,f882(f882(x42172,a870),a870),x42171),f330(x42172)),x42173)),x42174)),f328(f308(x42171,x42172,x42173),x42174)) % 154.70/154.55 [4311]E(f328(f248(x43111),f328(f328(f7(x43111,f882(f881(x43112,x43111),a870),a870),f328(f328(f8(f881(x43112,x43111),f882(f882(f881(x43112,x43111),a870),a870),x43111),f330(f881(x43112,x43111))),f328(f263(x43112,x43111),x43113))),x43114)),f328(f282(x43112,x43111,x43114),f328(f328(f306(x43112),x43113),f192(f882(x43112,a870))))) % 154.70/154.55 [4325]E(f328(f328(f151(f881(x43251,a875),x43251),f262(x43251,a875)),f328(f133(f881(x43251,a875),f328(f328(f8(a875,a870,f881(x43251,a875)),x43252),f328(f328(f8(a875,a875,f881(x43251,a875)),a116),f266(x43251,a875)))),f328(f328(f180(x43251,a875),x43253),x43254))),f328(f328(f151(f881(x43251,a875),x43251),f262(x43251,a875)),f328(f133(f881(x43251,a875),f328(f328(f8(a875,a870,f881(x43251,a875)),x43252),f266(x43251,a875))),f328(f328(f180(x43251,a875),x43253),f328(f328(f151(a875,a875),a116),x43254))))) % 154.70/154.55 [4333]P1(f328(f328(f242(f882(f882(x43331,a870),a870)),f328(f328(f41(x43332,f882(f882(x43331,a870),a870)),x43333),f328(f328(f8(f882(x43331,a870),f882(f882(x43331,a870),a870),x43332),f305(x43331)),x43334))),f328(f305(x43331),f328(f328(f41(x43332,f882(x43331,a870)),x43333),x43334)))) % 154.70/154.55 [4375]E(f328(f328(f86(a1,x43751),f328(f107(a1),f328(f328(f80(a1),x43752),a101))),f328(f328(f18(a1,x43751,x43751),f328(f328(f7(a1,x43751,f882(x43751,x43751)),f328(f328(f8(a870,f882(x43751,f882(x43751,x43751)),a1),f100(x43751)),a197)),x43753)),f328(f328(f18(a1,x43751,x43751),f328(f328(f8(a875,f882(x43751,x43751),a1),x43754),a108)),f328(f328(f8(a875,x43751,a1),f188(x43751,x43753,x43754)),a108)))),f328(f188(x43751,x43753,x43754),f328(f107(a875),x43752))) % 154.70/154.55 [4378]E(f328(f328(f151(x43781,x43782),f328(f73(f879(x43782),x43782,x43781,f239(x43782)),x43783)),f328(f133(x43781,f328(f328(f8(a870,a870,x43781),a323),f328(f328(f7(x43781,f879(x43782),a870),f328(f328(f8(f879(x43782),f882(f879(x43782),a870),x43781),a325),x43783)),f205(x43782)))),x43784)),f160(x43781,x43782,x43783,x43784)) % 154.70/154.55 [4401]E(f328(f248(f881(x44011,x44012)),f328(f267(x44011,x44012,a870),f328(f328(f7(x44011,f882(x44012,a870),f882(x44012,a870)),f328(f328(f8(f882(a870,a870),f882(f882(x44012,a870),f882(x44012,a870)),x44011),f8(a870,a870,x44012)),f328(f328(f8(a870,f882(a870,a870),x44011),a326),f328(f328(f7(x44011,f882(x44011,a870),a870),f330(x44011)),x44013)))),f328(f328(f7(x44012,f882(x44012,a870),a870),f330(x44012)),x44014)))),f229(x44011,x44012,x44013,x44014)) % 154.70/154.55 [4436]E(f328(f328(f41(x44361,f882(f881(x44361,x44362),a870)),x44363),f328(f328(f18(x44361,f882(x44362,f882(f881(x44361,x44362),a870)),f882(f881(x44361,x44362),a870)),f328(f328(f8(f882(x44362,a870),f882(f882(x44362,f882(f881(x44361,x44362),a870)),f882(f881(x44361,x44362),a870)),x44361),f41(x44362,f882(f881(x44361,x44362),a870))),x44364)),f328(f328(f7(x44361,f882(f881(x44361,x44362),a870),f882(x44362,f882(f881(x44361,x44362),a870))),f328(f328(f8(f882(x44362,f882(f882(f881(x44361,x44362),a870),f882(f881(x44361,x44362),a870))),f882(f882(f881(x44361,x44362),a870),f882(x44362,f882(f881(x44361,x44362),a870))),x44361),f7(x44362,f882(f881(x44361,x44362),a870),f882(f881(x44361,x44362),a870))),f328(f328(f8(f882(x44362,f881(x44361,x44362)),f882(x44362,f882(f882(f881(x44361,x44362),a870),f882(f881(x44361,x44362),a870))),x44361),f328(f8(f881(x44361,x44362),f882(f882(f881(x44361,x44362),a870),f882(f881(x44361,x44362),a870)),x44362),f306(f881(x44361,x44362)))),f263(x44361,x44362)))),f192(f882(f881(x44361,x44362),a870))))),f328(f328(f265(x44361,x44362),x44363),x44364)) % 154.70/154.55 [3989]E(f328(f328(f125(x39891),f328(f328(f173(x39891),x39892),x39893)),f328(f328(f173(x39891),f328(f328(f22(a875),x39892),f328(f193(f876(x39891)),x39893))),x39894)),f328(f328(f173(x39891),x39892),f328(f328(f125(x39891),x39893),x39894))) % 154.70/154.55 [3990]E(f328(f328(f125(x39901),f328(f328(f135(x39901),x39902),x39903)),f328(f328(f135(x39901),f328(f328(f22(a875),x39902),f328(f193(f876(x39901)),x39903))),x39904)),f328(f328(f135(x39901),x39902),f328(f328(f125(x39901),x39903),x39904))) % 154.70/154.55 [4042]E(f328(f328(f80(a875),f328(f328(f81(a875),x40421),x40422)),f328(f328(f80(a875),f328(f328(f81(a875),x40423),x40422)),x40424)),f328(f328(f80(a875),f328(f328(f81(a875),f328(f328(f80(a875),x40421),x40423)),x40422)),x40424)) % 154.70/154.55 [4242]P1(f328(f328(f242(f882(x42421,a870)),f328(f328(f22(f882(x42421,a870)),f328(f259(x42422,x42421),x42423)),f328(f259(x42422,x42421),x42424))),f328(f259(x42422,x42421),f328(f328(f22(f882(f881(x42422,x42421),a870)),x42423),x42424)))) % 154.70/154.55 [4243]P1(f328(f328(f242(f882(x42431,a870)),f328(f328(f22(f882(x42431,a870)),f328(f261(x42431,x42432),x42433)),f328(f261(x42431,x42432),x42434))),f328(f261(x42431,x42432),f328(f328(f22(f882(f881(x42431,x42432),a870)),x42433),x42434)))) % 154.70/154.55 [4353]E(f328(f328(f80(a1),f328(a89,f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),f328(f328(f263(a875,a875),x43531),x43532)),f192(f882(f881(a875,a875),a870)))))),f328(a89,f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),f328(f328(f263(a875,a875),x43533),x43534)),f192(f882(f881(a875,a875),a870)))))),f328(a89,f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),f328(f328(f263(a875,a875),f328(f328(f80(a875),x43531),x43533)),f328(f328(f80(a875),x43532),x43534))),f192(f882(f881(a875,a875),a870)))))) % 154.70/154.55 [4396]E(f328(f328(f81(a1),f328(a89,f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),f328(f328(f263(a875,a875),x43961),x43962)),f192(f882(f881(a875,a875),a870)))))),f328(a89,f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),f328(f328(f263(a875,a875),x43963),x43964)),f192(f882(f881(a875,a875),a870)))))),f328(a89,f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),f328(f328(f263(a875,a875),f328(f328(f80(a875),f328(f328(f81(a875),x43961),x43963)),f328(f328(f81(a875),x43962),x43964))),f328(f328(f80(a875),f328(f328(f81(a875),x43961),x43964)),f328(f328(f81(a875),x43962),x43963)))),f192(f882(f881(a875,a875),a870)))))) % 154.70/154.55 [4417]E(f328(f248(x44171),f328(f328(f8(f882(x44172,a870),a870,x44171),f88(x44172)),f328(f328(f8(f882(x44172,a870),f882(x44172,a870),x44171),f328(f18(x44172,a870,a870),f328(f328(f8(a870,f882(a870,a870),x44172),a331),f328(f328(f7(x44172,f882(x44172,a870),a870),f330(x44172)),x44173)))),f328(f328(f7(x44171,f882(x44172,f882(x44171,a870)),f882(x44172,a870)),f328(f328(f8(f882(f882(x44171,a870),a870),f882(f882(x44172,f882(x44171,a870)),f882(x44172,a870)),x44171),f8(f882(x44171,a870),a870,x44172)),f330(x44171))),x44174)))),f328(f328(f42(x44172,f882(x44171,a870)),x44173),x44174)) % 154.70/154.55 [4451]E(f328(f328(f285(x44511,x44511,x44511),f328(f328(f306(f881(x44511,x44511)),f328(f328(f263(x44511,x44511),x44512),x44513)),x44514)),f304(x44511,f328(f328(f306(f881(x44511,x44511)),f328(f328(f263(x44511,x44511),x44512),x44513)),x44514))),f328(f328(f114(f882(f881(x44511,x44511),a870)),f328(f328(f285(x44511,x44511,x44511),x44514),f304(x44511,x44514))),f328(f248(f881(x44511,x44511)),f328(f267(x44511,x44511,a870),f328(f328(f7(x44511,f882(x44511,a870),f882(x44511,a870)),f328(f328(f8(f882(a870,a870),f882(f882(x44511,a870),f882(x44511,a870)),x44511),f8(a870,a870,x44511)),f328(f328(f8(a870,f882(a870,a870),x44511),a326),f328(f328(f7(x44511,f882(f881(x44511,x44511),a870),a870),f328(f328(f8(f881(x44511,x44511),f882(f882(f881(x44511,x44511),a870),a870),x44511),f330(f881(x44511,x44511))),f328(f328(f7(x44511,x44511,f881(x44511,x44511)),f263(x44511,x44511)),x44512))),f304(x44511,x44514))))),f328(f328(f7(x44511,f882(f881(x44511,x44511),a870),a870),f328(f328(f8(f881(x44511,x44511),f882(f882(f881(x44511,x44511),a870),a870),x44511),f330(f881(x44511,x44511))),f328(f263(x44511,x44511),x44513))),f304(x44511,x44514))))))) % 154.70/154.55 [4244]E(f328(f133(x42441,f328(f328(f18(x42441,a870,a870),f328(f328(f8(a870,f882(a870,a870),x42441),a326),x42442)),x42443)),x42444),f328(f133(x42441,x42443),f328(f133(x42441,x42442),x42444))) % 154.70/154.55 [4347]E(f328(f328(f125(x43471),f328(f328(f328(f100(f876(x43471)),f328(f328(f330(a875),f2(a875)),x43472)),f328(f328(f148(x43471),x43473),f117(x43471))),f117(x43471))),f174(x43471,x43474,f328(f248(a875),f328(f328(f7(a875,f882(a875,a870),a870),f328(f328(f8(a875,f882(f882(a875,a870),a870),a875),f330(a875)),a116)),x43472)))),f174(x43471,f328(f328(f148(x43471),x43473),x43474),x43472)) % 154.70/154.55 [4445]E(f328(f248(f881(x44451,x44452)),f328(f328(f8(f882(a875,a870),a870,f881(x44451,x44452)),f87(a875)),f328(f328(f7(f881(x44451,x44452),f882(a875,a870),f882(a875,a870)),f328(f328(f8(f882(a875,f882(a870,a870)),f882(f882(a875,a870),f882(a875,a870)),f881(x44451,x44452)),f18(a875,a870,a870)),f328(f328(f8(f882(a875,a870),f882(a875,f882(a870,a870)),f881(x44451,x44452)),f328(f8(a870,f882(a870,a870),a875),a326)),f328(f328(f7(f881(x44451,x44452),f882(a875,f881(x44451,x44452)),f882(a875,a870)),f328(f328(f8(f882(f881(x44451,x44452),a870),f882(f882(a875,f881(x44451,x44452)),f882(a875,a870)),f881(x44451,x44452)),f8(f881(x44451,x44452),a870,a875)),a325)),f328(f328(f18(a875,x44452,f881(x44451,x44452)),f328(f328(f8(x44451,f882(x44452,f881(x44451,x44452)),a875),f263(x44451,x44452)),f328(f162(x44451),x44453))),f328(f162(x44452),x44454)))))),f328(f328(f7(a875,a875,a870),f243(a875)),f328(f328(f240(a875),f328(f193(f876(x44451)),x44453)),f328(f193(f876(x44452)),x44454)))))),f328(f170(f881(x44451,x44452)),f328(f328(f180(x44451,x44452),x44453),x44454))) % 154.70/154.55 [4366]E(f328(f248(f881(x43661,x43662)),f328(f267(x43661,x43662,a870),f328(f328(f7(x43661,f882(x43662,a870),f882(x43662,a870)),f328(f328(f8(f882(a870,a870),f882(f882(x43662,a870),f882(x43662,a870)),x43661),f8(a870,a870,x43662)),f328(f328(f8(a870,f882(a870,a870),x43661),a326),x43663))),x43664))),f328(f328(f265(x43661,x43662),f328(f248(x43661),x43663)),f328(f16(f882(x43662,a870),x43661),f328(f248(x43662),x43664)))) % 154.70/154.55 [4369]E(f328(f248(f881(x43691,x43692)),f328(f267(x43691,x43692,a870),f328(f328(f18(x43691,f882(x43692,a870),f882(x43692,a870)),f328(f328(f8(f882(a870,a870),f882(f882(x43692,a870),f882(x43692,a870)),x43691),f8(a870,a870,x43692)),f328(f328(f8(a870,f882(a870,a870),x43691),a326),x43693))),x43694))),f328(f328(f265(x43691,x43692),f328(f248(x43691),x43693)),f328(f328(f8(f882(x43692,a870),f882(x43692,a870),x43691),f248(x43692)),x43694))) % 154.70/154.55 [4385]E(f328(f248(x43851),f328(f328(f8(f882(x43852,a870),a870,x43851),f88(x43852)),f328(f328(f8(f882(x43852,a870),f882(x43852,a870),x43851),f328(f18(x43852,a870,a870),f328(f328(f8(a870,f882(a870,a870),x43852),a331),f328(f328(f7(x43852,f882(x43852,a870),a870),f330(x43852)),x43853)))),x43854))),f328(f328(f42(x43852,f882(x43851,a870)),x43853),f328(f328(f8(f882(x43851,a870),f882(x43851,a870),x43852),f248(x43851)),f328(f7(x43851,x43852,a870),x43854)))) % 154.70/154.55 [4431]E(f328(f328(f151(f881(x44311,a875),x44311),f262(x44311,a875)),f328(f133(f881(x44311,a875),f328(f328(f7(f881(x44311,a875),f882(a875,a870),a870),f328(f328(f8(a875,f882(f882(a875,a870),a870),f881(x44311,a875)),f330(a875)),f266(x44311,a875))),x44312)),f328(f328(f180(x44311,a875),x44313),f136(a875,f328(f298(a875,x44314),f328(f328(f80(a875),x44314),f328(f193(f876(x44311)),x44313))))))),f328(f328(f151(f881(x44311,a875),x44311),f262(x44311,a875)),f328(f133(f881(x44311,a875),f328(f328(f7(f881(x44311,a875),f882(a875,a870),a870),f328(f328(f8(a875,f882(f882(a875,a870),a870),f881(x44311,a875)),f330(a875)),f328(f328(f7(f881(x44311,a875),a875,a875),f328(f328(f8(a875,f882(a875,a875),f881(x44311,a875)),f80(a875)),f266(x44311,a875))),x44314))),x44312)),f328(f328(f180(x44311,a875),x44313),f136(a875,f328(f298(a875,f2(a875)),f328(f193(f876(x44311)),x44313))))))) % 154.70/154.55 [4432]E(f328(a116,f328(f328(f241(a875),f328(f193(f876(x44321)),x44322)),f328(f139(a875,f876(x44323),f328(f7(f876(x44323),a875,a875),f328(f328(f8(a875,f882(a875,a875),f876(x44323)),f241(a875)),f328(f328(f7(f876(x44323),a875,a875),f328(f328(f8(a875,f882(a875,a875),f876(x44323)),f22(a875)),f193(f876(x44323)))),f328(a116,f2(a875))))),f2(a875)),f328(f166(f876(x44323)),f328(f133(f876(x44323),f328(f328(f8(a870,a870,f876(x44323)),a323),f328(f328(f7(f876(x44323),f876(x44323),a870),a325),f117(x44323)))),x44324))))),f328(f328(f241(a875),f328(a116,f328(f193(f876(x44321)),x44322))),f328(f139(a875,f876(x44323),f328(f7(f876(x44323),a875,a875),f328(f328(f8(a875,f882(a875,a875),f876(x44323)),f241(a875)),f193(f876(x44323)))),f2(a875)),f328(f166(f876(x44323)),x44324)))) % 154.70/154.55 [4384]E(f328(f328(f125(x43841),f174(x43841,x43842,x43843)),f174(x43841,x43844,f328(f248(a875),f328(f328(f7(a875,f882(a875,a870),a870),f328(f328(f8(a875,f882(f882(a875,a870),a870),a875),f330(a875)),f328(f328(f7(a875,a875,a875),f80(a875)),f328(f193(f876(x43841)),x43842)))),x43843)))),f174(x43841,f328(f328(f125(x43841),x43842),x43844),x43843)) % 154.70/154.55 [4438]E(f328(f328(f148(f876(x44381)),f328(f328(f148(x44381),x44382),f328(f139(f876(x44381),f876(x44381),f125(x44381),f117(x44381)),f328(f328(f151(f876(x44381),f876(x44381)),f153(f876(x44381),x44381,f117(x44381),f328(f328(f8(f876(x44381),f882(f876(x44381),f876(x44381)),x44381),f16(f876(x44381),f876(x44381))),f328(f328(f7(x44381,f876(x44381),f876(x44381)),f148(x44381)),f117(x44381))))),x44383)))),f178(x44381,f328(f328(f148(f876(x44381)),x44384),f328(f139(f876(f876(x44381)),f876(f876(x44381)),f125(f876(x44381)),f117(f876(x44381))),f328(f328(f151(f876(x44381),f876(f876(x44381))),f153(f876(f876(x44381)),x44381,f117(f876(x44381)),f328(f16(f882(f876(x44381),f876(f876(x44381))),x44381),f328(f328(f7(f876(x44381),f876(f876(x44381)),f876(f876(x44381))),f148(f876(x44381))),f117(f876(x44381)))))),x44383))))),f178(x44381,f328(f328(f148(f876(x44381)),f328(f328(f148(x44381),x44382),x44384)),x44383))) % 154.70/154.55 [4446]E(f328(f248(f881(x44461,x44461)),f328(f267(x44461,x44461,a870),f328(f328(f7(x44461,f882(f881(x44462,x44462),a870),f882(x44461,a870)),f328(f328(f8(f882(x44461,f882(f882(f881(x44462,x44462),a870),a870)),f882(f882(f881(x44462,x44462),a870),f882(x44461,a870)),x44461),f7(x44461,f882(f881(x44462,x44462),a870),a870)),f328(f328(f8(f882(x44461,f881(x44462,x44462)),f882(x44461,f882(f882(f881(x44462,x44462),a870),a870)),x44461),f328(f8(f881(x44462,x44462),f882(f882(f881(x44462,x44462),a870),a870),x44461),f330(f881(x44462,x44462)))),f328(f328(f7(x44461,f882(x44461,x44462),f882(x44461,f881(x44462,x44462))),f328(f328(f8(f882(x44462,f881(x44462,x44462)),f882(f882(x44461,x44462),f882(x44461,f881(x44462,x44462))),x44461),f8(x44462,f881(x44462,x44462),x44461)),f328(f328(f8(x44462,f882(x44462,f881(x44462,x44462)),x44461),f263(x44462,x44462)),x44463))),x44463)))),x44464))),f328(f328(f284(x44462,x44461),x44464),x44463)) % 154.70/154.55 [4504]~E(f33(x45041,x45042),f30(x45043,x45044,x45045)) % 154.70/154.55 [4505]~E(f33(x45051,x45052),f29(x45053,x45054,x45055)) % 154.70/154.55 [4506]~E(f32(x45061,x45062),f30(x45063,x45064,x45065)) % 154.70/154.55 [4507]~E(f32(x45071,x45072),f29(x45073,x45074,x45075)) % 154.70/154.55 [4508]~E(f30(x45081,x45082,x45083),f33(x45084,x45085)) % 154.70/154.55 [4509]~E(f30(x45091,x45092,x45093),f32(x45094,x45095)) % 154.70/154.55 [4510]~E(f29(x45101,x45102,x45103),f33(x45104,x45105)) % 154.70/154.55 [4511]~E(f29(x45111,x45112,x45113),f32(x45114,x45115)) % 154.70/154.55 [3929]E(f328(f183(x39291,x39292,x39293,x39294),x39295),f328(f237(f879(x39292),x39292,f328(x39293,x39295),f235(x39292)),f328(x39294,x39295))) % 154.70/154.55 [4017]E(f183(x40171,x40172,f183(x40171,x40172,x40173,x40174),x40175),f183(x40171,x40172,x40173,f183(x40171,x40172,x40174,x40175))) % 154.70/154.55 [4191]E(f264(x41911,x41912,x41913,f252(x41912,x41911,x41914),f252(x41913,x41912,x41915)),f252(x41913,x41911,f264(x41913,x41912,x41911,x41915,x41914))) % 154.70/154.55 [4198]E(f328(f328(f114(f882(x41981,a870)),f328(f170(x41981),f328(f328(f173(x41981),f328(f193(f876(x41982)),x41983)),x41984))),f182(x41981,x41982,x41985)),f182(x41981,x41982,f185(x41981,x41982,x41985,x41984,x41983))) % 154.70/154.55 [3754]E(f328(f328(f267(x37541,x37542,x37543),x37544),x37545),f328(f328(x37544,f328(f262(x37541,x37542),x37545)),f328(f266(x37541,x37542),x37545))) % 154.70/154.55 [3779]E(f328(f237(x37791,x37792,x37793,x37794),f328(f235(x37792),x37795)),f328(x37794,x37795)) % 154.70/154.55 [3788]E(f328(f328(f328(f65(x37881,x37882,x37883),x37884),x37885),f192(f882(x37882,a870))),x37885) % 154.70/154.55 [3961]E(f238(x39611,x39612,x39613,x39614,f328(f235(x39612),x39615)),f328(x39614,x39615)) % 154.70/154.55 [4072]E(f328(f73(f879(x40721),f879(x40722),f879(x40723),f328(f206(x40721,x40722),x40724)),f328(f206(x40723,x40721),x40725)),f328(f206(x40723,x40722),f328(f73(x40721,x40722,x40723,x40724),x40725))) % 154.70/154.55 [4074]E(f328(f73(f876(x40741),f876(x40742),f876(x40743),f328(f151(x40741,x40742),x40744)),f328(f151(x40743,x40741),x40745)),f328(f151(x40743,x40742),f328(f73(x40741,x40742,x40743,x40744),x40745))) % 154.70/154.55 [4130]E(f328(f237(x41301,f881(x41302,f877(x41302)),x41303,f328(f267(x41302,f877(x41302),x41301),x41304)),f328(f132(x41302),x41305)),f130(x41301,x41302,x41303,x41304,x41305)) % 154.70/154.55 [4154]E(f85(x41541,f66(x41542,x41541,x41543,x41544,x41545)),f328(f328(f64(x41542,x41541,x41543),x41544),x41545)) % 154.70/154.55 [4189]E(f328(f328(f80(a875),f328(f328(f80(a875),f328(x41891,f328(f262(x41892,x41893),x41894))),f328(x41895,f328(f266(x41892,x41893),x41894)))),f328(a116,f2(a875))),f271(x41892,x41893,x41891,x41895,x41894)) % 154.70/154.55 [4380]E(f160(x43801,x43802,f328(f328(f7(x43801,f879(x43802),f879(x43802)),f328(f328(f18(x43801,f879(x43802),f882(f879(x43802),f879(x43802))),f328(f328(f8(a870,f882(f879(x43802),f882(f879(x43802),f879(x43802))),x43801),f100(f879(x43802))),x43803)),f328(f328(f8(x43802,f879(x43802),x43801),f235(x43802)),x43804))),f205(x43802)),x43805),f328(f328(f151(x43801,x43802),x43804),f328(f133(x43801,x43803),x43805))) % 154.70/154.55 [4547]~E(f328(f328(f328(f72(x45471,f879(x45472)),x45473),x45474),f328(f235(x45472),x45475)),f328(f16(f879(x45472),x45471),f205(x45472))) % 154.70/154.55 [3689]E(f328(f328(f173(x36891),x36892),f328(f328(f151(x36893,x36891),x36894),x36895)),f328(f328(f151(x36893,x36891),x36894),f328(f328(f173(x36893),x36892),x36895))) % 154.70/154.55 [3690]E(f328(f328(f135(x36901),x36902),f328(f328(f151(x36903,x36901),x36904),x36905)),f328(f328(f151(x36903,x36901),x36904),f328(f328(f135(x36903),x36902),x36905))) % 154.70/154.55 [3722]E(f328(f328(f151(x37221,x37222),x37223),f328(f328(f148(x37221),x37224),x37225)),f328(f328(f148(x37222),f328(x37223,x37224)),f328(f328(f151(x37221,x37222),x37223),x37225))) % 154.70/154.55 [3783]E(f328(f307(x37831,x37832,x37833),f328(f328(f306(x37831),x37834),x37835)),f328(f328(f306(x37832),f328(x37833,x37834)),f328(f307(x37831,x37832,x37833),x37835))) % 154.70/154.55 [3812]E(f171(x38121,f328(f328(f148(x38121),x38122),x38123),f328(f328(f148(x38121),x38124),x38125)),f328(f328(f148(x38121),x38122),f328(f328(f148(x38121),x38124),f171(x38121,x38123,x38125)))) % 154.70/154.55 [3848]E(f328(f328(f180(x38481,x38482),f328(f328(f173(x38481),x38483),x38484)),f328(f328(f173(x38482),x38483),x38485)),f328(f328(f173(f881(x38481,x38482)),x38483),f328(f328(f180(x38481,x38482),x38484),x38485))) % 154.70/154.55 [3849]E(f328(f328(f180(x38491,x38492),f328(f328(f135(x38491),x38493),x38494)),f328(f328(f135(x38492),x38493),x38495)),f328(f328(f135(f881(x38491,x38492)),x38493),f328(f328(f180(x38491,x38492),x38494),x38495))) % 154.70/154.55 [3861]E(f328(f328(f156(x38611,f328(f328(f148(x38611),x38612),x38613)),f328(a116,x38614)),x38615),f328(f328(f148(x38611),x38612),f328(f328(f156(x38611,x38613),x38614),x38615))) % 154.70/154.55 [3864]E(f328(f237(f879(x38641),x38642,f205(x38641),x38643),f328(f328(f16(f879(x38642),x38644),f205(x38642)),x38645)),f205(x38641)) % 154.70/154.55 [3866]E(f328(f328(f125(x38661),f328(f328(f151(x38662,x38661),x38663),x38664)),f328(f328(f151(x38662,x38661),x38663),x38665)),f328(f328(f151(x38662,x38661),x38663),f328(f328(f125(x38662),x38664),x38665))) % 154.70/154.55 [3870]E(f328(f328(x38701,x38702),f328(f328(f254(x38703,x38704,x38701),x38702),x38705)),f328(f328(f254(x38703,x38704,x38701),x38702),f328(a116,x38705))) % 154.70/154.55 [3900]E(f161(x39001,x39002,x39003,f328(f328(f148(x39001),x39004),x39005)),f328(f328(f125(x39002),f328(x39003,x39004)),f161(x39001,x39002,x39003,x39005))) % 154.70/154.55 [3913]E(f328(f328(f285(x39131,x39132,x39133),f328(f283(x39132,x39131),x39134)),f328(f283(x39133,x39132),x39135)),f328(f283(x39133,x39131),f328(f328(f285(x39133,x39132,x39131),x39135),x39134))) % 154.70/154.55 [3947]E(f328(f328(f328(f187(f876(x39471),f876(x39471)),x39472),f165(x39471)),f328(f328(f151(x39473,x39471),x39474),x39475)),f328(f328(f151(x39473,x39471),x39474),f328(f328(f328(f187(f876(x39473),f876(x39473)),x39472),f165(x39473)),x39475))) % 154.70/154.55 [3948]E(f328(f328(f269(x39481,x39482,x39481,x39483),f328(f263(x39482,x39481),x39484)),x39485),f328(x39485,x39484)) % 154.70/154.55 [3975]E(f152(x39751,x39752,f328(f328(f151(x39753,x39751),x39754),x39755)),f152(x39753,f328(f73(x39751,a875,x39753,x39752),x39754),x39755)) % 154.70/154.55 [4040]E(f328(f328(f73(f879(x40401),f879(x40402),x40403,f328(f206(x40401,x40402),x40404)),f328(f16(f879(x40401),x40403),f205(x40401))),x40405),f205(x40402)) % 154.70/154.55 [4041]E(f175(f881(x40411,x40412),f328(f73(x40412,a870,f881(x40411,x40412),x40413),f266(x40411,x40412)),f328(f328(f180(x40411,x40412),x40414),x40415)),f328(f328(f180(x40411,x40412),x40414),f175(x40412,x40413,x40415))) % 154.70/154.55 [4046]E(f328(f307(x40461,x40462,f328(f328(f8(x40463,x40462,x40461),x40464),x40465)),f251(f882(x40461,a870))),f328(f307(x40463,x40462,x40464),f328(f307(x40461,x40463,x40465),f251(f882(x40461,a870))))) % 154.70/154.55 [4059]E(f175(f881(x40591,x40592),f328(f73(x40591,a870,f881(x40591,x40592),x40593),f262(x40591,x40592)),f328(f328(f180(x40591,x40592),x40594),x40595)),f328(f328(f180(x40591,x40592),f175(x40591,x40593,x40594)),x40595)) % 154.70/154.55 [4078]E(f328(f328(f114(f882(x40781,a870)),f328(f308(x40781,x40782,x40783),f328(f328(f306(x40782),x40784),f192(f882(x40782,a870))))),f328(f308(x40781,x40782,x40783),x40785)),f328(f308(x40781,x40782,x40783),f328(f328(f306(x40782),x40784),x40785))) % 154.70/154.55 [4138]E(f328(f328(f125(f881(x41381,x41382)),f328(f328(f151(x41382,f881(x41381,x41382)),f328(f263(x41381,x41382),x41383)),x41384)),f59(x41381,x41382,x41385,x41384)),f59(x41381,x41382,f328(f328(f148(x41381),x41383),x41385),x41384)) % 154.70/154.55 [4139]E(f328(f328(f151(x41391,x41392),x41393),f175(x41391,f328(f73(x41392,a870,x41391,x41394),x41393),x41395)),f175(x41392,x41394,f328(f328(f151(x41391,x41392),x41393),x41395))) % 154.70/154.55 [4145]E(f328(f139(x41451,x41452,f328(f7(x41452,x41451,x41451),f328(f7(x41451,x41452,x41451),x41453)),x41454),f328(f166(x41452),f328(f166(x41452),x41455))),f328(f139(x41451,x41452,x41453,x41454),x41455)) % 154.70/154.55 [4146]E(f328(f328(f328(f72(x41461,f879(x41462)),f186(x41461,x41462,x41463,x41464)),x41465),f328(x41463,x41465)),f186(x41461,x41462,x41463,f328(f328(f306(x41461),x41465),x41464))) % 154.70/154.55 [4215]E(f328(f237(f876(x42151),x42151,f160(x42152,x42151,x42153,x42154),f328(f328(f7(x42151,f876(x42151),f876(x42151)),f148(x42151)),f160(x42152,x42151,x42153,x42154))),f328(x42153,x42155)),f160(x42152,x42151,x42153,f328(f328(f148(x42152),x42155),x42154))) % 154.70/154.55 [4252]P1(f328(f328(f242(f882(x42521,a870)),f328(f307(x42522,x42521,x42523),f328(f328(f105(f882(x42522,a870)),x42524),x42525))),f328(f328(f105(f882(x42521,a870)),f328(f307(x42522,x42521,x42523),x42524)),f328(f307(x42522,x42521,x42523),x42525)))) % 154.70/154.55 [4253]P1(f328(f328(f242(f882(x42531,a870)),f328(f282(x42532,x42531,x42533),f328(f328(f105(f882(x42532,a870)),x42534),x42535))),f328(f328(f105(f882(x42531,a870)),f328(f282(x42532,x42531,x42533),x42534)),f328(f282(x42532,x42531,x42533),x42535)))) % 154.70/154.55 [4354]E(f328(f266(x43541,x43542),f328(f268(x43543,x43541,x43542,x43542,x43544,f34(x43542)),x43545)),f328(f266(x43543,x43542),x43545)) % 154.70/154.55 [4355]E(f328(f262(x43551,x43552),f328(f268(x43551,x43551,x43553,x43552,f34(x43551),x43554),x43555)),f328(f262(x43551,x43553),x43555)) % 154.70/154.55 [4442]E(f328(f139(f882(x44421,f879(x44422)),f881(x44421,x44422),f328(f328(f8(f882(x44421,f882(x44422,f882(x44421,f879(x44422)))),f882(f881(x44421,x44422),f882(x44421,f879(x44422))),f882(x44421,f879(x44422))),f267(x44421,x44422,f882(x44421,f879(x44422)))),f328(f328(f7(f882(x44421,f879(x44422)),f882(x44422,f879(x44422)),f882(x44421,f882(x44422,f882(x44421,f879(x44422))))),f328(f328(f8(f882(x44421,f882(f882(x44422,f879(x44422)),f882(x44422,f882(x44421,f879(x44422))))),f882(f882(x44422,f879(x44422)),f882(x44421,f882(x44422,f882(x44421,f879(x44422))))),f882(x44421,f879(x44422))),f7(x44421,f882(x44422,f879(x44422)),f882(x44422,f882(x44421,f879(x44422))))),f328(f328(f8(f882(x44421,f882(f879(x44422),f882(x44421,f879(x44422)))),f882(x44421,f882(f882(x44422,f879(x44422)),f882(x44422,f882(x44421,f879(x44422))))),f882(x44421,f879(x44422))),f328(f8(f882(f879(x44422),f882(x44421,f879(x44422))),f882(f882(x44422,f879(x44422)),f882(x44422,f882(x44421,f879(x44422)))),x44421),f8(f879(x44422),f882(x44421,f879(x44422)),x44422))),f72(x44421,f879(x44422))))),f235(x44422))),x44423),f328(f328(f180(x44421,x44422),x44424),x44425)),f185(x44421,x44422,x44423,x44424,x44425)) % 154.70/154.55 [4444]P26(x44441,x44442,f328(f328(f306(f874(x44441)),f328(f328(f328(f92(x44441),f328(f328(f7(x44441,f882(a872,a870),f882(a872,a870)),f328(f328(f8(f882(a872,f882(a870,a870)),f882(f882(a872,a870),f882(a872,a870)),x44441),f18(a872,a870,a870)),f328(f328(f8(f882(a872,a870),f882(a872,f882(a870,a870)),x44441),f328(f8(a870,f882(a870,a870),a872),a326)),x44443))),f328(f328(f8(a870,a870,a872),a323),x44444))),f32(x44444,x44445)),x44443)),f192(f882(f874(x44441),a870)))) % 154.70/154.55 [3532]E(f328(f328(f328(f328(f211(x35321),x35322),x35323),x35324),x35325),f196(x35321,x35322)) % 154.70/154.55 [3533]E(f328(f328(f328(f328(f215(x35331),x35332),x35333),x35334),x35335),f207(x35331,x35332)) % 154.70/154.55 [3577]E(f97(x35771,x35772,f328(f328(f328(f92(x35771),x35773),x35774),x35775)),f2(a875)) % 154.70/154.55 [3673]E(f328(f328(f328(f328(f72(x36731,x36732),x36733),x36734),x36735),x36734),x36735) % 154.70/154.55 [3901]E(f328(f328(f41(x39011,f882(x39012,a870)),f328(f328(f306(x39011),x39013),x39014)),x39015),f328(f328(f114(f882(x39012,a870)),f328(x39015,x39013)),f328(f328(f41(x39011,f882(x39012,a870)),x39014),x39015))) % 154.70/154.55 [3902]E(f328(f328(f42(x39021,f882(x39022,a870)),f328(f328(f306(x39021),x39023),x39024)),x39025),f328(f328(f105(f882(x39022,a870)),f328(x39025,x39023)),f328(f328(f42(x39021,f882(x39022,a870)),x39024),x39025))) % 154.70/154.55 [3954]E(f328(f120(x39541,x39542,f328(x39543,x39544)),f328(f328(f7(x39541,a103,f877(x39542)),x39545),x39544)),f328(f203(x39541,x39542,x39543,x39545),x39544)) % 154.70/154.55 [3968]E(f328(f328(f114(f882(x39681,a870)),f328(f307(x39682,x39681,x39683),x39684)),f328(f307(x39682,x39681,x39683),x39685)),f328(f307(x39682,x39681,x39683),f328(f328(f114(f882(x39682,a870)),x39684),x39685))) % 154.70/154.55 [3969]E(f328(f328(f114(f882(x39691,a870)),f328(f308(x39691,x39692,x39693),x39694)),f328(f308(x39691,x39692,x39693),x39695)),f328(f308(x39691,x39692,x39693),f328(f328(f114(f882(x39692,a870)),x39694),x39695))) % 154.70/154.55 [3970]E(f328(f328(f22(f882(x39701,a870)),f328(f308(x39701,x39702,x39703),x39704)),f328(f308(x39701,x39702,x39703),x39705)),f328(f308(x39701,x39702,x39703),f328(f328(f22(f882(x39702,a870)),x39704),x39705))) % 154.70/154.55 [3971]E(f328(f328(f105(f882(x39711,a870)),f328(f308(x39711,x39712,x39713),x39714)),f328(f308(x39711,x39712,x39713),x39715)),f328(f308(x39711,x39712,x39713),f328(f328(f105(f882(x39712,a870)),x39714),x39715))) % 154.70/154.55 [3972]E(f328(f328(f114(f882(x39721,a870)),f328(f282(x39722,x39721,x39723),x39724)),f328(f282(x39722,x39721,x39723),x39725)),f328(f282(x39722,x39721,x39723),f328(f328(f114(f882(x39722,a870)),x39724),x39725))) % 154.70/154.55 [3974]E(f186(x39741,x39742,f186(x39741,x39742,x39743,x39744),x39745),f186(x39741,x39742,x39743,f328(f328(f105(f882(x39741,a870)),x39744),x39745))) % 154.70/154.55 [4036]E(f328(f328(f156(x40361,f328(f328(f125(x40361),x40362),f328(f328(f148(x40361),x40363),x40364))),f328(f193(f876(x40361)),x40362)),x40365),f328(f328(f125(x40361),x40362),f328(f328(f148(x40361),x40365),x40364))) % 154.70/154.55 [4044]E(f328(f328(f42(x40441,f882(x40442,a870)),x40443),f328(f328(f8(f882(x40442,a870),f882(x40442,a870),x40441),f328(f306(x40442),x40444)),x40445)),f328(f328(f306(x40442),x40444),f328(f328(f42(x40441,f882(x40442,a870)),x40443),x40445))) % 154.70/154.55 [4112]E(f186(x41121,x41122,f328(f328(f328(f72(x41121,f879(x41122)),x41123),x41124),f328(f235(x41122),x41125)),f328(f79(f882(x41121,a870)),f328(f328(f306(x41121),x41124),f192(f882(x41121,a870))))),f186(x41121,x41122,x41123,f328(f79(f882(x41121,a870)),f328(f328(f306(x41121),x41124),f192(f882(x41121,a870)))))) % 154.70/154.55 [4202]E(f328(f328(f151(x42021,x42022),x42023),f328(f133(x42021,f328(f73(x42022,a870,x42021,x42024),x42023)),x42025)),f328(f133(x42022,x42024),f328(f328(f151(x42021,x42022),x42023),x42025))) % 154.70/154.55 [4208]E(f328(f193(f876(x42081)),f328(f133(x42081,x42082),f328(f328(f151(x42083,x42081),x42084),x42085))),f328(f193(f876(x42083)),f328(f133(x42083,f328(f73(x42081,a870,x42083,x42082),x42084)),x42085))) % 154.70/154.55 [4346]E(f328(f328(f114(f882(x43461,a870)),f328(f328(f22(f882(x43461,a870)),f182(x43461,x43462,x43463)),f328(f248(x43461),f328(f328(f7(x43461,f882(x43461,a870),a870),f330(x43461)),f328(f328(f22(f882(x43461,a870)),x43464),f182(x43461,x43462,x43465)))))),f328(f248(x43461),f328(f328(f7(x43461,f882(x43461,a870),a870),f330(x43461)),f328(f328(f105(f882(x43461,a870)),x43464),f182(x43461,x43462,x43465))))),f182(x43461,x43462,f76(x43461,f879(x43462),x43463,x43465,x43464))) % 154.70/154.55 [4422]E(f328(f153(f876(f881(x44221,x44222)),x44222,f117(f881(x44221,x44222)),f328(f328(f7(x44222,f882(f876(x44222),f876(f881(x44221,x44222))),f882(f876(x44222),f876(f881(x44221,x44222)))),f328(f328(f8(f882(f876(f881(x44221,x44222)),f876(f881(x44221,x44222))),f882(f882(f876(x44222),f876(f881(x44221,x44222))),f882(f876(x44222),f876(f881(x44221,x44222)))),x44222),f8(f876(f881(x44221,x44222)),f876(f881(x44221,x44222)),f876(x44222))),f328(f328(f8(f881(x44221,x44222),f882(f876(f881(x44221,x44222)),f876(f881(x44221,x44222))),x44222),f148(f881(x44221,x44222))),f328(f263(x44221,x44222),x44223)))),f328(f180(x44221,x44222),x44224))),x44225),f328(f328(f180(x44221,x44222),f328(f328(f148(x44221),x44223),x44224)),x44225)) % 154.70/154.55 [3895]E(f328(f328(f156(x38951,f328(f328(f156(x38951,x38952),x38953),x38954)),x38953),x38955),f328(f328(f156(x38951,x38952),x38953),x38955)) % 154.70/154.55 [3949]E(f328(f259(x39491,x39492),f328(f328(f306(f881(x39491,x39492)),f328(f328(f263(x39491,x39492),x39493),x39494)),x39495)),f328(f328(f306(x39492),x39494),f328(f259(x39491,x39492),x39495))) % 154.70/154.55 [3950]E(f328(f261(x39501,x39502),f328(f328(f306(f881(x39501,x39502)),f328(f328(f263(x39501,x39502),x39503),x39504)),x39505)),f328(f328(f306(x39501),x39503),f328(f261(x39501,x39502),x39505))) % 154.70/154.55 [3999]E(f123(x39991,x39992,f328(x39993,x39994),f328(f328(f7(x39991,a103,f877(f879(x39992))),x39995),x39994)),f328(f201(x39991,x39992,x39993,x39995),x39994)) % 154.70/154.55 [4029]E(f328(f328(f114(f882(f881(x40291,x40292),a870)),f328(f328(f265(x40291,x40292),x40293),x40294)),f328(f328(f265(x40291,x40292),x40295),x40294)),f328(f328(f265(x40291,x40292),f328(f328(f114(f882(x40291,a870)),x40293),x40295)),x40294)) % 154.70/154.55 [4030]E(f328(f328(f22(f882(f881(x40301,x40302),a870)),f328(f328(f265(x40301,x40302),x40303),x40304)),f328(f328(f265(x40301,x40302),x40305),x40304)),f328(f328(f265(x40301,x40302),f328(f328(f22(f882(x40301,a870)),x40303),x40305)),x40304)) % 154.70/154.55 [4031]E(f328(f328(f105(f882(f881(x40311,x40312),a870)),f328(f328(f265(x40311,x40312),x40313),x40314)),f328(f328(f265(x40311,x40312),x40315),x40314)),f328(f328(f265(x40311,x40312),f328(f328(f105(f882(x40311,a870)),x40313),x40315)),x40314)) % 154.70/154.55 [4090]E(f328(f328(f114(f882(x40901,a870)),f328(f328(f41(x40902,f882(x40901,a870)),x40903),x40904)),f328(f328(f41(x40902,f882(x40901,a870)),x40905),x40904)),f328(f328(f41(x40902,f882(x40901,a870)),f328(f328(f114(f882(x40902,a870)),x40903),x40905)),x40904)) % 154.70/154.55 [4091]E(f328(f328(f105(f882(x40911,a870)),f328(f328(f42(x40912,f882(x40911,a870)),x40913),x40914)),f328(f328(f42(x40912,f882(x40911,a870)),x40915),x40914)),f328(f328(f42(x40912,f882(x40911,a870)),f328(f328(f114(f882(x40912,a870)),x40913),x40915)),x40914)) % 154.70/154.55 [4105]E(f328(f328(f41(x41051,f882(x41052,a870)),x41053),f328(f328(f8(f882(x41052,a870),f882(x41052,a870),x41051),f328(f22(f882(x41052,a870)),x41054)),x41055)),f328(f328(f22(f882(x41052,a870)),x41054),f328(f328(f42(x41051,f882(x41052,a870)),x41053),x41055))) % 154.70/154.55 [4106]E(f328(f328(f41(x41061,f882(x41062,a870)),x41063),f328(f328(f8(f882(x41062,a870),f882(x41062,a870),x41061),f328(f105(f882(x41062,a870)),x41064)),x41065)),f328(f328(f105(f882(x41062,a870)),x41064),f328(f328(f41(x41061,f882(x41062,a870)),x41063),x41065))) % 154.70/154.55 [4107]E(f328(f328(f42(x41071,f882(x41072,a870)),x41073),f328(f328(f8(f882(x41072,a870),f882(x41072,a870),x41071),f328(f114(f882(x41072,a870)),x41074)),x41075)),f328(f328(f114(f882(x41072,a870)),x41074),f328(f328(f42(x41071,f882(x41072,a870)),x41073),x41075))) % 154.70/154.55 [4144]E(f183(x41441,x41442,x41443,f328(f176(x41441,x41442),f328(f166(f881(x41441,x41442)),f328(f328(f180(x41441,x41442),x41444),x41445)))),f185(x41441,x41442,x41443,x41444,x41445)) % 154.70/154.55 [4166]E(f189(f876(x41661),f328(f328(f148(x41661),x41662),x41663),f328(f328(f8(f876(x41661),f876(x41661),a875),f328(f148(x41661),x41664)),f328(f328(f7(a875,x41661,f876(x41661)),f156(x41661,x41663)),x41662)),x41665),f328(f328(f156(x41661,f328(f328(f148(x41661),x41664),x41663)),x41665),x41662)) % 154.70/154.55 [4170]E(f328(f328(f41(x41701,f882(f881(x41702,x41703),a870)),x41704),f328(f328(f8(f882(f881(x41703,x41702),a870),f882(f881(x41702,x41703),a870),x41701),f283(x41703,x41702)),x41705)),f328(f283(x41703,x41702),f328(f328(f41(x41701,f882(f881(x41703,x41702),a870)),x41704),x41705))) % 154.70/154.55 [4171]E(f328(f328(f42(x41711,f882(f881(x41712,x41713),a870)),x41714),f328(f328(f8(f882(f881(x41713,x41712),a870),f882(f881(x41712,x41713),a870),x41711),f283(x41713,x41712)),x41715)),f328(f283(x41713,x41712),f328(f328(f42(x41711,f882(f881(x41713,x41712),a870)),x41714),x41715))) % 154.70/154.55 [4226]E(f182(x42261,x42262,f328(f328(f18(x42261,f879(x42263),f879(x42262)),f328(f328(f8(f882(x42263,x42262),f882(f879(x42263),f879(x42262)),x42261),f206(x42263,x42262)),x42264)),x42265)),f182(x42261,x42263,x42265)) % 154.70/154.55 [4277]P1(f328(f328(f242(f882(x42771,a870)),f328(f328(f22(f882(x42771,a870)),f328(f307(x42772,x42771,x42773),x42774)),f328(f307(x42772,x42771,x42773),x42775))),f328(f307(x42772,x42771,x42773),f328(f328(f22(f882(x42772,a870)),x42774),x42775)))) % 154.70/154.55 [4427]E(f328(f153(f876(f881(x44271,x44272)),x44271,f117(f881(x44271,x44272)),f328(f328(f7(x44271,f882(f876(x44271),f876(f881(x44271,x44272))),f882(f876(x44271),f876(f881(x44271,x44272)))),f328(f328(f8(f882(f876(f881(x44271,x44272)),f876(f881(x44271,x44272))),f882(f882(f876(x44271),f876(f881(x44271,x44272))),f882(f876(x44271),f876(f881(x44271,x44272)))),x44271),f8(f876(f881(x44271,x44272)),f876(f881(x44271,x44272)),f876(x44271))),f328(f328(f8(f881(x44271,x44272),f882(f876(f881(x44271,x44272)),f876(f881(x44271,x44272))),x44271),f148(f881(x44271,x44272))),f328(f328(f7(x44271,x44272,f881(x44271,x44272)),f263(x44271,x44272)),x44273)))),f328(f328(f7(f876(x44271),f876(x44272),f876(f881(x44271,x44272))),f180(x44271,x44272)),x44274))),x44275),f328(f328(f180(x44271,x44272),x44275),f328(f328(f148(x44272),x44273),x44274))) % 154.70/154.55 [4132]E(f328(f328(f114(f882(x41321,a870)),f328(f282(x41322,x41321,x41323),x41324)),f328(f282(x41322,x41321,x41325),x41324)),f328(f282(x41322,x41321,f328(f328(f114(f882(f881(x41322,x41321),a870)),x41323),x41325)),x41324)) % 154.70/154.55 [4173]E(f328(f328(f125(f881(x41731,x41732)),f328(f328(f180(x41731,x41732),x41733),f328(f328(f173(x41732),f328(f193(f876(x41731)),x41733)),x41734))),f328(f328(f180(x41731,x41732),x41735),f328(f328(f135(x41732),f328(f193(f876(x41731)),x41733)),x41734))),f328(f328(f180(x41731,x41732),f328(f328(f125(x41731),x41733),x41735)),x41734)) % 154.70/154.55 [4280]E(f328(f328(f265(x42801,x42802),x42803),f328(f328(f18(x42801,f882(x42802,a870),f882(x42802,a870)),f328(f328(f8(f882(x42802,a870),f882(f882(x42802,a870),f882(x42802,a870)),x42801),f114(f882(x42802,a870))),x42804)),x42805)),f328(f328(f114(f882(f881(x42801,x42802),a870)),f328(f328(f265(x42801,x42802),x42803),x42804)),f328(f328(f265(x42801,x42802),x42803),x42805))) % 154.70/154.55 [4281]E(f328(f328(f265(x42811,x42812),x42813),f328(f328(f18(x42811,f882(x42812,a870),f882(x42812,a870)),f328(f328(f8(f882(x42812,a870),f882(f882(x42812,a870),f882(x42812,a870)),x42811),f22(f882(x42812,a870))),x42814)),x42815)),f328(f328(f22(f882(f881(x42811,x42812),a870)),f328(f328(f265(x42811,x42812),x42813),x42814)),f328(f328(f265(x42811,x42812),x42813),x42815))) % 154.70/154.55 [4282]E(f328(f328(f265(x42821,x42822),x42823),f328(f328(f18(x42821,f882(x42822,a870),f882(x42822,a870)),f328(f328(f8(f882(x42822,a870),f882(f882(x42822,a870),f882(x42822,a870)),x42821),f105(f882(x42822,a870))),x42824)),x42825)),f328(f328(f105(f882(f881(x42821,x42822),a870)),f328(f328(f265(x42821,x42822),x42823),x42824)),f328(f328(f265(x42821,x42822),x42823),x42825))) % 154.70/154.55 [4286]E(f328(f328(f41(x42861,f882(x42862,a870)),x42863),f328(f328(f7(x42861,f882(x42862,a870),f882(x42862,a870)),f328(f328(f8(f882(x42862,a870),f882(f882(x42862,a870),f882(x42862,a870)),x42861),f22(f882(x42862,a870))),x42864)),x42865)),f328(f328(f22(f882(x42862,a870)),f328(f328(f41(x42861,f882(x42862,a870)),x42863),x42864)),x42865)) % 154.70/154.55 [4287]E(f328(f328(f41(x42871,f882(x42872,a870)),x42873),f328(f328(f7(x42871,f882(x42872,a870),f882(x42872,a870)),f328(f328(f8(f882(x42872,a870),f882(f882(x42872,a870),f882(x42872,a870)),x42871),f105(f882(x42872,a870))),x42874)),x42875)),f328(f328(f105(f882(x42872,a870)),f328(f328(f41(x42871,f882(x42872,a870)),x42873),x42874)),x42875)) % 154.70/154.55 [4288]E(f328(f328(f42(x42881,f882(x42882,a870)),x42883),f328(f328(f7(x42881,f882(x42882,a870),f882(x42882,a870)),f328(f328(f8(f882(x42882,a870),f882(f882(x42882,a870),f882(x42882,a870)),x42881),f114(f882(x42882,a870))),x42884)),x42885)),f328(f328(f114(f882(x42882,a870)),f328(f328(f42(x42881,f882(x42882,a870)),x42883),x42884)),x42885)) % 154.70/154.55 [4292]E(f328(f328(f41(x42921,f882(x42922,a870)),x42923),f328(f328(f18(x42921,f882(x42922,a870),f882(x42922,a870)),f328(f328(f8(f882(x42922,a870),f882(f882(x42922,a870),f882(x42922,a870)),x42921),f114(f882(x42922,a870))),x42924)),x42925)),f328(f328(f114(f882(x42922,a870)),f328(f328(f41(x42921,f882(x42922,a870)),x42923),x42924)),f328(f328(f41(x42921,f882(x42922,a870)),x42923),x42925))) % 154.70/154.55 [4293]E(f328(f328(f42(x42931,f882(x42932,a870)),x42933),f328(f328(f18(x42931,f882(x42932,a870),f882(x42932,a870)),f328(f328(f8(f882(x42932,a870),f882(f882(x42932,a870),f882(x42932,a870)),x42931),f105(f882(x42932,a870))),x42934)),x42935)),f328(f328(f105(f882(x42932,a870)),f328(f328(f42(x42931,f882(x42932,a870)),x42933),x42934)),f328(f328(f42(x42931,f882(x42932,a870)),x42933),x42935))) % 154.70/154.55 [4307]E(f328(f328(f41(x43071,f882(x43072,a870)),x43073),f328(f328(f18(x43071,f882(x43072,a870),f882(x43072,a870)),f328(f328(f8(f882(x43072,a870),f882(f882(x43072,a870),f882(x43072,a870)),x43071),f114(f882(x43072,a870))),x43074)),x43075)),f328(f328(f114(f882(x43072,a870)),f39(f882(x43072,a870),f328(f307(x43071,f882(x43072,a870),x43074),x43073))),f39(f882(x43072,a870),f328(f307(x43071,f882(x43072,a870),x43075),x43073)))) % 154.70/154.55 [4308]E(f328(f328(f42(x43081,f882(x43082,a870)),x43083),f328(f328(f18(x43081,f882(x43082,a870),f882(x43082,a870)),f328(f328(f8(f882(x43082,a870),f882(f882(x43082,a870),f882(x43082,a870)),x43081),f105(f882(x43082,a870))),x43084)),x43085)),f328(f328(f105(f882(x43082,a870)),f40(f882(x43082,a870),f328(f307(x43081,f882(x43082,a870),x43084),x43083))),f40(f882(x43082,a870),f328(f307(x43081,f882(x43082,a870),x43085),x43083)))) % 154.70/154.55 [4342]E(f328(f328(f135(x43421),f328(f193(f876(x43421)),f175(x43421,x43422,f328(f328(f151(x43423,x43421),x43424),x43425)))),f328(f328(f151(x43423,x43421),x43424),x43425)),f328(f328(f151(x43423,x43421),x43424),f328(f328(f135(x43423),f328(f193(f876(x43423)),f175(x43423,f328(f73(x43421,a870,x43423,x43422),x43424),x43425))),x43425))) % 154.70/154.55 [4216]E(f328(f328(f125(f881(x42161,x42162)),f328(f328(f180(x42161,x42162),f328(f328(f173(x42161),f328(f193(f876(x42162)),x42163)),x42164)),x42163)),f328(f328(f180(x42161,x42162),f328(f328(f135(x42161),f328(f193(f876(x42162)),x42163)),x42164)),x42165)),f328(f328(f180(x42161,x42162),x42164),f328(f328(f125(x42162),x42163),x42165))) % 154.70/154.55 [4334]E(f85(x43341,f328(f328(f18(x43341,a870,a870),f328(f328(f8(a870,f882(a870,a870),x43341),a326),f328(f328(f7(x43341,f882(x43341,a870),a870),f330(x43341)),x43342))),f328(f328(f7(x43341,x43343,a870),f328(f328(f8(x43343,f882(x43343,a870),x43341),a325),x43344)),x43345))),f328(f77(x43341,x43343,x43342,x43344),x43345)) % 154.70/154.55 [4386]E(f328(f328(f86(a1,x43861),f328(f107(a1),f328(f328(f80(a1),x43862),a101))),f328(f328(f18(a1,x43861,x43861),f328(f328(f7(a1,x43861,f882(x43861,x43861)),f328(f328(f8(a870,f882(x43861,f882(x43861,x43861)),a1),f100(x43861)),a197)),f189(x43861,x43863,x43864,x43865))),f328(f328(f8(a875,x43861,a1),x43864),f328(f328(f7(a1,a875,a875),f328(f328(f8(a875,f882(a875,a875),a1),f80(a875)),a108)),x43865)))),f189(x43861,x43863,x43864,f328(f328(f80(a875),f328(f107(a875),x43862)),x43865))) % 154.70/154.55 [4423]E(f328(f176(x44231,x44232),f328(f328(f151(f881(x44231,x44233),f881(x44231,x44232)),f328(f267(x44231,x44233,f881(x44231,x44232)),f328(f328(f7(x44231,f882(x44233,x44232),f882(x44233,f881(x44231,x44232))),f328(f328(f8(f882(x44232,f881(x44231,x44232)),f882(f882(x44233,x44232),f882(x44233,f881(x44231,x44232))),x44231),f8(x44232,f881(x44231,x44232),x44233)),f263(x44231,x44232))),x44234))),x44235)),f328(f73(f879(x44233),f879(x44232),x44231,f328(f206(x44233,x44232),x44234)),f328(f176(x44231,x44233),x44235))) % 154.70/154.55 [4379]E(f182(x43791,x43792,f328(f328(f18(x43791,f879(x43792),f879(x43792)),f328(f328(f18(x43791,f879(x43792),f882(f879(x43792),f879(x43792))),f328(f328(f8(a870,f882(f879(x43792),f882(f879(x43792),f879(x43792))),x43791),f100(f879(x43792))),x43793)),x43794)),x43795)),f328(f328(f114(f882(x43791,a870)),f328(f328(f105(f882(x43791,a870)),f182(x43791,x43792,x43794)),f328(f248(x43791),x43793))),f328(f328(f105(f882(x43791,a870)),f182(x43791,x43792,x43795)),f328(f248(x43791),f328(f328(f8(a870,a870,x43791),a323),x43793))))) % 154.70/154.55 [4421]E(f328(f328(f86(a1,x44211),f328(f107(a1),f328(f328(f80(a1),x44212),a101))),f328(f328(f18(a1,x44211,x44211),f328(f328(f7(a1,x44211,f882(x44211,x44211)),f328(f328(f8(a870,f882(x44211,f882(x44211,x44211)),a1),f100(x44211)),a197)),f328(f188(x44211,x44213,x44214),x44215))),f328(f328(f18(a1,x44211,x44211),f328(f328(f8(a875,f882(x44211,x44211),a1),x44214),f328(f328(f7(a1,a875,a875),f328(f328(f8(a875,f882(a875,a875),a1),f80(a875)),a108)),x44215))),f328(f328(f8(a875,x44211,a1),f188(x44211,x44213,x44214)),f328(f328(f7(a1,a875,a875),f328(f328(f8(a875,f882(a875,a875),a1),f80(a875)),a108)),x44215))))),f328(f188(x44211,x44213,x44214),f328(f328(f80(a875),f328(f107(a875),x44212)),x44215))) % 154.70/154.55 [4456]E(f328(f248(f881(x44561,x44562)),f328(f267(x44561,x44562,a870),f328(f328(f8(f882(x44562,f882(x44563,a870)),f882(x44562,a870),x44561),f328(f8(f882(x44563,a870),a870,x44562),f87(x44563))),f328(f328(f7(x44561,f882(x44562,f882(x44563,a870)),f882(x44562,f882(x44563,a870))),f328(f328(f8(f882(f882(x44563,a870),f882(x44563,a870)),f882(f882(x44562,f882(x44563,a870)),f882(x44562,f882(x44563,a870))),x44561),f8(f882(x44563,a870),f882(x44563,a870),x44562)),f328(f328(f8(f882(x44563,f882(a870,a870)),f882(f882(x44563,a870),f882(x44563,a870)),x44561),f18(x44563,a870,a870)),f328(f328(f8(f882(x44563,a870),f882(x44563,f882(a870,a870)),x44561),f328(f8(a870,f882(a870,a870),x44563),a326)),f328(f328(f7(x44561,f882(f881(x44561,x44563),a870),f882(x44563,a870)),f328(f328(f8(f882(x44563,f882(f882(f881(x44561,x44563),a870),a870)),f882(f882(f881(x44561,x44563),a870),f882(x44563,a870)),x44561),f7(x44563,f882(f881(x44561,x44563),a870),a870)),f328(f328(f8(f882(x44563,f881(x44561,x44563)),f882(x44563,f882(f882(f881(x44561,x44563),a870),a870)),x44561),f328(f8(f881(x44561,x44563),f882(f882(f881(x44561,x44563),a870),a870),x44563),f330(f881(x44561,x44563)))),f263(x44561,x44563)))),x44564))))),f328(f328(f7(x44562,f882(f881(x44563,x44562),a870),f882(x44563,a870)),f328(f328(f8(f882(x44563,f882(f882(f881(x44563,x44562),a870),a870)),f882(f882(f881(x44563,x44562),a870),f882(x44563,a870)),x44562),f7(x44563,f882(f881(x44563,x44562),a870),a870)),f328(f328(f8(f882(x44563,f881(x44563,x44562)),f882(x44563,f882(f882(f881(x44563,x44562),a870),a870)),x44562),f328(f8(f881(x44563,x44562),f882(f882(f881(x44563,x44562),a870),a870),x44563),f330(f881(x44563,x44562)))),f328(f7(x44563,x44562,f881(x44563,x44562)),f263(x44563,x44562))))),x44565))))),f328(f328(f285(x44561,x44563,x44562),x44564),x44565)) % 154.70/154.55 [4532]~E(f29(x45321,x45322,x45323),f30(x45324,x45325,x45326)) % 154.70/154.55 [3984]E(f130(x39841,x39842,x39843,x39844,f127(x39842,x39845,x39846)),f328(f328(x39844,x39845),x39846)) % 154.70/154.55 [4200]E(f185(x42001,x42002,f183(x42001,x42002,x42003,x42004),x42005,x42006),f183(x42001,x42002,x42003,f185(x42001,x42002,x42004,x42005,x42006))) % 154.70/154.55 [4323]E(f328(f73(f881(x43231,x43232),x43232,f881(x43233,x43234),f266(x43231,x43232)),f268(x43233,x43231,x43234,x43232,x43235,x43236)),f328(f73(x43234,x43232,f881(x43233,x43234),x43236),f266(x43233,x43234))) % 154.70/154.55 [4324]E(f328(f73(f881(x43241,x43242),x43241,f881(x43243,x43244),f262(x43241,x43242)),f268(x43243,x43241,x43244,x43242,x43245,x43246)),f328(f73(x43243,x43241,f881(x43243,x43244),x43245),f262(x43243,x43244))) % 154.70/154.55 [3924]E(f328(f328(f73(x39241,x39242,x39243,x39244),x39245),x39246),f328(x39244,f328(x39245,x39246))) % 154.70/154.55 [3720]E(f328(f328(f267(x37201,x37202,x37203),x37204),f328(f328(f263(x37201,x37202),x37205),x37206)),f328(f328(x37204,x37205),x37206)) % 154.70/154.55 [3780]E(f328(f328(f328(f8(x37801,x37802,x37803),x37804),x37805),x37806),f328(x37804,f328(x37805,x37806))) % 154.70/154.55 [3781]E(f328(f328(f328(f7(x37811,x37812,x37813),x37814),x37815),x37816),f328(f328(x37814,x37816),x37815)) % 154.70/154.55 [3798]E(f328(f328(f328(f18(x37981,x37982,x37983),x37984),x37985),x37986),f328(f328(x37984,x37986),f328(x37985,x37986))) % 154.70/154.55 [3820]E(f328(f153(x38201,x38202,x38203,x38204),f328(f328(f148(x38202),x38205),x38206)),f328(f328(x38204,x38205),x38206)) % 154.70/154.55 [3860]E(f168(f881(x38601,x38602),f328(f328(f240(a875),x38603),x38604),f328(f328(f263(x38601,x38602),x38605),x38606)),f328(f328(f180(x38601,x38602),f168(x38601,x38603,x38605)),f168(x38602,x38604,x38606))) % 154.70/154.55 [3928]E(f328(f328(f148(f881(x39281,x39282)),f328(f328(f263(x39281,x39282),x39283),x39284)),f328(f328(f180(x39281,x39282),x39285),x39286)),f328(f328(f180(x39281,x39282),f328(f328(f148(x39281),x39283),x39285)),f328(f328(f148(x39282),x39284),x39286))) % 154.70/154.55 [3930]E(f328(f328(f151(x39301,x39302),x39303),f328(f328(f156(x39301,x39304),x39305),x39306)),f328(f328(f156(x39302,f328(f328(f151(x39301,x39302),x39303),x39304)),x39305),f328(x39303,x39306))) % 154.70/154.55 [3973]E(f328(f139(x39731,x39732,x39733,x39734),f328(f328(f148(x39732),x39735),x39736)),f328(f139(x39731,x39732,x39733,f328(f328(x39733,x39734),x39735)),x39736)) % 154.70/154.55 [4000]E(f270(x40001,x40002,x40003,x40004,f328(f328(f263(x40001,x40002),x40005),x40006)),f328(f328(x40004,x40005),x40006)) % 154.70/154.55 [4083]E(f328(f328(f41(x40831,f882(x40832,a870)),x40833),f328(f73(x40834,f882(x40832,a870),x40831,x40835),x40836)),f328(f328(f41(x40834,f882(x40832,a870)),f328(f307(x40831,x40834,x40836),x40833)),x40835)) % 154.70/154.55 [4135]E(f328(f328(f151(x41351,x41352),x41353),f328(f328(f151(x41354,x41351),x41355),x41356)),f328(f328(f151(x41354,x41352),f328(f73(x41351,x41352,x41354,x41353),x41355)),x41356)) % 154.70/154.55 [4137]E(f328(f328(f206(x41371,x41372),x41373),f328(f328(f206(x41374,x41371),x41375),x41376)),f328(f328(f206(x41374,x41372),f328(f73(x41371,x41372,x41374,x41373),x41375)),x41376)) % 154.70/154.55 [4142]E(f328(f307(x41421,x41422,f328(f73(x41423,x41422,x41421,x41424),x41425)),x41426),f328(f307(x41423,x41422,x41424),f328(f307(x41421,x41423,x41425),x41426))) % 154.70/154.55 [4143]E(f328(f308(x41431,x41432,f328(f73(x41433,x41432,x41431,x41434),x41435)),x41436),f328(f308(x41431,x41433,x41435),f328(f308(x41433,x41432,x41434),x41436))) % 154.70/154.55 [4172]E(f183(x41721,x41722,x41723,f328(f328(f328(f72(x41721,f879(x41722)),x41724),x41725),f328(f235(x41722),x41726))),f328(f328(f328(f72(x41721,f879(x41722)),f183(x41721,x41722,x41723,x41724)),x41725),f328(f235(x41722),x41726))) % 154.70/154.55 [4174]E(f328(f139(x41741,x41742,x41743,f328(f139(x41741,x41742,x41743,x41744),x41745)),x41746),f328(f139(x41741,x41742,x41743,x41744),f328(f328(f125(x41742),x41745),x41746))) % 154.70/154.55 [4313]E(f328(f268(x43131,x43131,x43132,x43133,f34(x43131),x43134),f328(f328(f263(x43131,x43132),x43135),x43136)),f328(f328(f263(x43131,x43133),x43135),f328(x43134,x43136))) % 154.70/154.55 [4314]E(f328(f268(x43141,x43142,x43143,x43143,x43144,f34(x43143)),f328(f328(f263(x43141,x43143),x43145),x43146)),f328(f328(f263(x43142,x43143),f328(x43144,x43145)),x43146)) % 154.70/154.55 [4404]E(f328(f328(f151(f881(x44041,x44042),f881(x44041,x44043)),f328(f267(x44041,x44042,f881(x44041,x44043)),f328(f328(f7(x44041,f882(x44042,x44043),f882(x44042,f881(x44041,x44043))),f328(f328(f8(f882(x44043,f881(x44041,x44043)),f882(f882(x44042,x44043),f882(x44042,f881(x44041,x44043))),x44041),f8(x44043,f881(x44041,x44043),x44042)),f263(x44041,x44043))),x44044))),f328(f328(f180(x44041,x44042),x44045),x44046)),f328(f328(f180(x44041,x44043),x44045),f328(f328(f151(x44042,x44043),x44044),x44046))) % 154.70/154.55 [3785]E(f98(x37851,x37852,x37853,f328(f328(f328(f92(x37851),x37854),x37855),x37856)),f328(f328(f328(x37853,x37854),x37855),x37856)) % 154.70/154.55 [3786]E(f99(x37861,x37862,x37863,f328(f328(f328(f92(x37861),x37864),x37865),x37866)),f328(f328(f328(x37863,x37864),x37865),x37866)) % 154.70/154.55 [3983]E(f328(f328(f73(x39831,x39832,x39833,f328(f16(x39832,x39831),x39834)),x39835),x39836),x39834) % 154.70/154.55 [4019]E(f328(f307(x40191,x40192,x40193),f328(f307(x40194,x40191,x40195),x40196)),f328(f307(x40194,x40192,f328(f328(f8(x40191,x40192,x40194),x40193),x40195)),x40196)) % 154.70/154.55 [4025]E(f328(f328(f41(x40251,f882(x40252,a870)),f328(f307(x40253,x40251,x40254),x40255)),x40256),f328(f328(f41(x40253,f882(x40252,a870)),x40255),f328(f328(f8(x40251,f882(x40252,a870),x40253),x40256),x40254))) % 154.70/154.55 [4026]E(f328(f328(f42(x40261,f882(x40262,a870)),f328(f307(x40263,x40261,x40264),x40265)),x40266),f328(f328(f42(x40263,f882(x40262,a870)),x40265),f328(f328(f8(x40261,f882(x40262,a870),x40263),x40266),x40264))) % 154.70/154.55 [4027]E(f328(f328(f41(x40271,f882(x40272,a870)),x40273),f328(f328(f8(x40274,f882(x40272,a870),x40271),x40275),x40276)),f328(f328(f41(x40274,f882(x40272,a870)),f328(f307(x40271,x40274,x40276),x40273)),x40275)) % 154.70/154.55 [4028]E(f328(f328(f42(x40281,f882(x40282,a870)),x40283),f328(f328(f8(x40284,f882(x40282,a870),x40281),x40285),x40286)),f328(f328(f42(x40284,f882(x40282,a870)),f328(f307(x40281,x40284,x40286),x40283)),x40285)) % 154.70/154.55 [4085]E(f328(f328(f41(x40851,f882(x40852,a870)),x40853),f328(f328(f8(f882(x40854,a870),f882(x40852,a870),x40851),f307(x40854,x40852,x40855)),x40856)),f328(f307(x40854,x40852,x40855),f328(f328(f41(x40851,f882(x40854,a870)),x40853),x40856))) % 154.70/154.55 [4086]E(f328(f328(f41(x40861,f882(x40862,a870)),x40863),f328(f328(f8(f882(x40864,a870),f882(x40862,a870),x40861),f308(x40862,x40864,x40865)),x40866)),f328(f308(x40862,x40864,x40865),f328(f328(f41(x40861,f882(x40864,a870)),x40863),x40866))) % 154.70/154.55 [4087]E(f328(f328(f42(x40871,f882(x40872,a870)),x40873),f328(f328(f8(f882(x40874,a870),f882(x40872,a870),x40871),f308(x40872,x40874,x40875)),x40876)),f328(f308(x40872,x40874,x40875),f328(f328(f42(x40871,f882(x40874,a870)),x40873),x40876))) % 154.70/154.55 [4088]E(f328(f328(f41(x40881,f882(x40882,a870)),x40883),f328(f328(f8(f882(x40884,a870),f882(x40882,a870),x40881),f282(x40884,x40882,x40885)),x40886)),f328(f282(x40884,x40882,x40885),f328(f328(f41(x40881,f882(x40884,a870)),x40883),x40886))) % 154.70/154.55 [4180]E(f328(f139(x41801,x41802,f328(f7(x41802,x41801,x41801),x41803),x41804),f328(f166(x41802),f328(f328(f148(x41802),x41805),x41806))),f328(f328(x41803,x41805),f328(f139(x41801,x41802,f328(f7(x41802,x41801,x41801),x41803),x41804),f328(f166(x41802),x41806)))) % 154.70/154.55 [4239]E(f328(f328(f18(f881(x42391,x42392),x42392,x42393),f328(f328(f8(x42394,f882(x42392,x42393),f881(x42391,x42392)),x42395),f328(f328(f8(x42391,x42394,f881(x42391,x42392)),x42396),f262(x42391,x42392)))),f266(x42391,x42392)),f328(f267(x42391,x42392,x42393),f328(f328(f8(x42394,f882(x42392,x42393),x42391),x42395),x42396))) % 154.70/154.55 [4246]E(f328(f139(x42461,x42462,f328(f7(x42462,x42461,x42461),x42463),f328(f139(x42461,x42462,f328(f7(x42462,x42461,x42461),x42463),x42464),f328(f166(x42462),x42465))),f328(f166(x42462),x42466)),f328(f139(x42461,x42462,f328(f7(x42462,x42461,x42461),x42463),x42464),f328(f166(x42462),f328(f328(f125(x42462),x42466),x42465)))) % 154.70/154.55 [4248]E(f328(f328(f151(f881(x42481,x42482),f881(x42483,x42482)),f328(f267(x42481,x42482,f881(x42483,x42482)),f328(f328(f8(x42483,f882(x42482,f881(x42483,x42482)),x42481),f263(x42483,x42482)),x42484))),f328(f328(f180(x42481,x42482),x42485),x42486)),f328(f328(f180(x42483,x42482),f328(f328(f151(x42481,x42483),x42484),x42485)),x42486)) % 154.70/154.55 [4296]P1(f328(f328(f242(f882(x42961,a870)),f328(f282(x42962,x42961,x42963),f328(f328(f42(x42964,f882(x42962,a870)),x42965),x42966))),f328(f328(f42(x42964,f882(x42961,a870)),x42965),f328(f328(f8(f882(x42962,a870),f882(x42961,a870),x42964),f282(x42962,x42961,x42963)),x42966)))) % 154.70/154.55 [4098]E(f328(f328(f180(x40981,x40982),f328(f328(f156(x40981,x40983),x40984),f328(f262(x40981,x40982),x40985))),f328(f328(f156(x40982,x40986),x40984),f328(f266(x40981,x40982),x40985))),f328(f328(f156(f881(x40981,x40982),f328(f328(f180(x40981,x40982),x40983),x40986)),x40984),x40985)) % 154.70/154.55 [4161]E(f328(f328(f114(f882(f881(x41611,x41612),a870)),f328(f328(f285(x41611,x41613,x41612),x41614),x41615)),f328(f328(f285(x41611,x41613,x41612),x41614),x41616)),f328(f328(f285(x41611,x41613,x41612),x41614),f328(f328(f114(f882(f881(x41613,x41612),a870)),x41615),x41616))) % 154.70/154.55 [4259]E(f328(f328(f306(f881(x42591,x42592)),f328(f328(f263(x42591,x42592),x42593),x42594)),f328(f328(f114(f882(f881(x42591,x42592),a870)),f328(f328(f265(x42591,x42592),x42595),f328(f16(f882(x42592,a870),x42591),f328(f328(f306(x42592),x42594),x42596)))),f328(f328(f265(x42591,x42592),f328(f328(f306(x42591),x42593),x42595)),f328(f16(f882(x42592,a870),x42591),x42596)))),f328(f328(f265(x42591,x42592),f328(f328(f306(x42591),x42593),x42595)),f328(f16(f882(x42592,a870),x42591),f328(f328(f306(x42592),x42594),x42596)))) % 154.70/154.55 [4337]E(f328(f328(f105(f882(x43371,a870)),f328(f308(x43371,x43372,f328(f73(f881(x43372,x43373),x43372,x43371,f262(x43372,x43373)),x43374)),x43375)),f328(f308(x43371,x43373,f328(f73(f881(x43372,x43373),x43373,x43371,f266(x43372,x43373)),x43374)),x43376)),f328(f308(x43371,f881(x43372,x43373),x43374),f328(f328(f265(x43372,x43373),x43375),f328(f16(f882(x43373,a870),x43372),x43376)))) % 154.70/154.55 [4082]E(f328(f328(f328(f72(x40821,x40822),f328(f328(f328(f72(x40821,x40822),x40823),x40824),x40825)),x40824),x40826),f328(f328(f328(f72(x40821,x40822),x40823),x40824),x40826)) % 154.70/154.55 [4186]E(f328(f328(f114(f882(f881(x41861,x41862),a870)),f328(f328(f285(x41861,x41863,x41862),x41864),x41865)),f328(f328(f285(x41861,x41863,x41862),x41866),x41865)),f328(f328(f285(x41861,x41863,x41862),f328(f328(f114(f882(f881(x41861,x41863),a870)),x41864),x41866)),x41865)) % 154.70/154.55 [4321]E(f328(f328(f41(x43211,f882(x43212,a870)),x43213),f328(f328(f7(x43211,f882(x43214,f882(x43212,a870)),f882(x43212,a870)),f328(f328(f8(f882(x43214,a870),f882(f882(x43214,f882(x43212,a870)),f882(x43212,a870)),x43211),f41(x43214,f882(x43212,a870))),x43215)),x43216)),f328(f328(f41(x43214,f882(x43212,a870)),f328(f328(f41(x43211,f882(x43214,a870)),x43213),x43215)),x43216)) % 154.70/154.55 [4322]E(f328(f328(f42(x43221,f882(x43222,a870)),x43223),f328(f328(f7(x43221,f882(x43224,f882(x43222,a870)),f882(x43222,a870)),f328(f328(f8(f882(x43224,a870),f882(f882(x43224,f882(x43222,a870)),f882(x43222,a870)),x43221),f42(x43224,f882(x43222,a870))),x43225)),x43226)),f328(f328(f42(x43224,f882(x43222,a870)),f328(f328(f41(x43221,f882(x43224,a870)),x43223),x43225)),x43226)) % 154.70/154.55 [4374]E(f328(f267(x43741,x43742,f881(x43743,x43744)),f328(f328(f7(x43741,f882(x43742,x43744),f882(x43742,f881(x43743,x43744))),f328(f328(f8(f882(x43744,f881(x43743,x43744)),f882(f882(x43742,x43744),f882(x43742,f881(x43743,x43744))),x43741),f8(x43744,f881(x43743,x43744),x43742)),f328(f328(f8(x43743,f882(x43744,f881(x43743,x43744)),x43741),f263(x43743,x43744)),x43745))),x43746)),f268(x43741,x43743,x43742,x43744,x43745,x43746)) % 154.70/154.55 [4295]E(f328(f328(f328(f72(x42951,f879(x42952)),f186(x42951,x42952,x42953,f328(f328(f22(f882(x42951,a870)),x42954),f328(f328(f306(x42951),x42955),f192(f882(x42951,a870)))))),x42955),x42956),f328(f328(f328(f72(x42951,f879(x42952)),f186(x42951,x42952,x42953,x42954)),x42955),x42956)) % 154.70/154.55 [4399]E(f328(f307(x43991,x43992,f328(f328(f18(x43991,x43992,x43992),f328(f328(f18(x43991,x43992,f882(x43992,x43992)),f328(f328(f8(a870,f882(x43992,f882(x43992,x43992)),x43991),f100(x43992)),x43993)),x43994)),x43995)),x43996),f328(f328(f114(f882(x43992,a870)),f328(f307(x43991,x43992,x43994),f328(f328(f105(f882(x43991,a870)),x43996),f328(f248(x43991),x43993)))),f328(f307(x43991,x43992,x43995),f328(f328(f105(f882(x43991,a870)),x43996),f328(f248(x43991),f328(f328(f8(a870,a870,x43991),a323),x43993)))))) % 154.70/154.55 [4410]E(f328(f307(x44101,f881(x44102,x44103),f328(f328(f18(x44101,x44103,f881(x44102,x44103)),f328(f328(f8(x44102,f882(x44103,f881(x44102,x44103)),x44101),f263(x44102,x44103)),x44104)),x44105)),x44106),f328(f328(f265(x44102,x44103),f328(f307(x44101,x44102,x44104),x44106)),f328(f328(f8(f882(x44101,a870),f882(x44103,a870),x44102),f307(x44101,x44103,x44105)),f328(f328(f7(x44102,f882(x44101,a870),f882(x44101,a870)),f328(f328(f8(f882(x44101,a870),f882(f882(x44101,a870),f882(x44101,a870)),x44102),f105(f882(x44101,a870))),f328(f328(f8(f882(x44102,a870),f882(x44101,a870),x44102),f308(x44101,x44102,x44104)),f328(f328(f7(x44102,f882(x44102,a870),f882(x44102,a870)),f306(x44102)),f192(f882(x44102,a870)))))),x44106)))) % 154.70/154.55 [4356]E(f328(f266(x43561,x43562),f328(f268(x43563,x43561,x43564,x43562,x43565,x43566),x43567)),f328(x43566,f328(f266(x43563,x43564),x43567))) % 154.70/154.55 [4357]E(f328(f262(x43571,x43572),f328(f268(x43573,x43571,x43574,x43572,x43575,x43576),x43577)),f328(x43575,f328(f262(x43573,x43574),x43577))) % 154.70/154.55 [4060]E(f328(f328(f180(x40601,x40602),f328(f328(f156(x40601,x40603),x40604),x40605)),f328(f328(f156(x40602,x40606),x40604),x40607)),f328(f328(f156(f881(x40601,x40602),f328(f328(f180(x40601,x40602),x40603),x40606)),x40604),f328(f328(f263(x40601,x40602),x40605),x40607))) % 154.70/154.55 [4128]E(f328(f328(f328(f269(x41281,x41282,x41283,x41284),x41285),x41286),x41287),f328(f328(f267(x41282,x41283,x41284),x41286),f328(x41285,x41287))) % 154.70/154.55 [4141]E(f328(f328(f328(f269(x41411,x41412,x41413,x41414),x41415),x41416),x41417),f328(f328(x41416,f328(f262(x41412,x41413),f328(x41415,x41417))),f328(f266(x41412,x41413),f328(x41415,x41417)))) % 154.70/154.55 [4176]E(f185(x41761,x41762,f328(f328(f328(f72(x41761,f879(x41762)),x41763),x41764),f328(f235(x41762),x41765)),x41766,x41767),f185(x41761,x41762,x41763,f328(f328(f148(x41761),x41764),x41766),f328(f328(f148(x41762),x41765),x41767))) % 154.70/154.55 [4194]E(f328(f73(x41941,x41942,x41943,x41944),f328(f73(x41945,x41941,x41943,x41946),x41947)),f328(f73(x41945,x41942,x41943,f328(f73(x41941,x41942,x41945,x41944),x41946)),x41947)) % 154.70/154.55 [4255]E(f328(f73(f879(x42551),f879(x42552),x42553,f328(f206(x42551,x42552),x42554)),f328(f328(f328(f72(x42553,f879(x42551)),x42555),x42556),f328(f235(x42551),x42557))),f328(f328(f328(f72(x42553,f879(x42552)),f328(f73(f879(x42551),f879(x42552),x42553,f328(f206(x42551,x42552),x42554)),x42555)),x42556),f328(f235(x42552),f328(x42554,x42557)))) % 154.70/154.55 [4381]E(f328(f268(x43811,x43812,x43813,x43813,x43814,f34(x43813)),f328(f268(x43811,x43811,x43815,x43813,f34(x43811),x43816),x43817)),f328(f328(f263(x43812,x43813),f328(x43814,f328(f262(x43811,x43815),x43817))),f328(x43816,f328(f266(x43811,x43815),x43817)))) % 154.70/154.55 [4382]E(f328(f268(x43821,x43821,x43822,x43823,f34(x43821),x43824),f328(f268(x43825,x43821,x43822,x43822,x43826,f34(x43822)),x43827)),f328(f328(f263(x43821,x43823),f328(x43826,f328(f262(x43825,x43822),x43827))),f328(x43824,f328(f266(x43825,x43822),x43827)))) % 154.70/154.55 [4397]E(f328(f268(x43971,x43972,x43973,x43973,x43974,f34(x43973)),f328(f268(x43975,x43971,x43973,x43973,x43976,f34(x43973)),x43977)),f328(f268(x43975,x43972,x43973,x43973,f328(f73(x43971,x43972,x43975,x43974),x43976),f34(x43973)),x43977)) % 154.70/154.55 [4398]E(f328(f268(x43981,x43981,x43982,x43983,f34(x43981),x43984),f328(f268(x43981,x43981,x43985,x43982,f34(x43981),x43986),x43987)),f328(f268(x43981,x43981,x43985,x43983,f34(x43981),f328(f73(x43982,x43983,x43985,x43984),x43986)),x43987)) % 154.70/154.55 [4407]E(f328(f268(x44071,x44072,x44073,x44073,x44074,f34(x44073)),f328(f268(x44071,x44071,x44075,x44073,f34(x44071),x44076),x44077)),f328(f268(x44072,x44072,x44075,x44073,f34(x44072),x44076),f328(f268(x44071,x44072,x44075,x44075,x44074,f34(x44075)),x44077))) % 154.70/154.55 [4095]E(f328(f328(f285(x40951,x40952,x40953),f328(f328(f285(x40951,x40954,x40952),x40955),x40956)),x40957),f328(f328(f285(x40951,x40954,x40953),x40955),f328(f328(f285(x40954,x40952,x40953),x40956),x40957))) % 154.70/154.55 [4167]E(f328(f328(f267(x41671,x41672,x41673),f328(f73(x41674,f882(x41672,x41673),x41671,x41675),x41676)),x41677),f328(f328(x41675,f328(x41676,f328(f262(x41671,x41672),x41677))),f328(f266(x41671,x41672),x41677))) % 154.70/154.55 [4219]E(f328(f73(x42191,x42192,x42193,x42194),f328(f328(f328(f72(x42193,x42191),x42195),x42196),x42197)),f328(f328(f328(f72(x42193,x42192),f328(f73(x42191,x42192,x42193,x42194),x42195)),x42196),f328(x42194,x42197))) % 154.70/154.55 [4251]E(f328(f139(x42511,x42512,f328(f7(x42512,x42511,x42511),x42513),x42514),f328(f166(x42512),f328(f328(f151(x42515,x42512),x42516),x42517))),f328(f139(x42511,x42515,f328(f7(x42515,x42511,x42511),f328(f73(x42512,f882(x42511,x42511),x42515,x42513),x42516)),x42514),f328(f166(x42515),x42517))) % 154.70/154.55 [4195]E(f328(f328(f41(x41951,f882(f881(x41952,x41953),a870)),x41954),f328(f328(f8(f882(f881(x41955,x41953),a870),f882(f881(x41952,x41953),a870),x41951),f328(f285(x41952,x41955,x41953),x41956)),x41957)),f328(f328(f285(x41952,x41955,x41953),x41956),f328(f328(f41(x41951,f882(f881(x41955,x41953),a870)),x41954),x41957))) % 154.70/154.55 [4343]E(f328(f328(f41(x43431,f882(f881(x43432,x43433),a870)),x43434),f328(f328(f7(x43431,f882(f881(x43435,x43433),a870),f882(f881(x43432,x43433),a870)),f328(f328(f8(f882(f881(x43432,x43435),a870),f882(f882(f881(x43435,x43433),a870),f882(f881(x43432,x43433),a870)),x43431),f285(x43432,x43435,x43433)),x43436)),x43437)),f328(f328(f285(x43432,x43435,x43433),f328(f328(f41(x43431,f882(f881(x43432,x43435),a870)),x43434),x43436)),x43437)) % 154.70/154.55 [4344]E(f328(f139(x43441,x43442,f328(f328(f7(x43441,f882(x43442,x43443),f882(x43442,x43441)),f328(f328(f8(f882(x43443,x43441),f882(f882(x43442,x43443),f882(x43442,x43441)),x43441),f8(x43443,x43441,x43442)),x43444)),x43445),x43446),x43447),f328(f139(x43441,x43443,x43444,x43446),f328(f328(f151(x43442,x43443),x43445),x43447))) % 154.70/154.55 [4408]E(f328(f328(f42(x44081,f882(x44082,a870)),x44083),f328(f328(f8(f882(x44084,f882(x44082,a870)),f882(x44082,a870),x44081),f328(f42(x44084,f882(x44082,a870)),x44085)),f328(f328(f7(x44081,f882(x44084,f882(x44082,a870)),f882(x44084,f882(x44082,a870))),f328(f328(f8(f882(f882(x44082,a870),f882(x44082,a870)),f882(f882(x44084,f882(x44082,a870)),f882(x44084,f882(x44082,a870))),x44081),f8(f882(x44082,a870),f882(x44082,a870),x44084)),f328(f328(f8(f882(x44082,a870),f882(f882(x44082,a870),f882(x44082,a870)),x44081),f114(f882(x44082,a870))),x44086))),x44087))),f328(f328(f114(f882(x44082,a870)),f328(f328(f42(x44081,f882(x44082,a870)),x44083),x44086)),f328(f328(f42(x44084,f882(x44082,a870)),x44085),x44087))) % 154.70/154.55 [4409]E(f328(f328(f41(x44091,f882(x44092,a870)),x44093),f328(f328(f8(f882(x44094,f882(x44092,a870)),f882(x44092,a870),x44091),f328(f41(x44094,f882(x44092,a870)),x44095)),f328(f328(f7(x44091,f882(x44094,f882(x44092,a870)),f882(x44094,f882(x44092,a870))),f328(f328(f8(f882(f882(x44092,a870),f882(x44092,a870)),f882(f882(x44094,f882(x44092,a870)),f882(x44094,f882(x44092,a870))),x44091),f8(f882(x44092,a870),f882(x44092,a870),x44094)),f328(f328(f8(f882(x44092,a870),f882(f882(x44092,a870),f882(x44092,a870)),x44091),f105(f882(x44092,a870))),x44096))),x44097))),f328(f328(f105(f882(x44092,a870)),f328(f328(f41(x44091,f882(x44092,a870)),x44093),x44096)),f328(f328(f41(x44094,f882(x44092,a870)),x44095),x44097))) % 154.70/154.55 [4402]E(f203(x44021,x44022,f328(f328(f328(x44023,x44024),x44025),x44026),f328(f328(f7(x44021,f881(a103,a103),f882(a103,f877(x44022))),f328(f328(f7(x44021,a103,f882(f881(a103,a103),f882(a103,f877(x44022)))),f328(f328(f7(x44021,a103,f882(a103,f882(f881(a103,a103),f882(a103,f877(x44022))))),x44027),x44024)),x44025)),x44026)),f328(f328(f328(f216(x44021,x44022,x44023,x44027),x44024),x44025),x44026)) % 154.70/154.55 [4415]E(f204(x44151,x44152,f328(f328(f328(x44153,x44154),x44155),x44156),f328(f328(f7(x44151,f881(a103,a103),f882(a103,f877(x44152))),f328(f328(f7(x44151,a103,f882(f881(a103,a103),f882(a103,f877(x44152)))),f328(f328(f7(x44151,a103,f882(a103,f882(f881(a103,a103),f882(a103,f877(x44152))))),x44157),x44154)),x44155)),x44156)),f218(x44151,x44152,x44153,x44157,x44154,x44155,x44156)) % 154.70/154.55 [4406]E(f201(x44061,x44062,f328(f328(f328(x44063,x44064),x44065),x44066),f328(f328(f7(x44061,f881(a103,a103),f882(a103,f877(f879(x44062)))),f328(f328(f7(x44061,a103,f882(f881(a103,a103),f882(a103,f877(f879(x44062))))),f328(f328(f7(x44061,a103,f882(a103,f882(f881(a103,a103),f882(a103,f877(f879(x44062)))))),x44067),x44064)),x44065)),x44066)),f328(f328(f328(f212(x44061,x44062,x44063,x44067),x44064),x44065),x44066)) % 154.70/154.55 [4418]E(f202(x44181,x44182,f328(f328(f328(x44183,x44184),x44185),x44186),f328(f328(f7(x44181,f881(a103,a103),f882(a103,f877(f879(x44182)))),f328(f328(f7(x44181,a103,f882(f881(a103,a103),f882(a103,f877(f879(x44182))))),f328(f328(f7(x44181,a103,f882(a103,f882(f881(a103,a103),f882(a103,f877(f879(x44182)))))),x44187),x44184)),x44185)),x44186)),f214(x44181,x44182,x44183,x44187,x44184,x44185,x44186)) % 154.70/154.55 [4315]E(f328(f268(x43151,x43152,x43153,x43154,x43155,x43156),f328(f328(f263(x43151,x43153),x43157),x43158)),f328(f328(f263(x43152,x43154),f328(x43155,x43157)),f328(x43156,x43158))) % 154.70/154.55 [4420]E(f328(f328(f151(f881(x44201,x44202),f881(x44203,x44204)),f328(f267(x44201,x44202,f881(x44203,x44204)),f328(f328(f7(x44201,f882(x44202,x44204),f882(x44202,f881(x44203,x44204))),f328(f328(f8(f882(x44204,f881(x44203,x44204)),f882(f882(x44202,x44204),f882(x44202,f881(x44203,x44204))),x44201),f8(x44204,f881(x44203,x44204),x44202)),f328(f328(f8(x44203,f882(x44204,f881(x44203,x44204)),x44201),f263(x44203,x44204)),x44205))),x44206))),f328(f328(f180(x44201,x44202),x44207),x44208)),f328(f328(f180(x44203,x44204),f328(f328(f151(x44201,x44203),x44205),x44207)),f328(f328(f151(x44202,x44204),x44206),x44208))) % 154.70/154.55 [4424]E(f328(f328(f151(f881(x44241,x44242),x44243),f328(f267(x44241,x44242,x44243),f328(f328(f8(f882(x44242,f881(x44241,x44244)),f882(x44242,x44243),x44241),f328(f8(f881(x44241,x44244),x44243,x44242),x44245)),f328(f328(f7(x44241,f882(x44242,x44244),f882(x44242,f881(x44241,x44244))),f328(f328(f8(f882(x44244,f881(x44241,x44244)),f882(f882(x44242,x44244),f882(x44242,f881(x44241,x44244))),x44241),f8(x44244,f881(x44241,x44244),x44242)),f263(x44241,x44244))),x44246)))),f328(f328(f180(x44241,x44242),x44247),x44248)),f328(f328(f151(f881(x44241,x44244),x44243),x44245),f328(f328(f180(x44241,x44244),x44247),f328(f328(f151(x44242,x44244),x44246),x44248)))) % 154.70/154.55 [4348]E(f328(f328(f151(f881(x43481,x43482),x43483),f328(f267(x43481,x43482,x43483),f328(f328(f8(f882(x43482,f881(x43484,x43482)),f882(x43482,x43483),x43481),f328(f8(f881(x43484,x43482),x43483,x43482),x43485)),f328(f328(f8(x43484,f882(x43482,f881(x43484,x43482)),x43481),f263(x43484,x43482)),x43486)))),f328(f328(f180(x43481,x43482),x43487),x43488)),f328(f328(f151(f881(x43484,x43482),x43483),x43485),f328(f328(f180(x43484,x43482),f328(f328(f151(x43481,x43484),x43486),x43487)),x43488))) % 154.70/154.55 [4306]E(f328(f328(f267(x43061,x43062,x43063),f328(f328(f8(f882(x43062,f881(x43064,x43065)),f882(x43062,x43063),x43061),f328(f8(f881(x43064,x43065),x43063,x43062),f328(f267(x43064,x43065,x43063),x43066))),x43067)),x43068),f328(f328(f267(x43064,x43065,x43063),x43066),f328(f328(f267(x43061,x43062,f881(x43064,x43065)),x43067),x43068))) % 154.70/154.55 [4426]E(f328(f328(f41(f881(x44261,x44262),f882(f881(x44263,x44264),a870)),f328(f328(f265(x44261,x44262),x44265),f328(f16(f882(x44262,a870),x44261),x44266))),f328(f267(x44261,x44262,f882(f881(x44263,x44264),a870)),f328(f328(f7(x44261,f882(x44262,f882(x44263,f882(x44264,a870))),f882(x44262,f882(f881(x44263,x44264),a870))),f328(f328(f8(f882(f882(x44263,f882(x44264,a870)),f882(f881(x44263,x44264),a870)),f882(f882(x44262,f882(x44263,f882(x44264,a870))),f882(x44262,f882(f881(x44263,x44264),a870))),x44261),f8(f882(x44263,f882(x44264,a870)),f882(f881(x44263,x44264),a870),x44262)),f328(f328(f8(f882(x44263,a870),f882(f882(x44263,f882(x44264,a870)),f882(f881(x44263,x44264),a870)),x44261),f265(x44263,x44264)),x44267))),f328(f328(f8(f882(x44264,a870),f882(x44263,f882(x44264,a870)),x44262),f16(f882(x44264,a870),x44263)),x44268)))),f328(f328(f265(x44263,x44264),f328(f328(f41(x44261,f882(x44263,a870)),x44265),x44267)),f328(f16(f882(x44264,a870),x44263),f328(f328(f41(x44262,f882(x44264,a870)),x44266),x44268)))) % 154.70/154.55 [4362]E(f328(f328(f269(x43621,x43622,x43623,x43624),f328(f328(f269(x43621,x43625,x43626,f881(x43622,x43623)),x43627),x43628)),x43629),f328(f328(f269(x43621,x43625,x43626,x43624),x43627),f328(f328(f7(x43625,f882(x43622,f882(x43623,x43624)),f882(x43626,x43624)),f328(f328(f8(f882(x43626,f881(x43622,x43623)),f882(f882(x43622,f882(x43623,x43624)),f882(x43626,x43624)),x43625),f269(x43626,x43622,x43623,x43624)),x43628)),x43629))) % 154.70/154.55 [4394]E(f328(f73(f881(x43941,x43942),f881(x43943,x43944),f881(x43945,x43946),f268(x43941,x43943,x43942,x43944,x43947,x43948)),f268(x43945,x43941,x43946,x43942,x43949,x439410)),f268(x43945,x43943,x43946,x43944,f328(f73(x43941,x43943,x43945,x43947),x43949),f328(f73(x43942,x43944,x43946,x43948),x439410))) % 154.70/154.55 [4400]E(f328(f268(x44001,x44002,x44003,x44004,x44005,x44006),f328(f268(x44007,x44001,x44008,x44003,x44009,x440010),x440011)),f328(f268(x44007,x44002,x44008,x44004,f328(f73(x44001,x44002,x44007,x44005),x44009),f328(f73(x44003,x44004,x44008,x44006),x440010)),x440011)) % 154.70/154.55 [6447]P9(a5000)+P1(f328(f328(f330(f881(a873,a871)),a681),f328(f170(f881(a873,a871)),a27))) % 154.70/154.55 [8453]P9(a5000)+~P1(f328(f328(f267(a873,a871,a870),f328(f16(f882(a871,a870),a873),a25)),a681)) % 154.70/154.55 [4568]~P92(x45681)+E(f91(x45681),a325) % 154.70/154.55 [4569]~P4(x45691)+P4(f879(x45691)) % 154.70/154.55 [4570]~P59(x45701)+P59(f879(x45701)) % 154.70/154.55 [4573]~P134(x45731)+~E(f78(x45731),f2(x45731)) % 154.70/154.55 [4575]~E(x45751,f2(a103))+E(f328(a20,x45751),f2(a1)) % 154.70/154.55 [4576]~E(x45761,f2(a1))+E(f82(a1,x45761),f2(a1)) % 154.70/154.55 [4582]~P140(x45821)+P32(x45821,f2(x45821)) % 154.70/154.55 [4584]~P105(x45841)+P16(x45841,f117(x45841)) % 154.70/154.55 [4593]P1(x45931)+P1(f328(a323,x45931)) % 154.70/154.55 [4636]~P140(x46361)+~P32(x46361,f78(x46361)) % 154.70/154.55 [4682]~P1(x46821)+~P1(f328(a323,x46821)) % 154.70/154.55 [4705]E(f328(a108,x47051),f2(a875))+~P1(f328(a197,x47051)) % 154.70/154.55 [4769]~P99(x47691)+P17(x47691,x47691,f114(x47691)) % 154.70/154.55 [4770]~P100(x47701)+P17(x47701,x47701,f105(x47701)) % 154.70/154.55 [4771]~P94(x47711)+P17(x47711,x47711,f81(x47711)) % 154.70/154.55 [4772]~P105(x47721)+P17(x47721,x47721,f240(x47721)) % 154.70/154.55 [4773]~P105(x47731)+P17(x47731,x47731,f241(x47731)) % 154.70/154.55 [4774]~P70(x47741)+P18(x47741,x47741,f81(x47741)) % 154.70/154.55 [4579]~E(x45791,f2(a875))+E(f328(f104(a1),x45791),f2(a1)) % 154.70/154.55 [4586]~P90(x45861)+E(f328(f107(x45861),a83),f2(x45861)) % 154.70/154.55 [4589]~E(f596(x45891),f2(a875))+E(f328(f163(a875),x45891),f2(a875)) % 154.70/154.55 [4590]~P108(x45901)+E(f244(x45901,f242(x45901)),f240(x45901)) % 154.70/154.55 [4591]~P108(x45911)+E(f245(x45911,f242(x45911)),f241(x45911)) % 154.70/154.55 [4592]~P87(x45921)+E(f82(x45921,f2(x45921)),f2(x45921)) % 154.70/154.55 [4601]~P140(x46011)+E(f328(f104(x46011),f2(a875)),f2(x46011)) % 154.70/154.55 [4602]~P140(x46021)+E(f328(f104(x46021),f78(a875)),f78(x46021)) % 154.70/154.55 [4603]~P135(x46031)+E(f328(f106(x46031),f2(a1)),f2(x46031)) % 154.70/154.55 [4604]~P135(x46041)+E(f328(f106(x46041),f78(a1)),f78(x46041)) % 154.70/154.55 [4605]E(x46051,f2(a875))+~E(f328(f104(a1),x46051),f2(a1)) % 154.70/154.55 [4630]~P83(x46301)+E(f328(f75(x46301),f2(x46301)),f2(x46301)) % 154.70/154.55 [4631]~P121(x46311)+E(f328(f75(x46311),f78(x46311)),f78(x46311)) % 154.70/154.55 [4632]~P93(x46321)+E(f328(f79(x46321),f192(x46321)),f251(x46321)) % 154.70/154.55 [4633]~P93(x46331)+E(f328(f79(x46331),f251(x46331)),f192(x46331)) % 154.70/154.55 [4634]~P72(x46341)+E(f328(f79(x46341),f2(x46341)),f2(x46341)) % 154.70/154.55 [4635]~P77(x46351)+E(f328(f163(x46351),f117(x46351)),f2(x46351)) % 154.70/154.55 [4656]~P38(x46561)+P40(f328(f170(a1),x46561)) % 154.70/154.55 [4687]~P90(x46871)+E(f328(f79(x46871),f78(x46871)),f328(f107(x46871),a101)) % 154.70/154.55 [4704]~P90(x47041)+P32(x47041,f328(f107(x47041),a83)) % 154.70/154.55 [4721]~P59(x47211)+E(f328(f170(x47211),f55(x47211)),f251(f882(x47211,a870))) % 154.70/154.55 [4731]P38(x47311)+~P40(f328(f170(a1),x47311)) % 154.70/154.55 [4732]~P59(x47321)+P1(f328(f134(x47321),f55(x47321))) % 154.70/154.55 [4775]E(f328(f104(a1),f328(a108,x47751)),x47751)+P1(f328(a197,x47751)) % 154.70/154.55 [4792]~P108(x47921)+E(f93(x47921,x47921,f5(x47921)),f94(x47921)) % 154.70/154.55 [4845]~P112(x48451)+E(f254(x48451,f78(x48451),f81(x48451)),f253(x48451)) % 154.70/154.55 [4875]~P90(x48751)+~P32(x48751,f328(f107(x48751),a101)) % 154.70/154.55 [4885]E(f328(a28,x48851),f205(a871))+P1(f328(a25,f328(a26,x48851))) % 154.70/154.55 [5016]E(f328(f75(a1),x50161),x50161)+P1(f328(f328(f243(a1),x50161),f2(a1))) % 154.70/154.55 [5037]~E(f328(a108,x50371),f2(a875))+P1(f328(f328(f242(a1),x50371),f2(a1))) % 154.70/154.55 [5099]~P1(f328(a197,x50991))+P1(f328(f328(f243(a1),x50991),f2(a1))) % 154.70/154.55 [5139]~P135(x51391)+P1(f328(f328(f330(x51391),f2(x51391)),f113(x51391))) % 154.70/154.55 [5140]~P140(x51401)+P1(f328(f328(f330(x51401),f2(x51401)),f190(x51401))) % 154.70/154.55 [5141]~P135(x51411)+P1(f328(f328(f330(x51411),f78(x51411)),f113(x51411))) % 154.70/154.55 [5142]~P140(x51421)+P1(f328(f328(f330(x51421),f78(x51421)),f190(x51421))) % 154.70/154.55 [5143]~P123(x51431)+P1(f328(f328(f243(x51431),f2(x51431)),f78(x51431))) % 154.70/154.55 [5144]~P123(x51441)+P1(f328(f328(f242(x51441),f2(x51441)),f78(x51441))) % 154.70/154.55 [5146]E(f328(f235(a871),f691(x51461)),f328(a28,x51461))+~P1(f328(a25,f328(a26,x51461))) % 154.70/154.55 [5147]E(f328(f235(a871),f705(x51471)),f328(a28,x51471))+~P1(f328(a25,f328(a26,x51471))) % 154.70/154.55 [5202]E(x52021,f2(a875))+~P1(f328(f328(f242(a875),x52021),f2(a875))) % 154.70/154.55 [5246]E(f328(a108,x52461),f2(a875))+~P1(f328(f328(f242(a1),x52461),f2(a1))) % 154.70/154.55 [5308]P1(f328(a197,x53081))+~P1(f328(f328(f243(a1),x53081),f2(a1))) % 154.70/154.55 [5313]~P105(x53131)+P18(x53131,f876(x53131),f145(x53131,x53131,f5(x53131))) % 154.70/154.55 [5330]P40(x53301)+~P1(f328(f328(f242(a1),f2(a1)),f336(x53301))) % 154.70/154.55 [5336]E(f328(f75(a1),x53361),f328(f79(a1),x53361))+~P1(f328(f328(f243(a1),x53361),f2(a1))) % 154.70/154.55 [5508]~P123(x55081)+~P1(f328(f328(f243(x55081),f78(x55081)),f2(x55081))) % 154.70/154.55 [5509]~P123(x55091)+~P1(f328(f328(f242(x55091),f78(x55091)),f2(x55091))) % 154.70/154.55 [5519]~E(x55191,f2(a1))+P1(f328(f328(f243(a1),f328(f75(a1),x55191)),f78(a1))) % 154.70/154.55 [5520]~E(x55201,f2(a875))+P1(f328(f328(f242(a1),f328(f104(a1),x55201)),f2(a1))) % 154.70/154.55 [5639]~P77(x56391)+E(f139(x56391,x56391,f80(x56391),f2(x56391)),f163(x56391)) % 154.70/154.55 [5811]~P101(x58111)+P27(a875,x58111,f104(x58111),f251(f882(a875,a870))) % 154.70/154.55 [6003]E(x60031,f2(a875))+~P1(f328(f328(f242(a1),f328(f104(a1),x60031)),f2(a1))) % 154.70/154.55 [6004]E(x60041,f2(a1))+~P1(f328(f328(f243(a1),f328(f75(a1),x60041)),f78(a1))) % 154.70/154.55 [6803]~P1(f328(f328(f243(a1),x68031),f2(a1)))+P1(f328(f328(f243(a1),f328(f328(f80(a1),x68031),x68031)),f2(a1))) % 154.70/154.55 [7351]P1(f328(f328(f243(a1),x73511),f2(a1)))+~P1(f328(f328(f243(a1),f328(f328(f80(a1),x73511),x73511)),f2(a1))) % 154.70/154.55 [7911]E(x79111,f328(a3,f2(a875)))+P1(f328(f328(f243(a875),f328(f328(f22(a875),f328(a19,x79111)),f328(a116,f2(a875)))),f328(a19,x79111))) % 154.70/154.55 [8687]~P1(f328(f328(f243(a1),x86871),f2(a1)))+P1(f328(f328(f243(a1),f328(f328(f22(a1),f328(f328(f80(a1),x86871),x86871)),a101)),f2(a1))) % 154.70/154.55 [8773]~P1(f328(f328(f243(a1),x87731),f2(a1)))+P1(f328(f328(f243(a1),f328(f328(f80(a1),f328(f328(f80(a1),f78(a1)),x87731)),x87731)),f2(a1))) % 154.70/154.55 [9099]P1(f328(f328(f243(a1),x90991),f2(a1)))+~P1(f328(f328(f243(a1),f328(f328(f22(a1),f328(f328(f80(a1),x90991),x90991)),a101)),f2(a1))) % 154.70/154.55 [9162]P1(f328(f328(f243(a1),x91621),f2(a1)))+~P1(f328(f328(f243(a1),f328(f328(f80(a1),f328(f328(f80(a1),f78(a1)),x91621)),x91621)),f2(a1))) % 154.70/154.55 [4675]~E(a83,x46751)+E(f328(f328(f80(a1),x46751),x46751),a83) % 154.70/154.55 [4676]~E(x46761,a83)+E(f328(f328(f80(a1),x46761),x46761),a83) % 154.70/154.55 [4690]E(x46901,f2(a1))+E(f328(f328(f38(a1),x46901),x46901),f78(a1)) % 154.70/154.55 [4821]E(x48211,a83)+~E(f328(f328(f80(a1),x48211),x48211),a83) % 154.70/154.55 [4822]E(a83,x48221)+~E(f328(f328(f80(a1),x48221),x48221),a83) % 154.70/154.55 [4835]~P5(x48351)+E(f39(x48351,f192(f882(x48351,a870))),f192(x48351)) % 154.70/154.55 [4836]~P5(x48361)+E(f39(x48361,f251(f882(x48361,a870))),f251(x48361)) % 154.70/154.55 [4837]~P5(x48371)+E(f40(x48371,f192(f882(x48371,a870))),f251(x48371)) % 154.70/154.55 [4838]~P5(x48381)+E(f40(x48381,f251(f882(x48381,a870))),f192(x48381)) % 154.70/154.55 [4839]~P105(x48391)+E(f136(x48391,f192(f882(x48391,a870))),f117(x48391)) % 154.70/154.55 [4974]E(x49741,f2(a875))+P1(f328(f328(f243(a875),f2(a875)),x49741)) % 154.70/154.55 [4993]~P6(x49931)+P1(f328(f328(f242(a1),f2(a1)),x49931)) % 154.70/154.55 [5028]~E(f328(f107(a875),x50281),f2(a875))+P1(f328(f328(f242(a1),x50281),a83)) % 154.70/154.55 [5033]P40(x50331)+P1(f328(f328(f330(a1),f336(x50331)),x50331)) % 154.70/154.55 [5034]E(x50341,f328(a3,f2(a875)))+P1(f328(f328(f242(a103),f78(a103)),x50341)) % 154.70/154.55 [5073]P1(f328(a197,x50731))+P1(f328(f328(f242(a1),f2(a1)),x50731)) % 154.70/154.55 [5121]E(f328(f104(a1),f328(a108,x51211)),f2(a1))+P1(f328(f328(f242(a1),f2(a1)),x51211)) % 154.70/154.55 [5188]E(f328(f104(a1),f328(f107(a875),x51881)),f328(f107(a1),x51881))+P1(f328(a197,f328(f107(a1),x51881))) % 154.70/154.55 [5208]E(f328(f107(a875),x52081),f2(a875))+~P1(f328(a197,f328(f107(a1),x52081))) % 154.70/154.55 [5209]E(f328(f107(a875),x52091),f2(a875))+~P1(f328(f328(f242(a1),x52091),a83)) % 154.70/154.55 [5243]P6(x52431)+~P1(f328(f328(f242(a1),f2(a1)),x52431)) % 154.70/154.55 [5316]E(f328(a116,f806(x53161)),x53161)+~P1(f328(f328(f243(a875),f2(a875)),x53161)) % 154.70/154.55 [5324]E(f328(a116,f328(f107(a875),x53241)),f78(a875))+~P1(f328(a197,f328(f107(a1),x53241))) % 154.70/154.55 [5332]E(f328(f104(a1),f410(x53321)),x53321)+~P1(f328(f328(f243(a1),f2(a1)),x53321)) % 154.70/154.55 [5339]~E(x53391,f328(a3,f2(a875)))+~P1(f328(f328(f242(a103),f78(a103)),x53391)) % 154.70/154.55 [5346]E(f328(f104(a1),f328(f107(a875),x53461)),f2(a1))+~P1(f328(a197,f328(f107(a1),x53461))) % 154.70/154.55 [5372]E(f328(f163(a875),x53721),f2(a875))+P1(f328(f328(f330(a875),f596(x53721)),f328(f170(a875),x53721))) % 154.70/154.55 [5393]E(f328(f104(a1),f328(a108,x53931)),x53931)+~P1(f328(f328(f242(a1),f2(a1)),x53931)) % 154.70/154.55 [5402]~P1(f328(a197,x54021))+~P1(f328(f328(f242(a1),f2(a1)),x54021)) % 154.70/154.55 [5501]E(f328(f328(f80(a875),f78(a875)),f328(f107(a875),x55011)),f78(a875))+~P1(f328(f328(f243(a1),x55011),a83)) % 154.70/154.55 [5559]E(x55591,f2(a875))+~P1(f328(f328(f243(a875),x55591),f328(a116,f2(a875)))) % 154.70/154.55 [5598]E(f328(f328(f22(a875),f328(f107(a875),x55981)),f78(a875)),f2(a875))+~P1(f328(f328(f242(a1),x55981),a83)) % 154.70/154.55 [5599]E(f328(f328(f80(a875),f328(f107(a875),x55991)),f78(a875)),f78(a875))+~P1(f328(f328(f243(a1),x55991),a83)) % 154.70/154.55 [5609]~P40(x56091)+E(f328(f37(a875),f328(f307(a1,a875,a108),x56091)),f328(f37(a1),x56091)) % 154.70/154.55 [5640]~P105(x56401)+E(f244(x56401,f328(f7(x56401,x56401,a870),f242(x56401))),f241(x56401)) % 154.70/154.55 [5641]~P105(x56411)+E(f245(x56411,f328(f7(x56411,x56411,a870),f242(x56411))),f240(x56411)) % 154.70/154.55 [5651]E(f44(a875,f328(a116,f2(a875)),f328(f107(a875),x56511)),f328(a116,f2(a875)))+~P1(f328(a197,f328(f107(a1),x56511))) % 154.70/154.55 [5660]P1(f328(f328(f243(a1),f2(a1)),x56601))+~P1(f328(f328(f242(a1),f78(a1)),x56601)) % 154.70/154.55 [5661]~P1(f328(f328(f243(a1),f2(a1)),x56611))+P1(f328(f328(f242(a1),f78(a1)),x56611)) % 154.70/154.55 [5672]E(f328(a116,f328(f328(f22(a875),x56721),f78(a875))),x56721)+~P1(f328(f328(f243(a875),f2(a875)),x56721)) % 154.70/154.55 [5730]P1(f328(f328(f243(a875),f2(a875)),f410(x57301)))+~P1(f328(f328(f243(a1),f2(a1)),x57301)) % 154.70/154.55 [5789]E(f44(a1,f328(f107(a1),a101),x57891),f328(f328(f22(a1),x57891),f78(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x57891)) % 154.70/154.55 [5823]~P1(f328(f328(f243(a1),a83),x58231))+P1(f328(f328(f243(a875),f2(a875)),f328(f107(a875),x58231))) % 154.70/154.55 [5873]P1(f328(f328(f243(a875),f2(a875)),f328(a108,x58731)))+~P1(f328(f328(f243(a1),f2(a1)),x58731)) % 154.70/154.55 [5924]~P1(f328(f328(f243(a875),f2(a875)),x59241))+P1(f328(f328(f243(a1),f2(a1)),f328(f104(a1),x59241))) % 154.70/154.55 [5960]~P1(f328(f328(f243(a875),f2(a875)),f328(a108,x59601)))+P1(f328(f328(f243(a1),f2(a1)),x59601)) % 154.70/154.55 [5974]~P40(x59741)+E(f328(f307(a875,a1,f104(a1)),f328(f307(a1,a875,a108),x59741)),x59741) % 154.70/154.55 [5984]P1(f328(f328(f243(a1),a83),x59841))+~P1(f328(f328(f243(a875),f2(a875)),f328(f107(a875),x59841))) % 154.70/154.55 [6032]~P59(x60321)+E(f328(f328(f148(f879(x60321)),f205(x60321)),f328(f328(f151(x60321,f879(x60321)),f235(x60321)),f55(x60321))),f55(f879(x60321))) % 154.70/154.55 [6043]P1(f328(f328(f243(a875),f2(a875)),x60431))+~P1(f328(f328(f243(a1),f2(a1)),f328(f104(a1),x60431))) % 154.70/154.55 [6158]E(f328(f307(a875,a1,f104(a1)),f328(f249(a875),f328(a108,x61581))),f328(f298(a1,f2(a1)),x61581))+~P1(f328(f328(f242(a1),f2(a1)),x61581)) % 154.70/154.55 [6176]~P123(x61761)+P1(f328(f328(f243(x61761),f2(x61761)),f328(f328(f80(x61761),f78(x61761)),f78(x61761)))) % 154.70/154.55 [6227]P1(f328(f328(f243(a875),f328(a116,f2(a875))),f328(a108,x62271)))+~P1(f328(f328(f243(a1),f78(a1)),x62271)) % 154.70/154.55 [6322]E(x63221,f2(a1))+P1(f328(f48(f2(a1),x63221),f328(f328(f263(a1,a1),f2(a1)),f2(a1)))) % 154.70/154.55 [6486]~P1(f328(f328(f243(a875),f328(a116,f2(a875))),f328(a108,x64861)))+P1(f328(f328(f243(a1),f78(a1)),x64861)) % 154.70/154.55 [6914]~P113(x69141)+P39(x69141,f328(f248(f881(x69141,x69141)),f328(f267(x69141,x69141,a870),f243(x69141)))) % 154.70/154.55 [5546]E(f328(f107(a875),f328(f328(f22(a1),x55461),a101)),f328(a116,f328(f107(a875),x55461)))+P1(f328(a197,f328(f107(a1),x55461))) % 154.70/154.55 [5562]~P38(x55621)+E(f328(f328(f151(a875,a1),f104(a1)),f328(f328(f151(a1,a875),a108),x55621)),x55621) % 154.70/154.55 [5678]E(f328(f79(a1),f328(f104(a1),f328(a116,f454(x56781)))),x56781)+~P1(f328(f328(f243(a1),x56781),f2(a1))) % 154.70/154.55 [5688]E(f328(f328(f80(a875),f78(a875)),f328(f107(a875),x56881)),f328(f107(a875),f328(f328(f22(a1),x56881),a101)))+P1(f328(f328(f243(a1),x56881),a83)) % 154.70/154.55 [5732]E(f328(f328(f38(a1),f328(f107(a1),a101)),x57321),f328(f107(a1),a101))+~P1(f328(f328(f243(a1),f2(a1)),x57321)) % 154.70/154.55 [5819]E(f328(f328(f22(a875),f328(f107(a875),x58191)),f78(a875)),f328(f107(a875),f328(f328(f80(a1),x58191),a101)))+P1(f328(f328(f242(a1),x58191),a83)) % 154.70/154.55 [5820]E(f328(f328(f80(a875),f328(f107(a875),x58201)),f78(a875)),f328(f107(a875),f328(f328(f22(a1),x58201),a101)))+P1(f328(f328(f243(a1),x58201),a83)) % 154.70/154.55 [5861]E(f328(a108,f328(f328(f80(a1),f78(a1)),x58611)),f328(a116,f328(a108,x58611)))+~P1(f328(f328(f242(a1),f2(a1)),x58611)) % 154.70/154.55 [5897]E(f328(a116,f328(f328(f22(a875),x58971),f328(a116,f2(a875)))),x58971)+~P1(f328(f328(f243(a875),f2(a875)),x58971)) % 154.70/154.55 [6103]E(f44(a875,f328(a116,f2(a875)),f328(f107(a875),x61031)),f328(a108,f44(a1,f78(a1),f328(f107(a1),x61031))))+P1(f328(a197,f328(f107(a1),x61031))) % 154.70/154.55 [6148]~P1(f328(f328(f243(a1),a83),x61481))+P1(f328(f328(f243(a1),a83),f328(f328(f80(a1),x61481),x61481))) % 154.70/154.55 [6149]~P1(f328(f328(f243(a1),a101),x61491))+P1(f328(f328(f243(a1),a101),f328(f328(f80(a1),x61491),x61491))) % 154.70/154.55 [6150]~P1(f328(f328(f242(a1),a83),x61501))+P1(f328(f328(f242(a1),a83),f328(f328(f80(a1),x61501),x61501))) % 154.70/154.55 [6151]~P1(f328(f328(f243(a1),a101),x61511))+P1(f328(f328(f242(a1),a101),f328(f328(f80(a1),x61511),x61511))) % 154.70/154.55 [6152]~P1(f328(f328(f91(a1),a83),x61521))+P1(f328(f328(f91(a1),a83),f328(f328(f80(a1),x61521),x61521))) % 154.70/154.55 [6335]~P1(f328(f61(x63351),f251(f882(x63351,a870))))+P1(f328(f61(f879(x63351)),f251(f882(f879(x63351),a870)))) % 154.70/154.55 [6419]~P1(f328(f328(f242(a1),f2(a1)),x64191))+P1(f328(f328(f243(a1),f2(a1)),f328(f328(f80(a1),f78(a1)),x64191))) % 154.70/154.55 [6426]E(f328(f262(a1,a1),f46(f78(a1),f328(f107(a1),x64261))),f328(f328(f38(a1),f78(a1)),f328(f107(a1),x64261)))+~P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x64261))) % 154.70/154.55 [6446]E(f328(f266(a1,a1),f46(f78(a1),f328(f107(a1),x64461))),f44(a1,f78(a1),f328(f107(a1),x64461)))+~P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x64461))) % 154.70/154.55 [6458]P1(f328(f61(x64581),f251(f882(x64581,a870))))+~P1(f328(f61(f879(x64581)),f251(f882(f879(x64581),a870)))) % 154.70/154.55 [6487]P1(f328(f328(f243(a1),a83),x64871))+~P1(f328(f328(f243(a1),a83),f328(f328(f80(a1),x64871),x64871))) % 154.70/154.55 [6488]P1(f328(f328(f243(a1),a101),x64881))+~P1(f328(f328(f243(a1),a101),f328(f328(f80(a1),x64881),x64881))) % 154.70/154.55 [6489]P1(f328(f328(f243(a1),a101),x64891))+~P1(f328(f328(f242(a1),a101),f328(f328(f80(a1),x64891),x64891))) % 154.70/154.55 [6490]P1(f328(f328(f242(a1),a83),x64901))+~P1(f328(f328(f242(a1),a83),f328(f328(f80(a1),x64901),x64901))) % 154.70/154.55 [6491]P1(f328(f328(f91(a1),a83),x64911))+~P1(f328(f328(f91(a1),a83),f328(f328(f80(a1),x64911),x64911))) % 154.70/154.55 [6807]~P1(f328(f61(x68071),f251(f882(x68071,a870))))+P1(f328(f328(f243(a875),f2(a875)),f328(f37(x68071),f251(f882(x68071,a870))))) % 154.70/154.55 [7393]P1(f328(f61(a875),x73931))+~P1(f328(f61(a1),f328(f307(a875,a1,f104(a1)),x73931))) % 154.70/154.55 [5476]~E(a101,x54761)+E(f328(f328(f22(a1),f328(f328(f80(a1),x54761),x54761)),a101),a101) % 154.70/154.55 [5477]~E(x54771,a101)+E(f328(f328(f22(a1),f328(f328(f80(a1),x54771),x54771)),a101),a101) % 154.70/154.55 [5979]E(x59791,a101)+~E(f328(f328(f22(a1),f328(f328(f80(a1),x59791),x59791)),a101),a101) % 154.70/154.55 [5980]E(a101,x59801)+~E(f328(f328(f22(a1),f328(f328(f80(a1),x59801),x59801)),a101),a101) % 154.70/154.55 [6388]~E(f328(f107(a875),x63881),f2(a875))+P1(f328(a197,f328(f107(a1),f328(f328(f80(a1),x63881),a101)))) % 154.70/154.55 [6733]~P1(f328(a197,f328(f107(a1),x67331)))+P1(f328(a197,f328(f107(a1),f328(f328(f80(a1),x67331),x67331)))) % 154.70/154.55 [6734]~P1(f328(f328(f243(a1),x67341),a83))+P1(f328(f328(f243(a1),f328(f328(f80(a1),x67341),x67341)),a83)) % 154.70/154.55 [6735]~P1(f328(f328(f242(a1),x67351),a101))+P1(f328(f328(f243(a1),f328(f328(f80(a1),x67351),x67351)),a101)) % 154.70/154.55 [6736]~P1(f328(f328(f242(a1),x67361),a83))+P1(f328(f328(f242(a1),f328(f328(f80(a1),x67361),x67361)),a83)) % 154.70/154.55 [6737]~P1(f328(f328(f242(a1),x67371),a101))+P1(f328(f328(f242(a1),f328(f328(f80(a1),x67371),x67371)),a101)) % 154.70/154.55 [6738]~P1(f328(f328(f91(a1),x67381),a83))+P1(f328(f328(f91(a1),f328(f328(f80(a1),x67381),x67381)),a83)) % 154.70/154.55 [7059]E(f328(f107(a875),x70591),f2(a875))+~P1(f328(a197,f328(f107(a1),f328(f328(f80(a1),x70591),a101)))) % 154.70/154.55 [7300]~P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x73001)))+P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),f328(f328(f80(a1),x73001),x73001)))) % 154.70/154.55 [7301]P1(f328(a197,f328(f107(a1),x73011)))+~P1(f328(a197,f328(f107(a1),f328(f328(f80(a1),x73011),x73011)))) % 154.70/154.55 [7302]P1(f328(f328(f243(a1),x73021),a83))+~P1(f328(f328(f243(a1),f328(f328(f80(a1),x73021),x73021)),a83)) % 154.70/154.55 [7303]P1(f328(f328(f242(a1),x73031),a83))+~P1(f328(f328(f242(a1),f328(f328(f80(a1),x73031),x73031)),a83)) % 154.70/154.55 [7304]P1(f328(f328(f242(a1),x73041),a101))+~P1(f328(f328(f243(a1),f328(f328(f80(a1),x73041),x73041)),a101)) % 154.70/154.55 [7305]P1(f328(f328(f242(a1),x73051),a101))+~P1(f328(f328(f242(a1),f328(f328(f80(a1),x73051),x73051)),a101)) % 154.70/154.55 [7306]P1(f328(f328(f91(a1),x73061),a83))+~P1(f328(f328(f91(a1),f328(f328(f80(a1),x73061),x73061)),a83)) % 154.70/154.55 [7676]E(f328(a110,f584(x76761)),x76761)+~P1(f328(f328(f330(f882(f881(a875,a875),a870)),x76761),a102)) % 154.70/154.55 [6308]~P90(x63081)+E(f328(f107(x63081),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f78(x63081)) % 154.70/154.55 [6785]~P1(f328(a197,f328(f107(a1),x67851)))+E(f328(f107(a875),f328(f328(f22(a1),f328(f328(f80(a1),x67851),x67851)),a101)),f2(a875)) % 154.70/154.55 [7856]~P1(f328(f328(f243(a1),f328(f107(a1),x78561)),f2(a1)))+E(f328(f262(a1,a1),f328(a50,f49(f328(f79(a1),f78(a1)),f328(f79(a1),f328(f107(a1),x78561))))),f328(f328(f38(a1),f78(a1)),f328(f107(a1),x78561))) % 154.70/154.55 [7869]~P1(f328(f328(f243(a1),f328(f107(a1),x78691)),f2(a1)))+E(f328(f266(a1,a1),f328(a50,f49(f328(f79(a1),f78(a1)),f328(f79(a1),f328(f107(a1),x78691))))),f44(a1,f78(a1),f328(f107(a1),x78691))) % 154.70/154.55 [7917]~P1(f328(f328(f242(a1),a83),x79171))+P1(f328(f328(f243(a1),a83),f328(f328(f22(a1),f328(f328(f80(a1),x79171),x79171)),a101))) % 154.70/154.55 [7918]~P1(f328(f328(f243(a1),a101),x79181))+P1(f328(f328(f243(a1),a101),f328(f328(f22(a1),f328(f328(f80(a1),x79181),x79181)),a101))) % 154.70/154.55 [7919]~P1(f328(f328(f242(a1),a83),x79191))+P1(f328(f328(f242(a1),a83),f328(f328(f22(a1),f328(f328(f80(a1),x79191),x79191)),a101))) % 154.70/154.55 [7920]~P1(f328(f328(f242(a1),a101),x79201))+P1(f328(f328(f242(a1),a101),f328(f328(f22(a1),f328(f328(f80(a1),x79201),x79201)),a101))) % 154.70/154.55 [7921]~P1(f328(f328(f91(a1),a101),x79211))+P1(f328(f328(f91(a1),a101),f328(f328(f22(a1),f328(f328(f80(a1),x79211),x79211)),a101))) % 154.70/154.55 [8232]~P90(x82321)+~P32(x82321,f328(f107(x82321),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))) % 154.70/154.55 [8412]P1(f328(f328(f243(a1),a101),x84121))+~P1(f328(f328(f243(a1),a101),f328(f328(f22(a1),f328(f328(f80(a1),x84121),x84121)),a101))) % 154.70/154.55 [8413]P1(f328(f328(f242(a1),a83),x84131))+~P1(f328(f328(f243(a1),a83),f328(f328(f22(a1),f328(f328(f80(a1),x84131),x84131)),a101))) % 154.70/154.55 [8414]P1(f328(f328(f242(a1),a83),x84141))+~P1(f328(f328(f242(a1),a83),f328(f328(f22(a1),f328(f328(f80(a1),x84141),x84141)),a101))) % 154.70/154.55 [8415]P1(f328(f328(f242(a1),a101),x84151))+~P1(f328(f328(f242(a1),a101),f328(f328(f22(a1),f328(f328(f80(a1),x84151),x84151)),a101))) % 154.70/154.55 [8416]P1(f328(f328(f91(a1),a101),x84161))+~P1(f328(f328(f91(a1),a101),f328(f328(f22(a1),f328(f328(f80(a1),x84161),x84161)),a101))) % 154.70/154.55 [8731]E(f328(f107(a875),f328(f328(f22(a1),f328(f328(f80(a1),x87311),x87311)),a101)),f328(f328(f86(a875,a875),f328(f107(a875),x87311)),f328(f328(f8(a875,a875,a875),a116),f328(f328(f18(a875,a875,a875),f80(a875)),f5(a875)))))+P1(f328(a197,f328(f107(a1),x87311))) % 154.70/154.55 [9578]E(x95781,f192(f882(f881(a875,a875),a870)))+P1(f328(f328(f330(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f328(f328(f263(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),x95781),f192(f882(f881(a875,a875),a870)))),a68)) % 154.70/154.55 [8662]~P1(f328(a197,f328(f107(a1),x86621)))+P1(f328(a197,f328(f107(a1),f328(f328(f22(a1),f328(f328(f80(a1),x86621),x86621)),a101)))) % 154.70/154.55 [8663]~P1(f328(f328(f243(a1),x86631),a83))+P1(f328(f328(f243(a1),f328(f328(f22(a1),f328(f328(f80(a1),x86631),x86631)),a101)),a83)) % 154.70/154.55 [8664]~P1(f328(f328(f243(a1),x86641),a101))+P1(f328(f328(f243(a1),f328(f328(f22(a1),f328(f328(f80(a1),x86641),x86641)),a101)),a101)) % 154.70/154.55 [8665]~P1(f328(f328(f243(a1),x86651),a83))+P1(f328(f328(f242(a1),f328(f328(f22(a1),f328(f328(f80(a1),x86651),x86651)),a101)),a83)) % 154.70/154.55 [8666]~P1(f328(f328(f242(a1),x86661),a101))+P1(f328(f328(f242(a1),f328(f328(f22(a1),f328(f328(f80(a1),x86661),x86661)),a101)),a101)) % 154.70/154.55 [8667]~P1(f328(f328(f91(a1),x86671),a101))+P1(f328(f328(f91(a1),f328(f328(f22(a1),f328(f328(f80(a1),x86671),x86671)),a101)),a101)) % 154.70/154.55 [8766]~P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x87661)))+P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),f328(f328(f22(a1),f328(f328(f80(a1),x87661),x87661)),a101)))) % 154.70/154.55 [8925]~P90(x89251)+E(f328(f328(f80(x89251),f78(x89251)),f78(x89251)),f328(f107(x89251),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))) % 154.70/154.55 [9083]P1(f328(a197,f328(f107(a1),x90831)))+~P1(f328(a197,f328(f107(a1),f328(f328(f22(a1),f328(f328(f80(a1),x90831),x90831)),a101)))) % 154.70/154.55 [9084]P1(f328(f328(f243(a1),x90841),a83))+~P1(f328(f328(f243(a1),f328(f328(f22(a1),f328(f328(f80(a1),x90841),x90841)),a101)),a83)) % 154.70/154.55 [9085]P1(f328(f328(f243(a1),x90851),a83))+~P1(f328(f328(f242(a1),f328(f328(f22(a1),f328(f328(f80(a1),x90851),x90851)),a101)),a83)) % 154.70/154.55 [9086]P1(f328(f328(f243(a1),x90861),a101))+~P1(f328(f328(f243(a1),f328(f328(f22(a1),f328(f328(f80(a1),x90861),x90861)),a101)),a101)) % 154.70/154.55 [9087]P1(f328(f328(f242(a1),x90871),a101))+~P1(f328(f328(f242(a1),f328(f328(f22(a1),f328(f328(f80(a1),x90871),x90871)),a101)),a101)) % 154.70/154.55 [9088]P1(f328(f328(f91(a1),x90881),a101))+~P1(f328(f328(f91(a1),f328(f328(f22(a1),f328(f328(f80(a1),x90881),x90881)),a101)),a101)) % 154.70/154.55 [9624]~P1(f328(f61(f881(a875,a875)),x96241))+P1(f328(f328(f330(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f328(f328(f263(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),f192(f882(f881(a875,a875),a870))),x96241)),a69)) % 154.70/154.55 [9410]~P140(x94101)+E(f328(f328(f253(x94101),f2(x94101)),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f2(x94101)) % 154.70/154.55 [9411]~P140(x94111)+E(f328(f328(f253(x94111),f78(x94111)),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f78(x94111)) % 154.70/154.55 [9852]~P1(f328(f328(f243(a875),f78(a875)),x98521))+P1(f328(f328(f243(a875),f2(a875)),f328(f328(f38(a875),x98521),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))) % 154.70/154.55 [9864]~P1(f328(f328(f243(a875),f2(a875)),x98641))+P1(f328(f328(f243(a875),f2(a875)),f328(f328(f38(a875),f328(f328(f80(a875),x98641),f78(a875))),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))) % 154.70/154.55 [9906]~E(f44(a875,x99061,f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f78(a875))+P1(f328(f328(f243(a875),f2(a875)),f44(a875,x99061,f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))) % 154.70/154.55 [9925]E(f44(a875,x99251,f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f78(a875))+~P1(f328(f328(f243(a875),f2(a875)),f44(a875,x99251,f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))) % 154.70/154.55 [4609]~P39(x46091,x46092)+P54(x46091,x46092) % 154.70/154.55 [4610]~P45(x46101,x46102)+P54(x46101,x46102) % 154.70/154.55 [4571]~E(x45711,x45712)+E(f275(x45711,x45712),f78(a103)) % 154.70/154.55 [4574]E(f223(x45741,x45742),x45741)+~E(x45742,f2(a875)) % 154.70/154.55 [4581]~E(x45812,f117(x45811))+E(f149(x45811,x45812),f117(x45811)) % 154.70/154.55 [4600]~E(f149(x46002,x46001),f117(x46002))+E(x46001,f117(x46002)) % 154.70/154.55 [4614]~P2(x46142)+P2(f882(x46141,x46142)) % 154.70/154.55 [4615]~P98(x46152)+P98(f882(x46151,x46152)) % 154.70/154.55 [4616]~P2(x46162)+P99(f882(x46161,x46162)) % 154.70/154.55 [4617]~P95(x46172)+P3(f882(x46171,x46172)) % 154.70/154.55 [4618]~P64(x46182)+P64(f882(x46181,x46182)) % 154.70/154.55 [4619]~P2(x46192)+P100(f882(x46191,x46192)) % 154.70/154.55 [4620]~P96(x46202)+P96(f882(x46201,x46202)) % 154.70/154.55 [4621]~P5(x46212)+P5(f882(x46211,x46212)) % 154.70/154.55 [4622]~P104(x46222)+P104(f882(x46221,x46222)) % 154.70/154.55 [4623]~P95(x46232)+P97(f882(x46231,x46232)) % 154.70/154.55 [4624]~P106(x46242)+P106(f882(x46241,x46242)) % 154.70/154.55 [4625]~P107(x46252)+P107(f882(x46251,x46252)) % 154.70/154.55 [4626]~P108(x46262)+P108(f882(x46261,x46262)) % 154.70/154.55 [4627]~P93(x46272)+P93(f882(x46271,x46272)) % 154.70/154.55 [4628]~P86(x46282)+P86(f882(x46281,x46282)) % 154.70/154.55 [4629]~P95(x46292)+P95(f882(x46291,x46292)) % 154.70/154.55 [4641]E(x46411,x46412)+~E(f328(a26,x46411),f328(a26,x46412)) % 154.70/154.55 [4643]E(x46431,x46432)+~E(f328(a116,x46431),f328(a116,x46432)) % 154.70/154.55 [4644]E(x46441,x46442)+~E(f328(a110,x46441),f328(a110,x46442)) % 154.70/154.55 [4645]E(x46451,x46452)+~E(f328(a3,x46451),f328(a3,x46452)) % 154.70/154.55 [4647]E(x46471,x46472)+~E(f328(a19,x46471),f328(a19,x46472)) % 154.70/154.55 [4748]~P57(x47481)+E(f44(x47481,x47482,x47482),f2(x47481)) % 154.70/154.55 [4782]~P39(x47821,x47822)+P39(f876(x47821),f143(x47821,x47822)) % 154.70/154.55 [4783]~P39(x47831,x47832)+P39(f876(x47831),f142(x47831,x47832)) % 154.70/154.55 [4880]~P39(x48801,x48802)+P39(f882(x48801,a870),f321(x48801,x48802)) % 154.70/154.55 [4881]~P39(x48811,x48812)+P39(f882(x48811,a870),f319(x48811,x48812)) % 154.70/154.55 [4999]~P6(x49991)+P40(f299(a1,x49991,x49992)) % 154.70/154.55 [5102]~P39(x51021,x51022)+P56(x51021,f67(x51021,x51021,x51022)) % 154.70/154.55 [5603]~P81(x56031)+P27(x56031,x56031,f79(x56031),x56032) % 154.70/154.55 [4595]~E(x45952,f117(x45951))+E(f328(f165(x45951),x45952),f117(x45951)) % 154.70/154.55 [4596]~E(x45962,f117(x45961))+E(f328(f166(x45961),x45962),f117(x45961)) % 154.70/154.55 [4651]E(x46511,f328(a108,x46512))+~E(f328(f104(a1),x46511),x46512) % 154.70/154.55 [4654]E(x46541,f117(x46542))+~E(f328(f165(x46542),x46541),f117(x46542)) % 154.70/154.55 [4655]E(x46551,f117(x46552))+~E(f328(f166(x46552),x46551),f117(x46552)) % 154.70/154.55 [4672]~P90(x46721)+E(f328(f107(x46721),x46722),f328(f106(x46721),x46722)) % 154.70/154.55 [4679]~E(x46792,f205(x46791))+E(f234(x46791,x46792),f192(f882(x46791,a870))) % 154.70/154.55 [4681]~P4(x46811)+P1(f328(f61(x46811),x46812)) % 154.70/154.55 [4688]E(x46881,f205(x46882))+E(f328(f235(x46882),f684(x46882,x46881)),x46881) % 154.70/154.55 [4689]E(x46891,f205(x46892))+E(f328(f235(x46892),f717(x46892,x46891)),x46891) % 154.70/154.55 [4691]~E(f718(x46912,x46911),f117(x46911))+E(f178(x46911,x46912),f117(f876(x46911))) % 154.70/154.55 [4700]~E(x47002,f117(x47001))+E(f328(f170(x47001),x47002),f192(f882(x47001,a870))) % 154.70/154.55 [4701]~E(x47012,f117(x47011))+E(f192(f882(x47011,a870)),f328(f170(x47011),x47012)) % 154.70/154.55 [4703]E(x47031,x47032)+~E(f328(f104(a1),x47031),f328(f104(a1),x47032)) % 154.70/154.55 [4706]E(f221(x47061,x47062),f2(a875))+P1(f328(f61(x47061),x47062)) % 154.70/154.55 [4726]~P121(x47261)+E(f82(x47261,f82(x47261,x47262)),f82(x47261,x47262)) % 154.70/154.55 [4739]~P109(x47391)+E(f328(f328(f253(x47391),x47392),f78(a875)),x47392) % 154.70/154.55 [4740]~P79(x47401)+E(f328(f328(f253(x47401),x47402),f78(a875)),x47402) % 154.70/154.55 [4742]E(x47421,x47422)+E(f275(x47421,x47422),f328(f328(f80(a103),x47422),f78(a103))) % 154.70/154.55 [4745]E(f328(f37(x47451),x47452),f2(a875))+P1(f328(f61(x47451),x47452)) % 154.70/154.55 [4749]~E(f149(x47491,x47492),x47492)+P1(f328(f134(x47491),x47492)) % 154.70/154.55 [4752]~P3(x47521)+E(f328(f328(f114(x47521),x47522),f192(x47521)),x47522) % 154.70/154.55 [4753]~P72(x47531)+E(f328(f328(f22(x47531),x47532),f2(x47531)),x47532) % 154.70/154.55 [4754]~P97(x47541)+E(f328(f328(f105(x47541),x47542),f251(x47541)),x47542) % 154.70/154.55 [4755]~P66(x47551)+E(f328(f328(f80(x47551),x47552),f2(x47551)),x47552) % 154.70/154.55 [4756]~P77(x47561)+E(f328(f328(f80(x47561),x47562),f2(x47561)),x47562) % 154.70/154.55 [4757]~P109(x47571)+E(f328(f328(f80(x47571),x47572),f2(x47571)),x47572) % 154.70/154.55 [4758]~P109(x47581)+E(f328(f328(f81(x47581),x47582),f78(x47581)),x47582) % 154.70/154.55 [4759]~P73(x47591)+E(f328(f328(f81(x47591),x47592),f78(x47591)),x47592) % 154.70/154.55 [4760]~P79(x47601)+E(f328(f328(f81(x47601),x47602),f78(x47601)),x47602) % 154.70/154.55 [4761]~P117(x47611)+E(f328(f328(f286(x47611),x47612),f78(x47611)),x47612) % 154.70/154.55 [4762]~P57(x47621)+E(f328(f328(f38(x47621),x47622),f78(x47621)),x47622) % 154.70/154.55 [4763]~P109(x47631)+E(f328(f328(f253(x47631),x47632),f2(a875)),f78(x47631)) % 154.70/154.55 [4764]~P112(x47641)+E(f328(f328(f253(x47641),x47642),f2(a875)),f78(x47641)) % 154.70/154.55 [4765]~E(x47652,f192(f882(x47651,a870)))+E(f328(f37(x47651),x47652),f2(a875)) % 154.70/154.55 [4776]~P57(x47761)+E(f44(x47761,x47762,f2(x47761)),x47762) % 154.70/154.55 [4784]~P97(x47841)+E(f328(f328(f114(x47841),x47842),f251(x47841)),f251(x47841)) % 154.70/154.55 [4785]~P3(x47851)+E(f328(f328(f105(x47851),x47852),f192(x47851)),f192(x47851)) % 154.70/154.55 [4786]~P109(x47861)+E(f328(f328(f81(x47861),x47862),f2(x47861)),f2(x47861)) % 154.70/154.55 [4787]~P128(x47871)+E(f328(f328(f81(x47871),x47872),f2(x47871)),f2(x47871)) % 154.70/154.55 [4788]~P118(x47881)+E(f328(f328(f286(x47881),x47882),f2(x47881)),f2(x47881)) % 154.70/154.55 [4789]~P57(x47891)+E(f328(f328(f38(x47891),x47892),f2(x47891)),f2(x47891)) % 154.70/154.55 [4790]E(x47901,f205(x47902))+~E(f234(x47902,x47901),f192(f882(x47902,a870))) % 154.70/154.55 [4793]~P57(x47931)+E(f44(x47931,x47932,f78(x47931)),f2(x47931)) % 154.70/154.55 [4794]~P57(x47941)+E(f44(x47941,f2(x47941),x47942),f2(x47941)) % 154.70/154.55 [4823]E(x48231,f2(a875))+E(f54(x48232,x48231,f117(x48232)),f117(f876(x48232))) % 154.70/154.55 [4847]P39(x48471,x48472)+~E(f597(x48472,x48471),f192(f882(x48471,a870))) % 154.70/154.55 [4848]E(x48481,f117(x48482))+~E(f328(f170(x48482),x48481),f192(f882(x48482,a870))) % 154.70/154.55 [4849]E(x48491,f117(x48492))+~E(f192(f882(x48492,a870)),f328(f170(x48492),x48491)) % 154.70/154.55 [4852]~E(x48521,x48522)+P1(f328(f328(a325,x48521),x48522)) % 154.70/154.55 [4862]P1(x48621)+P1(f328(f328(a331,x48621),x48622)) % 154.70/154.55 [4863]E(x48631,f117(x48632))+E(f328(f328(f162(x48632),x48631),f2(a875)),f328(f138(x48632),x48631)) % 154.70/154.55 [4866]E(f149(x48661,x48662),x48662)+~P1(f328(f134(x48661),x48662)) % 154.70/154.55 [4871]~P1(x48712)+P1(f328(f328(a331,x48711),x48712)) % 154.70/154.55 [4872]~P1(x48722)+P1(f328(f328(a327,x48721),x48722)) % 154.70/154.55 [4873]~P1(x48731)+P1(f328(f328(a327,x48731),x48732)) % 154.70/154.55 [4883]~E(f685(x48832,x48831),f690(x48832,x48831))+P1(f328(f134(x48831),x48832)) % 154.70/154.55 [4891]E(f328(f248(x48911),x48912),f192(f882(x48911,a870)))+P1(f328(x48912,f334(x48912))) % 154.70/154.55 [4892]E(f192(f882(x48921,a870)),f328(f248(x48921),x48922))+P1(f328(x48922,f335(x48922))) % 154.70/154.55 [4956]~P121(x49561)+E(f328(f328(f81(x49561),x49562),f82(x49561,x49562)),f328(f75(x49561),x49562)) % 154.70/154.55 [4967]~E(x49671,f2(a1))+E(f45(x49671,x49672),f328(f328(f263(a1,a1),f2(a1)),f2(a1))) % 154.70/154.55 [4998]~P54(x49981,x49982)+P54(x49981,f328(f283(x49981,x49981),x49982)) % 154.70/154.55 [5017]~E(f328(a28,x50171),f328(f235(a871),x50172))+P1(f328(a25,f328(a26,x50171))) % 154.70/154.55 [5022]E(x50221,x50222)+~P1(f328(f328(a325,x50221),x50222)) % 154.70/154.55 [5026]~P1(f328(a25,x50262))+P1(f328(a25,f32(x50261,x50262))) % 154.70/154.55 [5035]P1(x50351)+~P1(f328(f328(a326,x50352),x50351)) % 154.70/154.55 [5036]P1(x50361)+~P1(f328(f328(a326,x50361),x50362)) % 154.70/154.55 [5041]~P104(x50411)+P1(f328(f328(f242(x50411),x50412),f251(x50411))) % 154.70/154.55 [5045]E(x50451,x50452)+~E(f328(x50451,f409(x50452,x50451)),f328(x50452,f409(x50452,x50451))) % 154.70/154.55 [5075]E(x50751,f2(a875))+E(f223(x50751,f44(a875,x50752,x50751)),f223(x50752,x50751)) % 154.70/154.55 [5080]~P105(x50801)+P16(x50801,f328(f328(f148(x50801),x50802),f117(x50801))) % 154.70/154.55 [5082]E(x50821,f2(a1))+P1(f328(f48(x50822,x50821),f45(x50822,x50821))) % 154.70/154.55 [5100]~E(x51001,x51002)+P1(f328(f328(f243(a875),x51001),f328(a116,x51002))) % 154.70/154.55 [5110]~E(x51101,f2(a875))+P1(f328(f328(f243(a875),x51101),f328(a116,x51102))) % 154.70/154.55 [5120]P1(f328(x51201,x51202))+P1(f328(f328(f242(a1),f2(a1)),f389(x51201))) % 154.70/154.55 [5156]P1(f328(a25,x51561))+~P1(f328(a25,f32(x51562,x51561))) % 154.70/154.55 [5158]P1(f328(a25,x51581))+~P1(f328(a25,f33(x51582,x51581))) % 154.70/154.55 [5160]P1(f328(a25,x51601))+~P1(f328(a25,f33(x51601,x51602))) % 154.70/154.55 [5192]P54(x51921,x51922)+~P54(x51921,f328(f283(x51921,x51921),x51922)) % 154.70/154.55 [5195]~E(f44(a875,x51952,x51951),f2(a875))+E(f328(f328(f81(a875),x51951),f452(x51951,x51952)),x51952) % 154.70/154.55 [5196]~E(f44(a1,x51962,x51961),f2(a1))+E(f328(f328(f81(a1),x51961),f453(x51961,x51962)),x51962) % 154.70/154.55 [5222]~P1(f328(x52221,x52222))+P1(f328(f328(f242(a1),f2(a1)),f337(x52221))) % 154.70/154.55 [5234]E(f328(f328(f22(a875),f328(a108,x52341)),f328(a108,x52342)),f328(a108,x52341))+~P1(f328(a197,x52342)) % 154.70/154.55 [5264]E(f276(x52641,x52642),f78(a103))+~P1(f328(f328(f242(a103),x52641),f78(a103))) % 154.70/154.55 [5358]E(f328(f328(f162(x53581),x53582),f685(x53582,x53581)),f328(f328(f162(x53581),x53582),f690(x53582,x53581)))+P1(f328(f134(x53581),x53582)) % 154.70/154.55 [5403]~P1(f328(x54031,f90(x54032,x54031)))+P1(f328(x54031,f611(x54032,x54031))) % 154.70/154.55 [5466]P56(x54661,x54662)+~P1(f328(f316(x54661,x54662),f553(x54662,x54661))) % 154.70/154.55 [5610]~E(f328(a116,f44(a875,x56101,x56102)),x56102)+E(f44(a875,f328(a116,x56101),x56102),f2(a875)) % 154.70/154.55 [5667]P39(x56671,x56672)+P1(f328(f328(f330(x56671),f631(x56672,x56671)),f632(x56672,x56671))) % 154.70/154.55 [5674]~P135(x56741)+P1(f328(f328(f330(x56741),f328(f104(x56741),x56742)),f113(x56741))) % 154.70/154.55 [5675]~P140(x56751)+P1(f328(f328(f330(x56751),f328(f104(x56751),x56752)),f190(x56751))) % 154.70/154.55 [5676]~P135(x56761)+P1(f328(f328(f330(x56761),f328(f106(x56761),x56762)),f113(x56761))) % 154.70/154.55 [5677]~P90(x56771)+P1(f328(f328(f330(x56771),f328(f107(x56771),x56772)),f113(x56771))) % 154.70/154.55 [5822]E(f328(a116,f44(a875,x58221,x58222)),x58222)+E(f44(a875,f328(a116,x58221),x58222),f328(a116,f44(a875,x58221,x58222))) % 154.70/154.55 [6239]P39(x62391,x62392)+~P1(f328(f328(f330(x62391),f556(x62392,x62391)),f317(x62391,x62392))) % 154.70/154.55 [6274]~P123(x62741)+~P1(f328(f328(f243(x62741),f328(f104(x62741),x62742)),f2(x62741))) % 154.70/154.55 [6275]~P83(x62751)+~P1(f328(f328(f243(x62751),f328(f75(x62751),x62752)),f2(x62751))) % 154.70/154.55 [6361]P1(f328(f328(f243(a1),x63611),f44(a1,x63612,x63611)))+~P1(f328(f328(f243(a1),x63611),f2(a1))) % 154.70/154.55 [6460]E(f328(f328(f306(a875),f328(a116,x64601)),f299(a875,x64602,x64601)),f299(a875,x64602,f328(a116,x64601)))+~P1(f328(f328(f242(a875),x64602),f328(a116,x64601))) % 154.70/154.55 [6547]~P105(x65471)+P16(x65471,f147(x65471,x65471,f5(x65471),x65472)) % 154.70/154.55 [6677]E(f328(f165(x66771),x66772),x66772)+~P1(f328(f328(f242(a875),f328(f193(f876(x66771)),x66772)),f78(a875))) % 154.70/154.55 [6697]~P83(x66971)+P1(f328(f328(f242(x66971),f328(f79(x66971),f328(f75(x66971),x66972))),f2(x66971))) % 154.70/154.55 [6730]~P39(x67301,x67302)+P39(x67301,f328(f328(f285(x67301,x67301,x67301),x67302),f304(x67301,x67302))) % 154.70/154.55 [6952]~P1(f328(f328(f243(a1),x69522),f2(a1)))+P1(f328(f328(f242(a1),f44(a1,x69521,x69522)),f2(a1))) % 154.70/154.55 [7348]~P140(x73481)+E(f194(x73481,f328(f328(f7(x73481,x73481,x73481),f80(x73481)),f78(x73481)),x73482,f2(x73481)),f328(f104(x73481),x73482)) % 154.70/154.55 [7376]~P120(x73761)+~P1(f328(f328(f243(x73761),f328(f328(f81(x73761),x73762),x73762)),f2(x73761))) % 154.70/154.55 [10015]~P121(x100151)+~P1(f328(f328(f243(x100151),f328(f328(f253(x100151),x100152),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f2(x100151))) % 154.70/154.55 [4652]~E(x46522,f117(x46521))+E(f328(f193(f876(x46521)),x46522),f2(a875)) % 154.70/154.55 [4692]~E(x46921,f2(a875))+E(f328(f328(f80(a875),x46921),x46922),x46922) % 154.70/154.55 [4693]~E(x46932,f2(a875))+E(f328(f328(f81(a875),x46931),x46932),f2(a875)) % 154.70/154.55 [4695]~E(x46951,f2(a875))+E(f328(f328(f81(a875),x46951),x46952),f2(a875)) % 154.70/154.55 [4696]~E(x46962,f2(a875))+E(f328(f328(f253(a875),x46961),x46962),f78(a875)) % 154.70/154.55 [4697]~E(x46972,f2(a1))+E(f328(f328(f38(a1),x46971),x46972),f2(a1)) % 154.70/154.55 [4707]E(x47071,f117(x47072))+~E(f328(f193(f876(x47072)),x47071),f2(a875)) % 154.70/154.55 [4708]~P2(x47081)+E(f328(f328(f114(x47081),x47082),x47082),x47082) % 154.70/154.55 [4710]~P99(x47101)+E(f328(f328(f114(x47101),x47102),x47102),x47102) % 154.70/154.55 [4711]~P2(x47111)+E(f328(f328(f105(x47111),x47112),x47112),x47112) % 154.70/154.55 [4713]~P100(x47131)+E(f328(f328(f105(x47131),x47132),x47132),x47132) % 154.70/154.55 [4715]~P94(x47151)+E(f328(f328(f81(x47151),x47152),x47152),x47152) % 154.70/154.55 [4717]~P105(x47171)+E(f328(f328(f240(x47171),x47172),x47172),x47172) % 154.70/154.55 [4719]~P105(x47191)+E(f328(f328(f241(x47191),x47192),x47192),x47192) % 154.70/154.55 [4738]~P72(x47381)+E(f328(f328(f22(x47381),x47382),x47382),f2(x47381)) % 154.70/154.55 [4750]~P72(x47501)+E(f328(f79(x47501),f328(f79(x47501),x47502)),x47502) % 154.70/154.55 [4751]~P93(x47511)+E(f328(f79(x47511),f328(f79(x47511),x47512)),x47512) % 154.70/154.55 [4768]~E(x47682,f2(a875))+E(f328(f328(f253(a875),x47681),x47682),f328(a116,f2(a875))) % 154.70/154.55 [4802]~P3(x48021)+E(f328(f328(f114(x48021),f192(x48021)),x48022),x48022) % 154.70/154.55 [4803]~P97(x48031)+E(f328(f328(f105(x48031),f251(x48031)),x48032),x48032) % 154.70/154.55 [4804]~P66(x48041)+E(f328(f328(f80(x48041),f2(x48041)),x48042),x48042) % 154.70/154.55 [4805]~P77(x48051)+E(f328(f328(f80(x48051),f2(x48051)),x48052),x48052) % 154.70/154.55 [4806]~P109(x48061)+E(f328(f328(f80(x48061),f2(x48061)),x48062),x48062) % 154.70/154.55 [4807]~P109(x48071)+E(f328(f328(f81(x48071),f78(x48071)),x48072),x48072) % 154.70/154.55 [4808]~P73(x48081)+E(f328(f328(f81(x48081),f78(x48081)),x48082),x48082) % 154.70/154.55 [4809]~P79(x48091)+E(f328(f328(f81(x48091),f78(x48091)),x48092),x48092) % 154.70/154.55 [4828]~P97(x48281)+E(f328(f328(f114(x48281),f251(x48281)),x48282),f251(x48281)) % 154.70/154.55 [4829]~P3(x48291)+E(f328(f328(f105(x48291),f192(x48291)),x48292),f192(x48291)) % 154.70/154.55 [4830]~P109(x48301)+E(f328(f328(f81(x48301),f2(x48301)),x48302),f2(x48301)) % 154.70/154.55 [4831]~P128(x48311)+E(f328(f328(f81(x48311),f2(x48311)),x48312),f2(x48311)) % 154.70/154.55 [4832]~P79(x48321)+E(f328(f328(f253(x48321),f78(x48321)),x48322),f78(x48321)) % 154.70/154.55 [4833]~P117(x48331)+E(f328(f328(f286(x48331),f2(x48331)),x48332),f2(x48331)) % 154.70/154.55 [4834]~P57(x48341)+E(f328(f328(f38(x48341),f2(x48341)),x48342),f2(x48341)) % 154.70/154.55 [4842]E(x48421,f117(x48422))+E(f141(x48422,f328(f166(x48422),x48421)),f328(f138(x48422),x48421)) % 154.70/154.55 [4843]E(x48431,f117(x48432))+E(f328(f138(x48432),f328(f166(x48432),x48431)),f141(x48432,x48431)) % 154.70/154.55 [4844]E(x48441,f2(a875))+~E(f328(f328(f80(a875),x48442),x48441),x48442) % 154.70/154.55 [4850]~P135(x48501)+E(f328(f106(x48501),f328(f104(a1),x48502)),f328(f104(x48501),x48502)) % 154.70/154.55 [4851]~P90(x48511)+E(f328(f106(x48511),f328(f107(a1),x48512)),f328(f107(x48511),x48512)) % 154.70/154.55 [4858]E(x48581,f2(a875))+~E(f328(f328(f80(a875),x48582),x48581),f2(a875)) % 154.70/154.55 [4859]E(x48591,f2(a875))+~E(f328(f328(f80(a875),x48591),x48592),f2(a875)) % 154.70/154.55 [4860]E(x48601,f78(a875))+~E(f328(f328(f81(a875),x48602),x48601),f78(a875)) % 154.70/154.55 [4861]E(x48611,f78(a875))+~E(f328(f328(f81(a875),x48611),x48612),f78(a875)) % 154.70/154.55 [4876]~P121(x48761)+E(f328(f75(x48761),f328(f104(x48761),x48762)),f328(f104(x48761),x48762)) % 154.70/154.55 [4877]~P83(x48771)+E(f328(f75(x48771),f328(f75(x48771),x48772)),f328(f75(x48771),x48772)) % 154.70/154.55 [4878]~P83(x48781)+E(f328(f75(x48781),f328(f79(x48781),x48782)),f328(f75(x48781),x48782)) % 154.70/154.55 [4879]~P66(x48791)+E(f328(f163(x48791),f328(f166(x48791),x48792)),f328(f163(x48791),x48792)) % 154.70/154.55 [4884]~E(x48841,f328(a116,f2(a875)))+E(f328(f328(f253(a875),x48841),x48842),f328(a116,f2(a875))) % 154.70/154.55 [4894]~P72(x48941)+E(f328(f328(f22(x48941),f2(x48941)),x48942),f328(f79(x48941),x48942)) % 154.70/154.55 [4895]~E(x48952,f2(a875))+E(f136(a875,f328(f298(a875,x48951),x48952)),f117(a875)) % 154.70/154.55 [4904]~P90(x49041)+E(f328(f328(f80(x49041),x49042),f328(f107(x49041),a83)),x49042) % 154.70/154.55 [4905]E(x49051,f2(a1))+E(f46(f328(f75(a1),x49052),f328(f75(a1),x49051)),f52(x49052,x49051)) % 154.70/154.55 [4919]~E(x49191,x49192)+P1(f328(f328(f242(a875),x49191),x49192)) % 154.70/154.55 [4926]~E(x49261,f2(a103))+E(f328(f328(f80(a875),f328(a19,x49261)),x49262),x49262) % 154.70/154.55 [4927]~E(f328(f107(a1),x49272),f328(f104(a1),x49271))+E(x49271,f328(a108,f328(f107(a1),x49272))) % 154.70/154.55 [4936]~P6(x49361)+P6(f328(f328(f253(a1),x49361),x49362)) % 154.70/154.55 [4937]~P93(x49371)+E(f328(f328(f114(x49371),x49372),f328(f79(x49371),x49372)),f251(x49371)) % 154.70/154.55 [4938]~P93(x49381)+E(f328(f328(f105(x49381),x49382),f328(f79(x49381),x49382)),f192(x49381)) % 154.70/154.55 [4939]~P72(x49391)+E(f328(f328(f80(x49391),x49392),f328(f79(x49391),x49392)),f2(x49391)) % 154.70/154.55 [4964]E(x49641,f2(a875))+~E(f328(f79(a1),f328(f104(a1),x49642)),f328(f104(a1),x49641)) % 154.70/154.55 [4965]E(x49651,f2(a875))+~E(f328(f79(a1),f328(f104(a1),x49651)),f328(f104(a1),x49652)) % 154.70/154.55 [4975]E(f199(x49751,x49752),f2(a1))+P1(f328(f328(f242(a1),x49752),x49751)) % 154.70/154.55 [4976]E(f177(x49761,x49762),f117(a1))+P1(f328(f328(f242(a1),x49761),x49762)) % 154.70/154.55 [4989]E(x49891,f328(a116,f2(a875)))+~E(f328(f328(f81(a875),x49892),x49891),f328(a116,f2(a875))) % 154.70/154.55 [4990]E(x49901,f328(a116,f2(a875)))+~E(f328(f328(f81(a875),x49901),x49902),f328(a116,f2(a875))) % 154.70/154.55 [4991]~P106(x49911)+P1(f328(f328(f242(x49911),x49912),x49912)) % 154.70/154.55 [4992]~P92(x49921)+P1(f328(f328(f91(x49921),x49922),x49922)) % 154.70/154.55 [4995]~P90(x49951)+E(f328(f328(f81(x49951),x49952),f328(f107(x49951),a101)),f328(f79(x49951),x49952)) % 154.70/154.55 [5013]~P135(x50131)+E(f328(f79(x50131),f328(f106(x50131),x50132)),f328(f106(x50131),f328(f79(a1),x50132))) % 154.70/154.55 [5014]~P90(x50141)+E(f328(f79(x50141),f328(f107(x50141),x50142)),f328(f107(x50141),f328(f79(a1),x50142))) % 154.70/154.55 [5046]~E(x50461,f328(a116,x50462))+P1(f328(f328(f243(a875),f2(a875)),x50461)) % 154.70/154.55 [5063]~P105(x50631)+E(f328(f79(f882(x50631,a870)),f328(f249(x50631),x50632)),f328(f250(x50631),x50632)) % 154.70/154.55 [5064]~P105(x50641)+E(f328(f79(f882(x50641,a870)),f328(f300(x50641),x50642)),f328(f297(x50641),x50642)) % 154.70/154.55 [5065]~P105(x50651)+E(f328(f79(f882(x50651,a870)),f328(f297(x50651),x50652)),f328(f300(x50651),x50652)) % 154.70/154.55 [5066]~P105(x50661)+E(f328(f79(f882(x50661,a870)),f328(f250(x50661),x50662)),f328(f249(x50661),x50662)) % 154.70/154.55 [5074]~E(f328(f104(a1),x50742),x50741)+P1(f328(f328(f242(a1),f2(a1)),x50741)) % 154.70/154.55 [5081]~E(x50812,f2(a1))+E(f52(x50811,x50812),f328(f328(f263(a1,a1),f2(a1)),f328(f75(a1),x50811))) % 154.70/154.55 [5083]~P98(x50831)+P1(f328(f328(f242(x50831),f192(x50831)),x50832)) % 154.70/154.55 [5115]E(x51151,x51152)+~E(f328(f328(f80(a1),x51151),x51151),f328(f328(f80(a1),x51152),x51152)) % 154.70/154.55 [5119]~P1(f328(x51191,x51192))+P1(f328(x51191,f328(a108,f337(x51191)))) % 154.70/154.55 [5145]~P121(x51451)+E(f328(f328(f81(x51451),f82(x51451,x51452)),f328(f75(x51451),x51452)),x51452) % 154.70/154.55 [5154]~E(x51542,f2(a875))+E(f85(f881(a875,a875),f47(x51541,x51542)),f328(f328(f263(a875,a875),f2(a875)),x51541)) % 154.70/154.55 [5165]~E(x51651,x51652)+~P1(f328(f328(f243(a875),x51651),x51652)) % 154.70/154.55 [5166]~E(x51661,x51662)+~P1(f328(f328(f243(a1),x51661),x51662)) % 154.70/154.55 [5169]~P140(x51691)+E(f328(f328(f80(x51691),f78(x51691)),f328(f104(x51691),x51692)),f328(f104(x51691),f328(a116,x51692))) % 154.70/154.55 [5173]~E(x51731,f2(a875))+~P1(f328(f328(f243(a875),x51732),x51731)) % 154.70/154.55 [5189]E(f149(x51891,x51892),x51892)+~E(f328(f193(f876(x51891)),f149(x51891,x51892)),f328(f193(f876(x51891)),x51892)) % 154.70/154.55 [5190]E(f328(f37(x51901),f328(f170(x51901),x51902)),f328(f193(f876(x51901)),x51902))+~P1(f328(f134(x51901),x51902)) % 154.70/154.55 [5200]~P1(f328(x52001,f338(x52001)))+P1(f328(x52001,f328(f104(a1),x52002))) % 154.70/154.55 [5211]E(f276(x52111,x52112),f78(a103))+~P1(f328(f328(f243(a103),x52112),x52111)) % 154.70/154.55 [5212]E(f177(x52121,x52122),f117(a1))+~P1(f328(f328(f243(a1),x52122),x52121)) % 154.70/154.55 [5215]~P107(x52151)+E(f299(x52151,x52152,x52152),f328(f328(f306(x52151),x52152),f192(f882(x52151,a870)))) % 154.70/154.55 [5237]~E(f328(f328(f22(a875),x52371),x52372),f2(a875))+P1(f328(f328(f242(a875),x52371),x52372)) % 154.70/154.55 [5238]~E(f328(f328(f22(a1),x52381),x52382),f2(a1))+P1(f328(f328(f91(a1),x52381),x52382)) % 154.70/154.55 [5261]~E(x52612,f2(a875))+E(f54(x52611,x52612,f117(x52611)),f328(f328(f148(f876(x52611)),f117(x52611)),f117(f876(x52611)))) % 154.70/154.55 [5265]~P106(x52651)+~P1(f328(f328(f243(x52651),x52652),x52652)) % 154.70/154.55 [5268]~E(f44(a1,x52681,x52682),f2(a1))+E(f44(a1,x52681,f328(f79(a1),x52682)),f2(a1)) % 154.70/154.55 [5270]~E(f44(a1,x52701,x52702),f2(a1))+E(f44(a1,f328(f79(a1),x52701),x52702),f2(a1)) % 154.70/154.55 [5279]E(f328(f298(a875,x52791),f328(a116,x52792)),f192(f882(a875,a870)))+P1(f328(f328(f242(a875),x52791),x52792)) % 154.70/154.55 [5299]E(f136(a875,f328(f298(a875,x52991),x52992)),f117(a875))+P1(f328(f328(f243(a875),x52991),x52992)) % 154.70/154.55 [5304]~E(f328(f37(x53041),f328(f170(x53041),x53042)),f328(f193(f876(x53041)),x53042))+P1(f328(f134(x53041),x53042)) % 154.70/154.55 [5309]~P1(f328(f134(x53091),x53092))+P1(f328(f134(x53091),f328(f165(x53091),x53092))) % 154.70/154.55 [5310]~P1(f328(f134(x53101),x53102))+P1(f328(f134(x53101),f328(f169(x53101),x53102))) % 154.70/154.55 [5311]~P1(f328(f134(x53111),x53112))+P1(f328(f134(x53111),f328(f166(x53111),x53112))) % 154.70/154.55 [5318]P1(f328(x53181,x53182))+~P1(f328(x53181,f328(a108,f389(x53181)))) % 154.70/154.55 [5319]P1(f328(f328(f242(a875),x53192),x53191))+P1(f328(f328(f242(a875),x53191),x53192)) % 154.70/154.55 [5320]P1(f328(f328(f242(a1),x53202),x53201))+P1(f328(f328(f242(a1),x53201),x53202)) % 154.70/154.55 [5322]~P83(x53221)+P1(f328(f328(f242(x53221),x53222),f328(f75(x53221),x53222))) % 154.70/154.55 [5325]P1(f328(x53251,f339(x53251)))+~P1(f328(x53251,f328(f104(a1),x53252))) % 154.70/154.55 [5350]E(f328(f328(f22(a875),x53501),x53502),f2(a875))+~P1(f328(f328(f242(a875),x53501),x53502)) % 154.70/154.55 [5351]E(f328(f328(f22(a1),x53511),x53512),f2(a1))+~P1(f328(f328(f91(a1),x53511),x53512)) % 154.70/154.55 [5352]E(f328(f328(f38(a875),x53521),x53522),f2(a875))+~P1(f328(f328(f243(a875),x53521),x53522)) % 154.70/154.55 [5370]E(f44(a875,x53701,x53702),x53701)+~P1(f328(f328(f243(a875),x53701),x53702)) % 154.70/154.55 [5379]E(f44(a1,x53791,f328(f79(a1),x53792)),f287(x53791,x53792))+P1(f328(f328(f242(a1),f2(a1)),x53792)) % 154.70/154.55 [5391]E(f328(f328(f22(a1),x53911),x53912),f199(x53911,x53912))+~P1(f328(f328(f242(a1),x53912),x53911)) % 154.70/154.55 [5410]P1(f328(f328(f242(a1),f2(a1)),f338(x54101)))+P1(f328(x54101,f328(f104(a1),x54102))) % 154.70/154.55 [5422]~P59(x54221)+P1(f328(f328(f330(x54221),x54222),f328(f170(x54221),f55(x54221)))) % 154.70/154.55 [5424]~P123(x54241)+P1(f328(f328(f242(x54241),f2(x54241)),f328(f104(x54241),x54242))) % 154.70/154.55 [5425]~P83(x54251)+P1(f328(f328(f242(x54251),f2(x54251)),f328(f75(x54251),x54252))) % 154.70/154.55 [5452]E(f328(f328(f80(a875),x54521),f340(x54522,x54521)),x54522)+~P1(f328(f328(f242(a875),x54521),x54522)) % 154.70/154.55 [5464]~E(f328(f107(a1),x54641),f328(f104(a1),x54642))+P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x54641))) % 154.70/154.55 [5467]E(f299(a1,x54671,x54672),f192(f882(a1,a870)))+~P1(f328(f328(f243(a1),x54672),x54671)) % 154.70/154.55 [5469]~P121(x54691)+E(f328(f328(f81(x54691),f328(f75(x54691),x54692)),f328(f75(x54691),x54692)),f328(f328(f81(x54691),x54692),x54692)) % 154.70/154.55 [5475]E(f136(a875,f328(f298(a875,x54751),f328(a116,x54752))),f117(a875))+P1(f328(f328(f242(a875),x54751),x54752)) % 154.70/154.55 [5479]E(f328(f328(f38(a1),x54791),x54792),f288(x54791,x54792))+~P1(f328(f328(f242(a1),f2(a1)),x54792)) % 154.70/154.55 [5499]P1(f328(f134(x54991),x54992))+~P1(f328(f134(x54991),f328(f165(x54991),x54992))) % 154.70/154.55 [5500]P1(f328(f134(x55001),x55002))+~P1(f328(f134(x55001),f328(f166(x55001),x55002))) % 154.70/154.55 [5521]P1(f328(f61(a875),x55211))+P1(f328(f328(f330(a875),f341(x55211,x55212)),x55211)) % 154.70/154.55 [5522]P1(f328(f61(a875),x55221))+P1(f328(f328(f330(a875),f356(x55221,x55222)),x55221)) % 154.70/154.55 [5523]P1(f328(f328(f243(a875),x55232),f328(a116,x55231)))+P1(f328(f328(f243(a875),x55231),x55232)) % 154.70/154.55 [5524]E(f44(a1,x55241,x55242),f287(x55241,x55242))+~P1(f328(f328(f242(a1),f2(a1)),x55242)) % 154.70/154.55 [5527]E(f136(a875,f328(f298(a875,x55271),x55272)),f117(a875))+~P1(f328(f328(f242(a875),x55272),x55271)) % 154.70/154.55 [5528]~P81(x55281)+E(f328(f307(x55281,x55281,f79(x55281)),f328(f249(x55281),x55282)),f328(f300(x55281),f328(f79(x55281),x55282))) % 154.70/154.55 [5529]~P81(x55291)+E(f328(f307(x55291,x55291,f79(x55291)),f328(f300(x55291),x55292)),f328(f249(x55291),f328(f79(x55291),x55292))) % 154.70/154.55 [5530]~P81(x55301)+E(f328(f307(x55301,x55301,f79(x55301)),f328(f297(x55301),x55302)),f328(f250(x55301),f328(f79(x55301),x55302))) % 154.70/154.55 [5531]~P81(x55311)+E(f328(f307(x55311,x55311,f79(x55311)),f328(f250(x55311),x55312)),f328(f297(x55311),f328(f79(x55311),x55312))) % 154.70/154.55 [5542]E(x55421,f192(f882(x55422,a870)))+P1(f328(f328(f330(x55422),f630(x55421,x55422)),x55421)) % 154.70/154.55 [5543]E(x55431,f192(f882(x55432,a870)))+P1(f328(f328(f330(x55432),f554(x55431,x55432)),x55431)) % 154.70/154.55 [5554]~P1(f328(f328(f243(a875),x55541),x55542))+P1(f328(f328(f242(a875),x55541),x55542)) % 154.70/154.55 [5555]~P1(f328(f328(f243(a1),x55551),x55552))+P1(f328(f328(f242(a1),x55551),x55552)) % 154.70/154.55 [5571]E(f46(x55711,x55712),f328(f328(f263(a1,a1),f2(a1)),x55711))+~P1(f328(f328(f243(a1),x55711),x55712)) % 154.70/154.55 [5572]E(f222(f328(f79(a1),x55721),f328(f79(a1),x55722)),f222(x55721,x55722))+~P1(f328(f328(f243(a1),x55722),f2(a1))) % 154.70/154.55 [5580]E(x55801,x55802)+~P1(f328(f328(f328(a198,a24),x55801),x55802)) % 154.70/154.55 [5584]E(x55841,x55842)+~E(f328(a3,f328(a116,f328(a19,x55841))),f328(a3,f328(a116,f328(a19,x55842)))) % 154.70/154.55 [5589]E(f46(x55891,x55892),f328(f328(f263(a1,a1),f2(a1)),x55891))+~P1(f328(f328(f242(a1),x55892),f2(a1))) % 154.70/154.55 [5616]E(f44(a875,f328(f107(a875),x56161),f328(f107(a875),x56162)),f2(a875))+~P1(f328(a197,f328(f107(a1),x56161))) % 154.70/154.55 [5631]P1(f328(f328(f242(a1),f2(a1)),f339(x56311)))+~P1(f328(x56311,f328(f104(a1),x56312))) % 154.70/154.55 [5665]P40(f299(a1,x56651,x56652))+~P1(f328(f328(f242(a1),f2(a1)),x56651)) % 154.70/154.55 [5670]~P1(f328(f61(x56701),x56702))+P1(f328(f61(f882(x56701,a870)),f328(f305(x56701),x56702))) % 154.70/154.55 [5683]E(f328(f328(f80(a1),x56831),f328(f104(a1),f365(x56832,x56831))),x56832)+~P1(f328(f328(f242(a1),x56831),x56832)) % 154.70/154.55 [5691]P1(f328(f328(f242(a875),x56911),x56912))+P1(f328(f328(f242(a875),f328(a116,x56912)),x56911)) % 154.70/154.55 [5736]E(f328(f328(f38(a875),f328(f107(a875),x57361)),f328(f107(a875),x57362)),f2(a875))+~P1(f328(a197,f328(f107(a1),x57361))) % 154.70/154.55 [5737]E(f328(f328(f81(a875),f328(f107(a875),x57371)),f328(f107(a875),x57372)),f2(a875))+~P1(f328(f328(f243(a1),x57371),a83)) % 154.70/154.55 [5739]P1(f328(f328(f243(a875),x57391),f328(a116,x57392)))+~P1(f328(f328(f243(a875),x57391),x57392)) % 154.70/154.55 [5741]P1(f328(f328(f243(a875),x57411),f328(a116,x57412)))+~P1(f328(f328(f242(a875),x57411),x57412)) % 154.70/154.55 [5743]P1(f328(f328(f242(a875),x57431),f328(a116,x57432)))+~P1(f328(f328(f242(a875),x57431),x57432)) % 154.70/154.55 [5746]~E(x57461,x57462)+P1(f328(f328(f243(a1),x57461),f328(f328(f80(a1),x57462),f78(a1)))) % 154.70/154.55 [5749]E(f44(a1,x57491,x57492),f2(a1))+E(f328(f328(f22(a1),x57492),f44(a1,x57491,x57492)),f44(a1,f328(f79(a1),x57491),x57492)) % 154.70/154.55 [5758]E(x57581,f117(x57582))+P1(f328(f328(f330(x57582),f141(x57582,x57581)),f328(f170(x57582),x57581))) % 154.70/154.55 [5770]E(f85(f881(a875,a875),f47(x57701,x57702)),f328(f328(f263(a875,a875),f2(a875)),x57701))+~P1(f328(f328(f243(a875),x57701),x57702)) % 154.70/154.55 [5803]E(f328(f328(f22(a875),f328(f107(a875),x58031)),f328(f107(a875),x58032)),f328(f107(a875),x58031))+~P1(f328(f328(f243(a1),x58032),a83)) % 154.70/154.55 [5804]E(f328(f328(f80(a875),f328(f107(a875),x58041)),f328(f107(a875),x58042)),f328(f107(a875),x58042))+~P1(f328(f328(f243(a1),x58041),a83)) % 154.70/154.55 [5809]E(f328(a116,f328(f328(f80(a875),x58091),f808(x58092,x58091))),x58092)+~P1(f328(f328(f243(a875),x58091),x58092)) % 154.70/154.55 [5832]P1(f328(x58321,x58322))+~P1(f328(x58321,f328(a89,f570(x58322,x58321)))) % 154.70/154.55 [5840]~P1(f328(f328(f243(a875),x58401),f328(a116,x58402)))+P1(f328(f328(f242(a875),x58401),x58402)) % 154.70/154.55 [5886]E(f328(f328(f306(a875),x58861),f328(f298(a875,x58862),x58861)),f328(f298(a875,x58862),f328(a116,x58861)))+~P1(f328(f328(f242(a875),x58862),x58861)) % 154.70/154.55 [5890]E(x58901,f117(x58902))+E(f328(f328(f125(x58902),f118(x58902,x58901)),f328(f328(f148(x58902),f141(x58902,x58901)),f117(x58902))),x58901) % 154.70/154.55 [5904]P1(f328(f61(x59041),x59042))+~P1(f328(f328(f243(a875),f2(a875)),f328(f37(x59041),x59042))) % 154.70/154.55 [5906]~E(x59061,f192(f882(x59062,a870)))+~P1(f328(f328(f243(a875),f2(a875)),f328(f37(x59062),x59061))) % 154.70/154.55 [5918]~P1(f328(f328(f243(a875),x59181),x59182))+P1(f328(f328(f242(a875),f328(a116,x59181)),x59182)) % 154.70/154.55 [5925]~P105(x59251)+E(f147(x59251,x59251,f5(x59251),f149(x59251,x59252)),f136(x59251,f328(f170(x59251),x59252))) % 154.70/154.55 [5928]E(x59281,f117(x59282))+P1(f328(f328(f330(x59282),f328(f138(x59282),x59281)),f328(f170(x59282),x59281))) % 154.70/154.55 [5934]~P123(x59341)+P1(f328(f328(f243(x59341),x59342),f328(f328(f80(x59341),x59342),f78(x59341)))) % 154.70/154.55 [5936]~P83(x59361)+P1(f328(f328(f242(x59361),f328(f79(x59361),x59362)),f328(f75(x59361),x59362))) % 154.70/154.55 [5967]P1(f328(f61(a875),x59671))+~P1(f328(f328(f243(a875),f341(x59671,x59672)),x59672)) % 154.70/154.55 [5968]P1(f328(f61(a875),x59681))+~P1(f328(f328(f242(a875),f356(x59681,x59682)),x59682)) % 154.70/154.55 [5971]~P1(f328(f61(f881(x59711,x59711)),x59712))+P1(f328(f61(x59711),f328(f281(x59711),x59712))) % 154.70/154.55 [6024]~P1(f328(f328(f243(a875),x60242),f328(a116,x60241)))+~P1(f328(f328(f243(a875),x60241),x60242)) % 154.70/154.55 [6025]~P107(x60251)+E(f328(f328(f105(f882(x60251,a870)),f328(f297(x60251),x60252)),f328(f250(x60251),x60252)),f328(f328(f306(x60251),x60252),f192(f882(x60251,a870)))) % 154.70/154.55 [6038]P1(f328(f61(x60381),x60382))+~P1(f328(f61(f882(x60381,a870)),f328(f305(x60381),x60382))) % 154.70/154.55 [6063]P1(f328(f328(f243(a875),f328(a116,x60631)),f328(a116,x60632)))+~P1(f328(f328(f243(a875),x60631),x60632)) % 154.70/154.55 [6064]P1(f328(f328(f243(a875),f328(a19,x60641)),f328(a19,x60642)))+~P1(f328(f328(f243(a103),x60641),x60642)) % 154.70/154.55 [6065]P1(f328(f328(f243(a103),f328(a3,x60651)),f328(a3,x60652)))+~P1(f328(f328(f243(a875),x60651),x60652)) % 154.70/154.55 [6066]P1(f328(f328(f242(a875),f328(a116,x60661)),f328(a116,x60662)))+~P1(f328(f328(f242(a875),x60661),x60662)) % 154.70/154.55 [6067]P1(f328(f328(f242(a875),f328(a19,x60671)),f328(a19,x60672)))+~P1(f328(f328(f242(a103),x60671),x60672)) % 154.70/154.55 [6068]P1(f328(f328(f242(a103),f328(a3,x60681)),f328(a3,x60682)))+~P1(f328(f328(f242(a875),x60681),x60682)) % 154.70/154.55 [6071]E(x60711,x60712)+~E(f328(f307(a875,a1,f104(a1)),x60711),f328(f307(a875,a1,f104(a1)),x60712)) % 154.70/154.55 [6087]P1(f328(f328(f243(a875),x60871),x60872))+~P1(f328(f328(f243(a875),f328(a116,x60871)),x60872)) % 154.70/154.55 [6090]P1(f328(f328(f243(a875),x60901),x60902))+~P1(f328(f328(f242(a875),f328(a116,x60901)),x60902)) % 154.70/154.55 [6091]P1(f328(f328(f242(a875),x60911),x60912))+~P1(f328(f328(f242(a875),f328(a116,x60911)),x60912)) % 154.70/154.55 [6106]E(f44(a1,x61061,x61062),f2(a1))+E(f328(f328(f22(a1),f44(a1,x61061,x61062)),x61062),f44(a1,x61061,f328(f79(a1),x61062))) % 154.70/154.55 [6179]E(f328(f37(f882(x61791,a870)),f328(f305(x61791),x61792)),f328(f328(f253(a875),f328(a116,f328(a116,f2(a875)))),f328(f37(x61791),x61792)))+~P1(f328(f61(x61791),x61792)) % 154.70/154.55 [6182]E(x61821,f117(x61822))+E(f328(f328(f162(x61822),x61821),f328(f328(f22(a875),f328(f193(f876(x61822)),x61821)),f78(a875))),f141(x61822,x61821)) % 154.70/154.55 [6207]E(x62071,f117(x62072))+E(f328(f328(f125(x62072),f328(f169(x62072),x62071)),f328(f328(f148(x62072),f328(f138(x62072),x62071)),f117(x62072))),f328(f165(x62072),x62071)) % 154.70/154.55 [6236]~P1(f328(f61(x62361),f39(f882(x62361,a870),x62362)))+P1(f328(f61(f882(x62361,a870)),x62362)) % 154.70/154.55 [6259]P1(f328(f328(f242(a875),f328(f107(a875),x62591)),f328(f107(a875),x62592)))+~P1(f328(f328(f242(a1),x62591),a83)) % 154.70/154.55 [6276]~P1(f328(f328(f243(a1),x62761),x62762))+P1(f328(f328(f243(a1),x62761),f328(f328(f80(a1),x62762),f78(a1)))) % 154.70/154.55 [6277]~P1(f328(f328(f242(a1),x62771),x62772))+P1(f328(f328(f243(a1),x62771),f328(f328(f80(a1),x62772),f78(a1)))) % 154.70/154.55 [6278]~P1(f328(f328(f243(a1),x62781),x62782))+P1(f328(f328(f242(a1),x62781),f328(f328(f22(a1),x62782),f78(a1)))) % 154.70/154.55 [6281]~P1(f328(f328(f243(a875),x62811),x62812))+P1(f328(f328(f243(a1),f328(f104(a1),x62811)),f328(f104(a1),x62812))) % 154.70/154.55 [6282]~P1(f328(f328(f243(a1),x62821),x62822))+P1(f328(f328(f243(a1),f328(f107(a1),x62821)),f328(f107(a1),x62822))) % 154.70/154.55 [6283]~P1(f328(f328(f242(a1),x62831),x62832))+P1(f328(f328(f242(a875),f328(f107(a875),x62831)),f328(f107(a875),x62832))) % 154.70/154.55 [6285]~P1(f328(f328(f242(a875),x62851),x62852))+P1(f328(f328(f242(a1),f328(f104(a1),x62851)),f328(f104(a1),x62852))) % 154.70/154.55 [6286]~P1(f328(f328(f242(a1),x62861),x62862))+P1(f328(f328(f242(a1),f328(f107(a1),x62861)),f328(f107(a1),x62862))) % 154.70/154.55 [6287]~P1(f328(f328(f91(a1),x62871),x62872))+P1(f328(f328(f91(a1),f328(f107(a1),x62871)),f328(f107(a1),x62872))) % 154.70/154.55 [6305]~P1(f328(f328(f242(a875),x63051),x63052))+~P1(f328(f328(f242(a875),f328(a116,x63052)),x63051)) % 154.70/154.55 [6348]~P1(f328(f328(f243(a875),f328(a116,x63481)),f328(a116,x63482)))+P1(f328(f328(f243(a875),x63481),x63482)) % 154.70/154.55 [6349]~P1(f328(f328(f243(a103),f328(a3,x63491)),f328(a3,x63492)))+P1(f328(f328(f243(a875),x63491),x63492)) % 154.70/154.55 [6350]~P1(f328(f328(f243(a875),f328(a108,x63501)),f328(a108,x63502)))+P1(f328(f328(f243(a1),x63501),x63502)) % 154.70/154.55 [6351]~P1(f328(f328(f243(a875),f328(a19,x63511)),f328(a19,x63512)))+P1(f328(f328(f243(a103),x63511),x63512)) % 154.70/154.55 [6352]~P1(f328(f328(f242(a875),f328(a116,x63521)),f328(a116,x63522)))+P1(f328(f328(f242(a875),x63521),x63522)) % 154.70/154.55 [6353]~P1(f328(f328(f242(a103),f328(a3,x63531)),f328(a3,x63532)))+P1(f328(f328(f242(a875),x63531),x63532)) % 154.70/154.55 [6354]~P1(f328(f328(f242(a875),f328(a19,x63541)),f328(a19,x63542)))+P1(f328(f328(f242(a103),x63541),x63542)) % 154.70/154.55 [6394]~P1(f328(f328(f243(a875),f328(a108,x63942)),f328(a108,x63941)))+P1(f328(f328(f243(a1),f2(a1)),x63941)) % 154.70/154.55 [6425]P1(f328(f328(f242(a1),f2(a1)),f44(a1,x64251,x64252)))+~P1(f328(f328(f243(a1),f2(a1)),x64252)) % 154.70/154.55 [6582]P39(x65821,x65822)+~E(f328(f328(f285(x65821,x65821,x65821),x65822),x65822),f192(f882(f881(x65821,x65821),a870))) % 154.70/154.55 [6594]~P39(x65941,x65942)+P39(x65941,f328(f328(f285(x65941,x65941,x65941),x65942),x65942)) % 154.70/154.55 [6606]P1(f328(f328(f243(a1),x66061),x66062))+~P1(f328(f328(f242(a1),x66061),f328(f328(f22(a1),x66062),f78(a1)))) % 154.70/154.55 [6607]P1(f328(f328(f242(a1),x66071),x66072))+~P1(f328(f328(f243(a1),x66071),f328(f328(f80(a1),x66072),f78(a1)))) % 154.70/154.55 [6610]P1(f328(f328(f243(a875),x66101),x66102))+~P1(f328(f328(f243(a1),f328(f104(a1),x66101)),f328(f104(a1),x66102))) % 154.70/154.55 [6611]P1(f328(f328(f243(a1),x66111),x66112))+~P1(f328(f328(f243(a875),f328(f107(a875),x66111)),f328(f107(a875),x66112))) % 154.70/154.55 [6612]P1(f328(f328(f243(a1),x66121),x66122))+~P1(f328(f328(f243(a1),f328(f107(a1),x66121)),f328(f107(a1),x66122))) % 154.70/154.55 [6614]P1(f328(f328(f242(a875),x66141),x66142))+~P1(f328(f328(f242(a1),f328(f104(a1),x66141)),f328(f104(a1),x66142))) % 154.70/154.55 [6615]P1(f328(f328(f242(a1),x66151),x66152))+~P1(f328(f328(f242(a1),f328(f107(a1),x66151)),f328(f107(a1),x66152))) % 154.70/154.55 [6616]P1(f328(f328(f91(a1),x66161),x66162))+~P1(f328(f328(f91(a1),f328(f107(a1),x66161)),f328(f107(a1),x66162))) % 154.70/154.55 [6710]~E(f734(x67102,x67101),f117(x67101))+E(f328(f139(f876(x67101),f876(x67101),f125(x67101),f117(x67101)),x67102),f117(x67101)) % 154.70/154.55 [6711]~E(f740(x67112,x67111),f117(x67111))+E(f328(f139(f876(x67111),f876(x67111),f125(x67111),f117(x67111)),x67112),f117(x67111)) % 154.70/154.55 [6718]~P5(x67181)+E(f328(f139(x67181,x67181,f114(x67181),f192(x67181)),x67182),f39(x67181,f328(f170(x67181),x67182))) % 154.70/154.55 [6719]~P5(x67191)+E(f328(f139(x67191,x67191,f105(x67191),f251(x67191)),x67192),f40(x67191,f328(f170(x67191),x67192))) % 154.70/154.55 [6731]E(x67311,f2(a103))+E(f328(f328(f80(a875),f328(a19,f328(f328(f22(a103),x67311),f78(a103)))),f328(a116,x67312)),f328(f328(f80(a875),f328(a19,x67311)),x67312)) % 154.70/154.55 [6781]P1(f328(f328(f243(a1),f328(f328(f22(a1),x67811),x67812)),f2(a1)))+~P1(f328(f328(f243(a1),x67811),x67812)) % 154.70/154.55 [6809]~P105(x68091)+E(f328(f328(f114(f882(x68091,a870)),f328(f328(f306(x68091),x68092),f192(f882(x68091,a870)))),f328(f300(x68091),x68092)),f328(f250(x68091),x68092)) % 154.70/154.55 [6885]~P56(x68851,x68852)+P39(x68851,f328(f248(f881(x68851,x68851)),f328(f267(x68851,x68851,a870),x68852))) % 154.70/154.55 [6886]~P56(x68861,x68862)+P54(x68861,f328(f248(f881(x68861,x68861)),f328(f267(x68861,x68861,a870),x68862))) % 154.70/154.55 [6887]E(x68871,f192(f882(x68872,a870)))+~P1(f328(f328(f242(f882(x68872,a870)),x68871),f192(f882(x68872,a870)))) % 154.70/154.55 [6968]~P1(f328(f328(f243(a875),f2(a875)),x69682))+P1(f328(f328(f243(a875),f44(a875,x69681,x69682)),x69682)) % 154.70/154.55 [6970]~P1(f328(f328(f243(a1),f2(a1)),x69702))+P1(f328(f328(f243(a1),f44(a1,x69701,x69702)),x69702)) % 154.70/154.55 [6971]~P1(f328(f328(f243(a875),f2(a875)),x69712))+P1(f328(f328(f242(a875),f44(a875,x69711,x69712)),x69712)) % 154.70/154.55 [6972]~P1(f328(f328(f242(a1),f2(a1)),x69721))+P1(f328(f328(f242(a1),f44(a1,x69721,x69722)),x69721)) % 154.70/154.55 [7048]~P107(x70481)+E(f328(f328(f22(f882(x70481,a870)),f328(f328(f306(x70481),x70482),f192(f882(x70481,a870)))),f328(f249(x70481),x70482)),f328(f328(f306(x70481),x70482),f192(f882(x70481,a870)))) % 154.70/154.55 [7121]~P50(x71211,x71212)+P41(x71211,f251(f882(x71211,a870)),f328(f248(f881(x71211,x71211)),f328(f267(x71211,x71211,a870),x71212))) % 154.70/154.55 [7122]P1(f328(x71221,x71222))+P1(f328(f328(f330(f882(f881(a875,a875),a870)),f570(x71222,x71221)),a102)) % 154.70/154.55 [7167]E(f328(f328(f125(a875),f136(a875,f328(f298(a875,x71671),x71672))),f328(f328(f148(a875),x71672),f117(a875))),f136(a875,f328(f298(a875,x71671),f328(a116,x71672))))+~P1(f328(f328(f242(a875),x71671),x71672)) % 154.70/154.55 [7310]E(x73101,f2(a875))+~E(f328(f139(a875,a875,f80(a875),x73101),x73102),f2(a875)) % 154.70/154.55 [7338]~P1(f328(f328(f243(a1),f328(f328(f22(a1),x73381),x73382)),f2(a1)))+P1(f328(f328(f243(a1),x73381),x73382)) % 154.70/154.55 [7367]P39(x73671,x73672)+~P39(x73671,f328(f328(f285(x73671,x73671,x73671),x73672),x73672)) % 154.70/154.55 [7396]~P1(f328(f328(f242(a875),f328(a116,x73961)),x73962))+P1(f189(a870,a246,f328(f242(a875),x73961),x73962)) % 154.70/154.55 [7553]P27(a875,a875,f328(f328(f7(a875,a875,a875),f22(a875)),x75531),x75532)+P1(f328(f328(f330(a875),f447(x75531,x75532)),x75532)) % 154.70/154.55 [7611]E(f328(f328(f328(f65(a875,x76111,f80(a875)),f328(f16(a875,x76111),f78(a875))),f2(a875)),x76112),f328(f37(x76111),x76112))+~P1(f328(f61(x76111),x76112)) % 154.70/154.55 [7653]P27(a875,a875,f328(f328(f7(a875,a875,a875),f22(a875)),x76531),x76532)+~P1(f328(f328(f242(a875),x76531),f447(x76531,x76532))) % 154.70/154.55 [7711]P39(x77111,x77112)+P1(f328(f328(f242(f882(x77111,a870)),f597(x77112,x77111)),f328(f282(x77111,x77111,x77112),f597(x77112,x77111)))) % 154.70/154.55 [7716]P56(x77161,x77162)+~P39(x77161,f328(f248(f881(x77161,x77161)),f328(f267(x77161,x77161,a870),x77162))) % 154.70/154.55 [7788]P1(f328(f328(f242(a875),f328(a116,x77881)),x77882))+~P1(f189(a870,a246,f328(f242(a875),x77881),x77882)) % 154.70/154.55 [7844]P1(f328(f328(f330(f881(a875,a875)),f328(f328(f263(a875,a875),x78441),x78442)),f304(a875,a318)))+~P1(f328(f328(f242(a875),x78441),x78442)) % 154.70/154.55 [7941]P50(x79411,x79412)+~P41(x79411,f251(f882(x79411,a870)),f328(f248(f881(x79411,x79411)),f328(f267(x79411,x79411,a870),x79412))) % 154.70/154.55 [7995]~P1(f328(f134(x79951),x79952))+P1(f328(f134(f882(x79951,a870)),f328(f328(f151(f876(x79951),f882(x79951,a870)),f170(x79951)),f53(x79951,x79952)))) % 154.70/154.55 [8206]~P39(x82061,f328(f283(x82061,x82061),x82062))+P39(x82061,f328(f283(x82061,x82061),f328(f328(f285(x82061,x82061,x82061),x82062),f304(x82061,x82062)))) % 154.70/154.55 [8330]P1(f328(f61(f881(x83301,x83301)),f328(f328(f285(x83301,x83301,x83301),x83302),f304(x83301,x83302))))+~P1(f328(f61(f881(x83301,x83301)),x83302)) % 154.70/154.55 [8361]E(x83611,f2(a1))+P1(f328(f48(x83612,x83611),f328(f328(f263(a1,a1),f328(f328(f38(a1),x83612),x83611)),f44(a1,x83612,x83611)))) % 154.70/154.55 [8372]~P1(f328(f328(f330(f881(a875,a875)),f328(f328(f263(a875,a875),x83721),x83722)),f304(a875,a318)))+P1(f328(f328(f242(a875),x83721),x83722)) % 154.70/154.55 [8387]~P77(x83871)+E(f328(f139(x83871,x83871,f328(f7(x83871,x83871,x83871),f80(x83871)),f2(x83871)),f328(f166(x83871),x83872)),f328(f139(x83871,x83871,f80(x83871),f2(x83871)),x83872)) % 154.70/154.55 [8568]~P105(x85681)+E(f328(f139(f876(x85681),x85681,f328(f7(x85681,f876(x85681),f876(x85681)),f145(x85681,x85681,f5(x85681))),f117(x85681)),x85682),f147(x85681,x85681,f5(x85681),x85682)) % 154.70/154.55 [8672]~P54(x86721,f328(f248(f881(x86721,x86721)),f328(f267(x86721,x86721,a870),x86722)))+P54(x86721,f328(f248(f881(x86721,x86721)),f328(f267(x86721,x86721,a870),f252(x86721,x86721,x86722)))) % 154.70/154.55 [8686]P1(f328(f328(f330(f881(a875,a875)),f328(f328(f263(a875,a875),x86861),x86862)),f328(f328(f285(a875,a875,a875),a318),f304(a875,a318))))+~P1(f328(f328(f243(a875),x86861),x86862)) % 154.70/154.55 [8729]~P1(f328(f61(f881(x87291,x87291)),f328(f328(f285(x87291,x87291,x87291),x87292),f304(x87291,x87292))))+P1(f328(f61(f881(x87291,x87291)),x87292)) % 154.70/154.55 [8780]~P54(x87801,f328(f248(f881(x87801,x87801)),f328(f267(x87801,x87801,a870),f252(x87801,x87801,x87802))))+P54(x87801,f328(f248(f881(x87801,x87801)),f328(f267(x87801,x87801,a870),x87802))) % 154.70/154.55 [8983]P54(x89831,x89832)+P1(f328(f328(f330(f881(x89831,x89831)),f328(f328(f263(x89831,x89831),f625(x89832,x89831)),f625(x89832,x89831))),f328(f328(f285(x89831,x89831,x89831),x89832),f304(x89831,x89832)))) % 154.70/154.55 [8984]P54(x89841,x89842)+P1(f328(f328(f330(f881(x89841,x89841)),f328(f328(f263(x89841,x89841),f636(x89842,x89841)),f636(x89842,x89841))),f328(f328(f285(x89841,x89841,x89841),x89842),f304(x89841,x89842)))) % 154.70/154.55 [9102]~P1(f328(f328(f330(f881(a875,a875)),f328(f328(f263(a875,a875),x91021),x91022)),f328(f328(f285(a875,a875,a875),a318),f304(a875,a318))))+P1(f328(f328(f243(a875),x91021),x91022)) % 154.70/154.55 [5059]~P90(x50591)+E(f328(f328(f80(x50591),f328(f107(x50591),a83)),x50592),x50592) % 154.70/154.55 [5088]~P93(x50881)+E(f328(f328(f114(x50881),f328(f79(x50881),x50882)),x50882),f251(x50881)) % 154.70/154.55 [5089]~P93(x50891)+E(f328(f328(f105(x50891),f328(f79(x50891),x50892)),x50892),f192(x50891)) % 154.70/154.55 [5090]~P65(x50901)+E(f328(f328(f80(x50901),f328(f79(x50901),x50902)),x50902),f2(x50901)) % 154.70/154.55 [5091]~P72(x50911)+E(f328(f328(f80(x50911),f328(f79(x50911),x50912)),x50912),f2(x50911)) % 154.70/154.55 [5123]~P90(x51231)+E(f328(f328(f81(x51231),f328(f107(x51231),a101)),x51232),f328(f79(x51231),x51232)) % 154.70/154.55 [5293]~P111(x52931)+E(f328(f328(f81(x52931),f328(f79(x52931),f78(x52931))),x52932),f328(f79(x52931),x52932)) % 154.70/154.55 [5335]E(f328(f75(a1),x53351),f78(a1))+~E(f328(f75(a1),f328(f328(f81(a1),x53351),x53352)),f78(a1)) % 154.70/154.55 [5427]~P90(x54271)+E(f328(f328(f80(x54271),f78(x54271)),f328(f107(x54271),x54272)),f328(f107(x54271),f328(f328(f22(a1),x54272),a101))) % 154.70/154.55 [5480]~P2(x54801)+E(f10(x54801,f328(f328(f306(x54801),x54802),f192(f882(x54801,a870)))),x54802) % 154.70/154.55 [5481]~P2(x54811)+E(f11(x54811,f328(f328(f306(x54811),x54812),f192(f882(x54811,a870)))),x54812) % 154.70/154.55 [5482]~P5(x54821)+E(f39(x54821,f328(f328(f306(x54821),x54822),f192(f882(x54821,a870)))),x54822) % 154.70/154.55 [5483]~P5(x54831)+E(f40(x54831,f328(f328(f306(x54831),x54832),f192(f882(x54831,a870)))),x54832) % 154.70/154.55 [5484]~P105(x54841)+E(f14(x54841,f328(f328(f306(x54841),x54842),f192(f882(x54841,a870)))),x54842) % 154.70/154.55 [5485]~P105(x54851)+E(f15(x54851,f328(f328(f306(x54851),x54852),f192(f882(x54851,a870)))),x54852) % 154.70/154.55 [5507]E(f328(f328(f80(a875),x55071),f328(f328(f22(a875),x55072),x55071)),x55072)+P1(f328(f328(f243(a875),x55072),x55071)) % 154.70/154.55 [5537]E(x55371,f117(x55372))+P1(f328(f328(f243(a875),f2(a875)),f328(f193(f876(x55372)),x55371))) % 154.70/154.55 [5662]~P105(x56621)+E(f12(x56621,f241(x56621),f328(f328(f306(x56621),x56622),f192(f882(x56621,a870)))),x56622) % 154.70/154.55 [5663]~P105(x56631)+E(f13(x56631,f240(x56631),f328(f328(f306(x56631),x56632),f192(f882(x56631,a870)))),x56632) % 154.70/154.55 [5726]E(f328(f328(f22(a875),x57261),f328(f328(f22(a875),x57261),x57262)),x57262)+~P1(f328(f328(f242(a875),x57262),x57261)) % 154.70/154.55 [5727]E(f328(f328(f80(a875),x57271),f328(f328(f22(a875),x57272),x57271)),x57272)+~P1(f328(f328(f242(a875),x57271),x57272)) % 154.70/154.55 [5748]E(f44(a875,f328(f328(f22(a875),x57481),x57482),x57482),f44(a875,x57481,x57482))+P1(f328(f328(f243(a875),x57481),x57482)) % 154.70/154.55 [5759]E(f328(f79(a1),f328(f328(f38(a1),x57591),f328(f79(a1),x57592))),f288(x57591,x57592))+P1(f328(f328(f242(a1),f2(a1)),x57592)) % 154.70/154.55 [5761]~E(x57612,f2(a875))+P1(f328(f328(f243(a875),f2(a875)),f328(f328(f253(a875),x57611),x57612))) % 154.70/154.55 [5812]~P90(x58121)+E(f328(f328(f80(x58121),f328(f79(x58121),f78(x58121))),f328(f107(x58121),x58122)),f328(f107(x58121),f328(f328(f80(a1),x58122),a101))) % 154.70/154.55 [5813]E(f328(f328(f253(a875),f328(f107(a875),x58131)),x58132),f328(f328(f253(a875),f2(a875)),x58132))+~P1(f328(a197,f328(f107(a1),x58131))) % 154.70/154.55 [5910]E(f328(f138(a875),f136(a875,f328(f298(a875,x59101),x59102))),x59101)+~P1(f328(f328(f243(a875),x59101),x59102)) % 154.70/154.55 [5929]E(f328(f328(f81(a875),f328(f107(a875),x59291)),f328(f107(a875),x59292)),f328(f107(a875),f328(f328(f81(a1),x59291),x59292)))+P1(f328(f328(f243(a1),x59291),a83)) % 154.70/154.55 [5935]~P120(x59351)+P1(f328(f328(f242(x59351),f2(x59351)),f328(f328(f81(x59351),x59352),x59352))) % 154.70/154.55 [5947]E(f328(f328(f22(a875),f328(a116,x59471)),x59472),f328(a116,f328(f328(f22(a875),x59471),x59472)))+~P1(f328(f328(f242(a875),x59472),x59471)) % 154.70/154.55 [5950]E(f44(a875,f328(f328(f22(a875),x59501),x59502),x59502),f44(a875,x59501,x59502))+~P1(f328(f328(f242(a875),x59502),x59501)) % 154.70/154.55 [5999]E(f328(f328(f253(a875),f328(a108,x59991)),x59992),f328(a108,f328(f328(f253(a1),x59991),x59992)))+~P1(f328(f328(f242(a1),f2(a1)),x59991)) % 154.70/154.55 [6015]P1(f328(f134(x60151),x60152))+P1(f328(f328(f243(a875),f685(x60152,x60151)),f328(f193(f876(x60151)),x60152))) % 154.70/154.55 [6016]P1(f328(f134(x60161),x60162))+P1(f328(f328(f243(a875),f690(x60162,x60161)),f328(f193(f876(x60161)),x60162))) % 154.70/154.55 [6031]~E(x60311,f117(x60312))+~P1(f328(f328(f243(a875),f2(a875)),f328(f193(f876(x60312)),x60311))) % 154.70/154.55 [6045]E(f141(a875,f136(a875,f328(f298(a875,x60451),x60452))),f328(f328(f22(a875),x60452),f78(a875)))+~P1(f328(f328(f243(a875),x60451),x60452)) % 154.70/154.55 [6048]E(f328(f328(f80(a1),x60481),f328(f104(a1),f328(a116,f364(x60482,x60481)))),x60482)+~P1(f328(f328(f243(a1),x60481),x60482)) % 154.70/154.55 [6055]E(x60551,f2(a875))+E(f328(f328(f81(a875),x60552),f328(f328(f253(a875),x60552),f328(f328(f22(a875),x60551),f78(a875)))),f328(f328(f253(a875),x60552),x60551)) % 154.70/154.55 [6081]E(f328(f328(f81(a875),f328(a108,x60811)),f328(a108,x60812)),f328(a108,f328(f328(f81(a1),x60811),x60812)))+~P1(f328(f328(f242(a1),f2(a1)),x60811)) % 154.70/154.55 [6082]E(f328(f328(f38(a875),f328(a108,x60821)),f328(a108,x60822)),f328(a108,f328(f328(f38(a1),x60821),x60822)))+~P1(f328(f328(f242(a1),f2(a1)),x60821)) % 154.70/154.55 [6096]~P109(x60961)+E(f328(f328(f80(x60961),x60962),x60962),f328(f328(f81(x60961),f328(f328(f80(x60961),f78(x60961)),f78(x60961))),x60962)) % 154.70/154.55 [6113]E(f328(f328(f22(a1),f328(f104(a1),x61131)),f328(f104(a1),x61132)),f328(f104(a1),f328(f328(f22(a875),x61131),x61132)))+~P1(f328(f328(f242(a875),x61132),x61131)) % 154.70/154.55 [6115]E(f328(f328(f263(a1,a1),f328(f107(a1),a101)),f328(f328(f80(a1),x61151),x61152)),f49(x61151,x61152))+~P1(f328(f328(f242(a1),x61152),f2(a1))) % 154.70/154.55 [6155]E(f178(x61551,x61552),f117(f876(x61551)))+P1(f328(f328(f330(f876(x61551)),f718(x61552,x61551)),f328(f170(f876(x61551)),x61552))) % 154.70/154.55 [6242]E(f328(f328(f148(a1),x62421),f177(f328(f328(f80(a1),x62421),f78(a1)),x62422)),f177(x62421,x62422))+~P1(f328(f328(f242(a1),x62421),x62422)) % 154.70/154.55 [6279]~P1(f328(f328(f243(a875),x62792),x62791))+P1(f328(f328(f243(a875),f2(a875)),f328(f328(f22(a875),x62791),x62792))) % 154.70/154.55 [6310]~P1(f328(f328(f243(a875),x63101),f328(a108,x63102)))+P1(f328(f328(f243(a1),f328(f104(a1),x63101)),x63102)) % 154.70/154.55 [6339]~P105(x63391)+E(f328(f328(f114(f882(x63391,a870)),f328(f249(x63391),x63392)),f328(f328(f306(x63391),x63392),f192(f882(x63391,a870)))),f328(f297(x63391),x63392)) % 154.70/154.55 [6342]~P1(f328(f328(f243(a875),f2(a875)),x63421))+P1(f328(f328(f243(a875),f2(a875)),f328(f328(f253(a875),x63421),x63422))) % 154.70/154.55 [6343]~P1(f328(f328(f242(a1),f2(a1)),x63431))+P1(f328(f328(f242(a1),f2(a1)),f328(f328(f253(a1),x63431),x63432))) % 154.70/154.55 [6370]~E(f328(x63701,f2(a875)),f2(a875))+E(f328(f328(f6(a875,a875),x63701),f299(a875,f328(a116,f2(a875)),x63702)),f328(f328(f6(a875,a875),x63701),f299(a875,f2(a875),x63702))) % 154.70/154.55 [6433]~P90(x64331)+E(f328(f328(f81(x64331),f328(f328(f80(x64331),f78(x64331)),f78(x64331))),f328(f107(x64331),x64332)),f328(f107(x64331),f328(f328(f80(a1),x64332),x64332))) % 154.70/154.55 [6449]E(f328(f328(f306(a1),x64491),f299(a1,f328(f328(f80(a1),x64491),f78(a1)),x64492)),f299(a1,x64491,x64492))+P1(f328(f328(f243(a1),x64492),x64491)) % 154.70/154.55 [6450]P1(f328(f328(f243(a875),x64501),f328(a108,x64502)))+~P1(f328(f328(f243(a1),f328(f104(a1),x64501)),x64502)) % 154.70/154.55 [6550]E(f328(a108,f328(f328(f38(a1),f328(f107(a1),x65501)),f328(f107(a1),x65502))),f328(f328(f38(a875),f328(f107(a875),x65501)),f328(f107(a875),x65502)))+P1(f328(a197,f328(f107(a1),x65501))) % 154.70/154.55 [6608]P1(f328(f328(f243(a875),x66081),x66082))+~P1(f328(f328(f243(a875),f2(a875)),f328(f328(f22(a875),x66082),x66081))) % 154.70/154.55 [6653]P1(f328(f328(f243(a875),f2(a875)),x66531))+~P1(f328(f328(f243(a875),f2(a875)),f328(f328(f81(a875),x66532),x66531))) % 154.70/154.55 [6654]P1(f328(f328(f243(a875),f2(a875)),x66541))+~P1(f328(f328(f243(a875),f2(a875)),f328(f328(f81(a875),x66541),x66542))) % 154.70/154.55 [6671]~P1(f328(f328(f242(a1),x66711),f2(a1)))+E(f328(f328(f81(a875),f328(a108,f328(f79(a1),x66711))),f328(a108,f328(f79(a1),x66712))),f328(a108,f328(f328(f81(a1),x66711),x66712))) % 154.70/154.55 [6729]~E(x67292,f192(f882(x67291,a870)))+P1(f328(f328(f242(f882(x67291,a870)),x67292),f328(f79(f882(x67291,a870)),x67292))) % 154.70/154.55 [6792]~P90(x67921)+E(f328(f328(f80(x67921),f328(f328(f80(x67921),f2(x67921)),f328(f107(x67921),x67922))),f328(f107(x67921),x67922)),f328(f107(x67921),f328(f328(f80(a1),x67922),x67922))) % 154.70/154.55 [6849]~P1(f328(f328(f243(a1),x68491),x68492))+P1(f328(f328(f242(a1),f328(f328(f80(a1),x68491),f78(a1))),x68492)) % 154.70/154.55 [6915]E(x69151,f2(a875))+~P1(f328(f328(f242(a1),f328(f104(a1),x69152)),f328(f79(a1),f328(f104(a1),x69151)))) % 154.70/154.55 [6916]E(x69161,f2(a875))+~P1(f328(f328(f242(a1),f328(f104(a1),x69161)),f328(f79(a1),f328(f104(a1),x69162)))) % 154.70/154.55 [7019]E(f328(f328(f263(a1,a1),f328(f107(a1),a101)),f328(f328(f80(a1),x70191),x70192)),f49(x70191,x70192))+~P1(f328(f328(f242(a1),f2(a1)),f328(f328(f80(a1),x70191),x70192))) % 154.70/154.55 [7061]~P28(x70611,x70612)+P39(x70611,f328(f262(f882(f881(x70611,x70611),a870),f882(f881(x70611,x70611),a870)),x70612)) % 154.70/154.55 [7079]~P1(f328(f328(f242(a875),f328(a116,f2(a875))),x70791))+P1(f328(f328(f242(a875),f328(a116,f2(a875))),f328(f328(f253(a875),x70791),x70792))) % 154.70/154.55 [7244]~P1(f328(f328(f243(a1),x72441),x72442))+P1(f328(f328(f243(a1),f328(f328(f80(a1),x72441),x72441)),f328(f328(f80(a1),x72442),x72442))) % 154.70/154.55 [7256]~P1(f328(f328(f242(a1),x72561),x72562))+P1(f328(f328(f242(a1),f328(f328(f80(a1),x72561),x72561)),f328(f328(f80(a1),x72562),x72562))) % 154.70/154.55 [7257]~P1(f328(f328(f91(a1),x72571),x72572))+P1(f328(f328(f91(a1),f328(f328(f80(a1),x72571),x72571)),f328(f328(f80(a1),x72572),x72572))) % 154.70/154.55 [7312]~P1(f328(f328(f243(a875),f2(a875)),x73121))+P1(f328(f328(f243(a875),f328(f328(f22(a875),x73121),f328(a116,x73122))),x73121)) % 154.70/154.55 [7349]P1(f328(f328(f242(a875),f328(a116,f2(a875))),x73491))+~P1(f328(f328(f242(a875),f328(a116,f2(a875))),f328(f328(f81(a875),x73492),x73491))) % 154.70/154.55 [7350]P1(f328(f328(f242(a875),f328(a116,f2(a875))),x73501))+~P1(f328(f328(f242(a875),f328(a116,f2(a875))),f328(f328(f81(a875),x73501),x73502))) % 154.70/154.55 [7354]P1(f328(f328(f242(a875),f328(f328(f162(a875),x73541),x73542)),f328(f163(a875),x73541)))+~P1(f328(f328(f243(a875),x73542),f328(f193(f876(a875)),x73541))) % 154.70/154.55 [7395]P1(f328(f328(f243(a1),x73951),x73952))+~P1(f328(f328(f242(a1),f328(f328(f80(a1),x73951),f78(a1))),x73952)) % 154.70/154.55 [7439]P1(f328(f61(x74391),f251(f882(x74391,a870))))+~P1(f328(f61(f882(x74392,x74391)),f251(f882(f882(x74392,x74391),a870)))) % 154.70/154.55 [7440]P1(f328(f61(x74401),f251(f882(x74401,a870))))+~P1(f328(f61(f880(x74402,x74401)),f251(f882(f880(x74402,x74401),a870)))) % 154.70/154.55 [7441]P1(f328(f61(x74411),f251(f882(x74411,a870))))+~P1(f328(f61(f880(x74411,x74412)),f251(f882(f880(x74411,x74412),a870)))) % 154.70/154.55 [7483]E(x74831,f192(f882(x74832,a870)))+~P1(f328(f328(f242(f882(x74832,a870)),x74831),f328(f79(f882(x74832,a870)),x74831))) % 154.70/154.55 [7621]E(f328(f139(f876(x76211),f876(x76211),f125(x76211),f117(x76211)),x76212),f117(x76211))+P1(f328(f328(f330(f876(x76211)),f734(x76212,x76211)),f328(f170(f876(x76211)),x76212))) % 154.70/154.55 [7622]E(f328(f139(f876(x76221),f876(x76221),f125(x76221),f117(x76221)),x76222),f117(x76221))+P1(f328(f328(f330(f876(x76221)),f740(x76222,x76221)),f328(f170(f876(x76221)),x76222))) % 154.70/154.55 [7863]P1(f328(f328(f243(a1),x78631),x78632))+~P1(f328(f328(f243(a1),f328(f328(f80(a1),x78631),x78631)),f328(f328(f80(a1),x78632),x78632))) % 154.70/154.55 [7866]P1(f328(f328(f242(a1),x78661),x78662))+~P1(f328(f328(f242(a1),f328(f328(f80(a1),x78661),x78661)),f328(f328(f80(a1),x78662),x78662))) % 154.70/154.55 [7867]P1(f328(f328(f91(a1),x78671),x78672))+~P1(f328(f328(f91(a1),f328(f328(f80(a1),x78671),x78671)),f328(f328(f80(a1),x78672),x78672))) % 154.70/154.55 [7961]~P109(x79611)+E(f328(f328(f81(x79611),f328(f328(f80(x79611),f78(x79611)),f78(x79611))),f328(f328(f6(a875,x79611),f104(x79611)),f299(a875,f78(a875),x79612))),f328(f328(f81(x79611),f328(f104(x79611),x79612)),f328(f328(f80(x79611),f328(f104(x79611),x79612)),f78(x79611)))) % 154.70/154.55 [8009]P1(f328(f328(f330(a875),x80091),x80092))+~P1(f328(f328(f330(a1),f328(f104(a1),x80091)),f328(f307(a875,a1,f104(a1)),x80092))) % 154.70/154.55 [8174]~P1(f328(f61(x81741),x81742))+E(f328(f307(a875,x81741,f460(x81742,x81741)),f328(f248(a875),f328(f328(f7(a875,a875,a870),f243(a875)),f461(x81742,x81741)))),x81742) % 154.70/154.55 [8462]P43(x84621,x84622)+P1(f328(f328(f330(f881(x84621,x84621)),f328(f328(f263(x84621,x84621),f539(x84622,x84621)),f539(x84622,x84621))),x84622)) % 154.70/154.55 [8609]~P90(x86091)+E(f328(f328(f22(x86091),f78(x86091)),f328(f107(x86091),x86092)),f328(f107(x86091),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f79(a1),x86092)))) % 154.70/154.55 [8725]~P1(f328(f328(f243(f882(a875,a870)),x87251),x87252))+P1(f328(f328(f243(f882(a1,a870)),f328(f307(a875,a1,f104(a1)),x87251)),f328(f307(a875,a1,f104(a1)),x87252))) % 154.70/154.55 [8754]~P1(f328(f328(f243(a1),x87541),x87542))+P1(f328(f328(f243(a1),f328(f328(f22(a1),f328(f328(f80(a1),x87541),x87541)),a101)),f328(f328(f80(a1),x87542),x87542))) % 154.70/154.55 [8756]~P1(f328(f328(f243(a1),x87561),x87562))+P1(f328(f328(f242(a1),f328(f328(f22(a1),f328(f328(f80(a1),x87561),x87561)),a101)),f328(f328(f80(a1),x87562),x87562))) % 154.70/154.55 [8826]~P1(f328(f328(f330(a875),x88261),f328(f170(a875),x88262)))+P1(f328(f328(f242(a875),x88261),f328(f139(a875,a875,f80(a875),f2(a875)),x88262))) % 154.70/154.55 [8918]P47(x89181,x89182)+~P1(f328(f328(f330(f881(x89181,x89181)),f328(f328(f263(x89181,x89181),f531(x89182,x89181)),f531(x89182,x89181))),x89182)) % 154.70/154.55 [9065]~P1(f328(f328(f243(f882(a1,a870)),f328(f307(a875,a1,f104(a1)),x90651)),f328(f307(a875,a1,f104(a1)),x90652)))+P1(f328(f328(f243(f882(a875,a870)),x90651),x90652)) % 154.70/154.55 [9066]~P1(f328(f328(f242(f882(a1,a870)),f328(f307(a875,a1,f104(a1)),x90661)),f328(f307(a875,a1,f104(a1)),x90662)))+P1(f328(f328(f242(f882(a875,a870)),x90661),x90662)) % 154.70/154.55 [9149]P1(f328(f328(f243(a1),x91491),x91492))+~P1(f328(f328(f243(a1),f328(f328(f22(a1),f328(f328(f80(a1),x91491),x91491)),a101)),f328(f328(f80(a1),x91492),x91492))) % 154.70/154.55 [9151]P1(f328(f328(f243(a1),x91511),x91512))+~P1(f328(f328(f242(a1),f328(f328(f22(a1),f328(f328(f80(a1),x91511),x91511)),a101)),f328(f328(f80(a1),x91512),x91512))) % 154.70/154.55 [10056]~P1(f328(f61(x100561),x100562))+E(f328(f193(f876(x100561)),f90(f876(x100561),f328(f328(f18(f876(x100561),a870,a870),f328(f328(f8(a870,f882(a870,a870),f876(x100561)),a326),f328(f328(f7(f876(x100561),f882(x100561,a870),a870),f328(f328(f8(f882(x100561,a870),f882(f882(x100561,a870),a870),f876(x100561)),a325),f170(x100561))),x100562))),f134(x100561)))),f221(x100561,x100562)) % 154.70/154.55 [10194]~P26(a872,x101941,f328(f328(f306(f874(a872)),f328(f328(f328(f92(a872),a325),x101942),f328(a198,x101942))),f192(f882(f874(a872),a870))))+P26(a872,x101941,f328(f328(f306(f874(a872)),f328(f328(f328(f92(a872),f328(f328(f8(f882(a872,f882(a872,a870)),f882(a872,a870),a872),f328(f8(f882(a872,a870),a870,a872),f88(a872))),f328(f328(f8(f882(a872,a870),f882(a872,f882(a872,a870)),a872),f328(f7(a872,f882(a872,a870),f882(a872,a870)),f328(f328(f8(f882(a872,f882(a870,a870)),f882(f882(a872,a870),f882(a872,a870)),a872),f18(a872,a870,a870)),f328(f328(f8(f882(a872,a870),f882(a872,f882(a870,a870)),a872),f328(f8(a870,f882(a870,a870),a872),a331)),f328(a198,x101942))))),a325))),x101942),a325)),f192(f882(f874(a872),a870)))) % 154.70/154.55 [6044]E(f328(f328(f80(a875),f328(f328(f22(a875),x60441),x60442)),x60442),x60441)+~P1(f328(f328(f242(a875),x60442),x60441)) % 154.70/154.55 [6109]E(f328(f328(f38(a875),f328(f328(f81(a875),x61091),x61092)),x61092),x61091)+~P1(f328(f328(f243(a875),f2(a875)),x61092)) % 154.70/154.55 [6110]E(f328(f328(f38(a875),f328(f328(f81(a875),x61101),x61102)),x61101),x61102)+~P1(f328(f328(f243(a875),f2(a875)),x61101)) % 154.70/154.55 [6114]~P66(x61141)+E(f328(f328(f6(a875,x61141),f328(f162(x61141),x61142)),f328(f298(a875,f2(a875)),f328(f193(f876(x61141)),x61142))),f328(f163(x61141),x61142)) % 154.70/154.55 [6234]E(f44(a875,f328(a116,f328(f328(f81(a875),x62341),x62342)),x62341),f78(a875))+~P1(f328(f328(f243(a875),f78(a875)),x62341)) % 154.70/154.55 [6240]E(f328(a116,f328(f328(f80(a875),f328(f107(a875),x62401)),x62402)),f328(f328(f80(a875),f78(a875)),x62402))+~P1(f328(a197,f328(f107(a1),x62401))) % 154.70/154.55 [6268]E(f328(a108,f328(f328(f253(a1),f328(f107(a1),x62681)),x62682)),f328(f328(f253(a875),f328(f107(a875),x62681)),x62682))+P1(f328(a197,f328(f107(a1),x62681))) % 154.70/154.55 [6503]E(f328(f328(f22(a875),x65031),f328(f107(a875),f328(f328(f80(a1),x65032),a101))),f328(f328(f22(a875),f328(a116,x65031)),f328(f107(a875),x65032)))+~P1(f328(f328(f243(a1),a83),x65032)) % 154.70/154.55 [6581]E(x65811,f2(a875))+E(f328(a116,f328(f328(f80(a875),f328(f328(f22(a875),x65811),f78(a875))),x65812)),f328(f328(f80(a875),x65811),x65812)) % 154.70/154.55 [6622]E(x66221,f2(a1))+P1(f328(f328(f243(a1),f2(a1)),f328(f328(f253(a1),f328(f75(a1),x66221)),x66222))) % 154.70/154.55 [6638]~E(x66382,f2(a875))+P1(f328(f328(f243(a1),f2(a1)),f328(f328(f253(a1),f328(f75(a1),x66381)),x66382))) % 154.70/154.55 [6675]E(x66751,f2(a875))+E(f328(f328(f80(a875),x66752),f328(f328(f81(a875),f328(f328(f22(a875),x66751),f78(a875))),x66752)),f328(f328(f81(a875),x66751),x66752)) % 154.70/154.55 [6723]~P1(f328(f328(f242(a1),x67231),x67232))+P1(f328(f328(f243(a1),f328(f328(f80(a1),x67231),a101)),x67232)) % 154.70/154.55 [6852]E(f328(f328(f148(a875),x68521),f136(a875,f328(f298(a875,f328(a116,x68521)),x68522))),f136(a875,f328(f298(a875,x68521),x68522)))+~P1(f328(f328(f243(a875),x68521),x68522)) % 154.70/154.55 [7052]E(x70521,x70522)+~E(f328(f328(f22(a1),f328(f328(f80(a1),x70521),x70521)),a101),f328(f328(f22(a1),f328(f328(f80(a1),x70522),x70522)),a101)) % 154.70/154.55 [7055]E(x70551,f117(x70552))+E(f272(x70552,f328(f328(f151(x70552,f881(a103,x70552)),f328(f263(a103,x70552),f78(a103))),x70551)),f279(x70552,x70551)) % 154.70/154.55 [7281]P1(f328(f328(f242(a1),x72811),x72812))+~P1(f328(f328(f243(a1),f328(f328(f80(a1),x72811),a101)),x72812)) % 154.70/154.55 [7765]~P1(f328(f328(f243(a875),x77651),x77652))+P1(f328(f328(f330(f881(a875,a875)),f328(f328(f263(a875,a875),x77651),x77652)),a247)) % 154.70/154.55 [7986]~P1(f328(f328(f243(a103),f2(a103)),x79861))+P1(f328(f328(f243(a103),f328(f262(a103,f881(a103,a103)),f328(f273(x79861),x79862))),x79861)) % 154.70/154.55 [8308]~P83(x83081)+P1(f328(f328(f242(x83081),f328(f75(x83081),f328(f163(x83081),x83082))),f328(f163(x83081),f328(f328(f151(x83081,x83081),f75(x83081)),x83082)))) % 154.70/154.55 [8332]P1(f328(f328(f243(a875),x83321),x83322))+~P1(f328(f328(f330(f881(a875,a875)),f328(f328(f263(a875,a875),x83321),x83322)),a247)) % 154.70/154.55 [8483]E(f328(f328(f263(x84831,x84831),f634(x84832,x84831)),f634(x84832,x84831)),x84832)+~P1(f328(f328(f330(f881(x84831,x84831)),x84832),f304(x84831,f192(f882(f881(x84831,x84831),a870))))) % 154.70/154.55 [8527]E(f328(f298(a875,x85271),f328(f328(f80(a875),x85271),f328(f37(a875),x85272))),x85272)+~P1(f328(f328(f242(f882(a875,a870)),x85272),f328(f298(a875,x85271),f328(f328(f80(a875),x85271),f328(f37(a875),x85272))))) % 154.70/154.55 [8865]E(f328(f328(f38(a1),f328(f107(a1),f328(f328(f22(a1),f328(f328(f80(a1),x88651),x88651)),a101))),f328(f107(a1),f328(f328(f80(a1),x88652),x88652))),f328(f328(f38(a1),f328(f107(a1),x88651)),f328(f107(a1),x88652)))+~P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x88652))) % 154.70/154.55 [8994]E(f175(f876(x89941),f328(f328(f8(a870,a870,f876(x89941)),a323),f328(f328(f7(f876(x89941),f876(x89941),a870),a325),f117(x89941))),x89942),f178(x89941,f178(x89941,x89942)))+~P16(a875,f328(f166(a875),f328(f328(f151(f876(x89941),a875),f193(f876(x89941))),x89942))) % 154.70/154.55 [8997]E(f328(f328(f38(a1),f328(f107(a1),f328(f328(f22(a1),f328(f328(f80(a1),x89971),x89971)),a101))),f328(f107(a1),f328(f328(f80(a1),x89972),x89972))),f328(f328(f38(a1),f328(f328(f80(a1),f328(f107(a1),x89971)),f78(a1))),f328(f107(a1),x89972)))+P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x89972))) % 154.70/154.55 [9682]P26(a872,x96821,f328(f328(f306(f874(a872)),f328(f328(f328(f92(a872),a325),f328(a26,x96822)),f328(a198,f328(a26,x96822)))),f192(f882(f874(a872),a870))))+~P26(a872,f328(f328(f306(f874(a872)),f328(f328(f328(f92(a872),a325),f328(a26,x96822)),f328(a198,f328(a26,x96822)))),x96821),f328(f328(f306(f874(a872)),f328(f328(f328(f92(a872),a325),f328(f239(a871),f328(a28,x96822))),f328(a198,f328(f239(a871),f328(a28,x96822))))),f192(f882(f874(a872),a870)))) % 154.70/154.55 [9832]P1(f328(a197,x98322))+E(f328(f328(f86(a1,a875),f328(f328(f22(a1),x98321),x98322)),f328(f328(f18(a1,a875,a875),f328(f328(f7(a1,a875,f882(a875,a875)),f328(f328(f8(a870,f882(a875,f882(a875,a875)),a1),f100(a875)),a197)),f2(a875))),a108)),f328(f328(f22(a875),f328(a108,x98321)),f328(a108,x98322))) % 154.70/154.55 [9840]E(f328(f328(f86(a1,a875),f328(f107(a1),f328(f328(f80(a1),x98401),f328(f79(a1),x98402)))),f328(f328(f18(a1,a875,a875),f328(f328(f7(a1,a875,f882(a875,a875)),f328(f328(f8(a870,f882(a875,f882(a875,a875)),a1),f100(a875)),a197)),f2(a875))),a108)),f328(f328(f22(a875),f328(f107(a875),x98401)),f328(f107(a875),x98402)))+P1(f328(f328(f243(a1),x98402),a83)) % 154.70/154.55 [9841]~P28(x98411,x98412)+P1(f328(f328(f242(f882(f881(x98411,x98411),a870)),f328(f328(f285(x98411,x98411,x98411),f328(f262(f882(f881(x98411,x98411),a870),f882(f881(x98411,x98411),a870)),x98412)),f328(f266(f882(f881(x98411,x98411),a870),f882(f881(x98411,x98411),a870)),x98412))),f328(f262(f882(f881(x98411,x98411),a870),f882(f881(x98411,x98411),a870)),x98412))) % 154.70/154.55 [9907]~E(f328(f37(a875),f328(f248(a875),f328(f328(f18(a875,a870,a870),f328(f328(f8(a870,f882(a870,a870),a875),a326),f328(f328(f7(a875,f882(a875,a870),a870),f330(a875)),x99071))),f328(f328(f7(a875,a875,a870),f243(a875)),f328(a116,x99072))))),f2(a875))+~P1(f328(f328(f330(a875),f2(a875)),x99071)) % 154.70/154.55 [9963]E(f44(a1,f328(f107(a1),f328(f328(f22(a1),f328(f328(f80(a1),x99631),x99631)),a101)),f328(f107(a1),f328(f328(f80(a1),x99632),x99632))),f328(f328(f80(a1),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f44(a1,f328(f107(a1),x99631),f328(f107(a1),x99632)))),f78(a1)))+~P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x99632))) % 154.70/154.55 [9972]E(f44(a1,f328(f107(a1),f328(f328(f22(a1),f328(f328(f80(a1),x99721),x99721)),a101)),f328(f107(a1),f328(f328(f80(a1),x99722),x99722))),f328(f328(f22(a1),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f44(a1,f328(f328(f80(a1),f328(f107(a1),x99721)),f78(a1)),f328(f107(a1),x99722)))),f78(a1)))+P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x99722))) % 154.70/154.55 [10024]~P5(x100241)+E(f39(x100241,f328(f248(x100241),f328(f328(f8(f882(x100241,a870),a870,x100241),f88(x100241)),f328(f328(f8(f882(x100241,a870),f882(x100241,a870),x100241),f328(f18(x100241,a870,a870),f328(f328(f8(a870,f882(a870,a870),x100241),a331),f328(f328(f7(x100241,f882(x100241,a870),a870),f330(x100241)),x100242)))),f242(x100241))))),f40(x100241,x100242)) % 154.70/154.55 [10049]~P39(x100491,x100492)+P56(x100491,f328(f328(f7(x100491,f882(f881(x100491,x100491),a870),f882(x100491,a870)),f328(f328(f8(f882(x100491,f882(f882(f881(x100491,x100491),a870),a870)),f882(f882(f881(x100491,x100491),a870),f882(x100491,a870)),x100491),f7(x100491,f882(f881(x100491,x100491),a870),a870)),f328(f328(f8(f882(x100491,f881(x100491,x100491)),f882(x100491,f882(f882(f881(x100491,x100491),a870),a870)),x100491),f328(f8(f881(x100491,x100491),f882(f882(f881(x100491,x100491),a870),a870),x100491),f330(f881(x100491,x100491)))),f263(x100491,x100491)))),x100492)) % 154.70/154.55 [10050]~P8(x100501,f251(f882(x100501,a870)),x100502)+P7(x100501,f328(f328(f7(x100501,f882(f881(x100501,x100501),a870),f882(x100501,a870)),f328(f328(f8(f882(x100501,f882(f882(f881(x100501,x100501),a870),a870)),f882(f882(f881(x100501,x100501),a870),f882(x100501,a870)),x100501),f7(x100501,f882(f881(x100501,x100501),a870),a870)),f328(f328(f8(f882(x100501,f881(x100501,x100501)),f882(x100501,f882(f882(f881(x100501,x100501),a870),a870)),x100501),f328(f8(f881(x100501,x100501),f882(f882(f881(x100501,x100501),a870),a870),x100501),f330(f881(x100501,x100501)))),f263(x100501,x100501)))),x100502)) % 154.70/154.55 [10087]P39(x100871,x100872)+~P56(x100871,f328(f328(f7(x100871,f882(f881(x100871,x100871),a870),f882(x100871,a870)),f328(f328(f8(f882(x100871,f882(f882(f881(x100871,x100871),a870),a870)),f882(f882(f881(x100871,x100871),a870),f882(x100871,a870)),x100871),f7(x100871,f882(f881(x100871,x100871),a870),a870)),f328(f328(f8(f882(x100871,f881(x100871,x100871)),f882(x100871,f882(f882(f881(x100871,x100871),a870),a870)),x100871),f328(f8(f881(x100871,x100871),f882(f882(f881(x100871,x100871),a870),a870),x100871),f330(f881(x100871,x100871)))),f263(x100871,x100871)))),x100872)) % 154.70/154.55 [10088]P8(x100881,f251(f882(x100881,a870)),x100882)+~P7(x100881,f328(f328(f7(x100881,f882(f881(x100881,x100881),a870),f882(x100881,a870)),f328(f328(f8(f882(x100881,f882(f882(f881(x100881,x100881),a870),a870)),f882(f882(f881(x100881,x100881),a870),f882(x100881,a870)),x100881),f7(x100881,f882(f881(x100881,x100881),a870),a870)),f328(f328(f8(f882(x100881,f881(x100881,x100881)),f882(x100881,f882(f882(f881(x100881,x100881),a870),a870)),x100881),f328(f8(f881(x100881,x100881),f882(f882(f881(x100881,x100881),a870),a870),x100881),f330(f881(x100881,x100881)))),f263(x100881,x100881)))),x100882)) % 154.70/154.55 [7232]E(f328(f328(f80(a875),f328(f107(a875),f328(f328(f22(a1),x72321),a101))),x72322),f328(a116,f328(f328(f80(a875),f328(f107(a875),x72321)),x72322)))+P1(f328(a197,f328(f107(a1),x72321))) % 154.70/154.55 [7680]~P90(x76801)+E(f328(f328(f80(x76801),f328(f328(f80(x76801),f78(x76801)),f328(f107(x76801),x76802))),f328(f107(x76801),x76802)),f328(f107(x76801),f328(f328(f22(a1),f328(f328(f80(a1),x76802),x76802)),a101))) % 154.70/154.55 [8334]~P1(f328(f328(f242(a1),x83341),x83342))+P1(f328(f328(f243(a1),f328(f328(f80(a1),x83341),x83341)),f328(f328(f22(a1),f328(f328(f80(a1),x83342),x83342)),a101))) % 154.70/154.55 [8336]~P1(f328(f328(f242(a1),x83361),x83362))+P1(f328(f328(f242(a1),f328(f328(f80(a1),x83361),x83361)),f328(f328(f22(a1),f328(f328(f80(a1),x83362),x83362)),a101))) % 154.70/154.55 [8758]P1(f328(f328(f242(a1),x87581),x87582))+~P1(f328(f328(f243(a1),f328(f328(f80(a1),x87581),x87581)),f328(f328(f22(a1),f328(f328(f80(a1),x87582),x87582)),a101))) % 154.70/154.55 [8760]P1(f328(f328(f242(a1),x87601),x87602))+~P1(f328(f328(f242(a1),f328(f328(f80(a1),x87601),x87601)),f328(f328(f22(a1),f328(f328(f80(a1),x87602),x87602)),a101))) % 154.70/154.55 [9053]~P1(f328(f328(f243(a1),x90531),x90532))+P1(f328(f328(f243(a1),f328(f328(f22(a1),f328(f328(f80(a1),x90531),x90531)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),x90532),x90532)),a101))) % 154.70/154.55 [9055]~P1(f328(f328(f242(a1),x90551),x90552))+P1(f328(f328(f242(a1),f328(f328(f22(a1),f328(f328(f80(a1),x90551),x90551)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),x90552),x90552)),a101))) % 154.70/154.55 [9056]~P1(f328(f328(f91(a1),x90561),x90562))+P1(f328(f328(f91(a1),f328(f328(f22(a1),f328(f328(f80(a1),x90561),x90561)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),x90562),x90562)),a101))) % 154.70/154.55 [9322]P1(f328(f328(f243(a1),x93221),x93222))+~P1(f328(f328(f243(a1),f328(f328(f22(a1),f328(f328(f80(a1),x93221),x93221)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),x93222),x93222)),a101))) % 154.70/154.55 [9324]P1(f328(f328(f242(a1),x93241),x93242))+~P1(f328(f328(f242(a1),f328(f328(f22(a1),f328(f328(f80(a1),x93241),x93241)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),x93242),x93242)),a101))) % 154.70/154.55 [9325]P1(f328(f328(f91(a1),x93251),x93252))+~P1(f328(f328(f91(a1),f328(f328(f22(a1),f328(f328(f80(a1),x93251),x93251)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),x93252),x93252)),a101))) % 154.70/154.55 [9357]~P1(f328(f61(x93571),x93572))+P1(f328(f61(f882(x93571,a870)),f328(f248(f882(x93571,a870)),f328(f328(f7(f882(x93571,a870),f882(x93571,a870),a870),f242(f882(x93571,a870))),x93572)))) % 154.70/154.55 [9405]~E(f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),x94051),f192(f882(f881(a875,a875),a870)))),f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),x94052),f192(f882(f881(a875,a875),a870)))))+P1(f328(f328(f330(f881(f881(a875,a875),f881(a875,a875))),f328(f328(f263(f881(a875,a875),f881(a875,a875)),x94051),x94052)),a112)) % 154.70/154.55 [9489]E(f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),x94891),f192(f882(f881(a875,a875),a870)))),f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),x94892),f192(f882(f881(a875,a875),a870)))))+~P1(f328(f328(f330(f881(f881(a875,a875),f881(a875,a875))),f328(f328(f263(f881(a875,a875),f881(a875,a875)),x94891),x94892)),a112)) % 154.70/154.55 [9525]P1(f328(f328(f242(a1),f2(a1)),f657(x95251,x95252)))+E(f328(f248(a1),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a326),f328(f242(a1),f2(a1)))),x95251)),f328(f248(a1),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a326),f328(f242(a1),f2(a1)))),x95252))) % 154.70/154.55 [10034]~P5(x100341)+E(f40(x100341,f328(f248(x100341),f328(f328(f8(f882(x100341,a870),a870,x100341),f88(x100341)),f328(f328(f8(f882(x100341,a870),f882(x100341,a870),x100341),f328(f18(x100341,a870,a870),f328(f328(f8(a870,f882(a870,a870),x100341),a331),f328(f328(f7(x100341,f882(x100341,a870),a870),f330(x100341)),x100342)))),f328(f7(x100341,x100341,a870),f242(x100341)))))),f39(x100341,x100342)) % 154.70/154.55 [10055]P1(f328(f328(f330(a875),f2(a875)),x100551))+E(f328(f37(a875),f328(f248(a875),f328(f328(f18(a875,a870,a870),f328(f328(f8(a870,f882(a870,a870),a875),a326),f328(f328(f7(a875,f882(a875,a870),a870),f328(f328(f8(a875,f882(f882(a875,a870),a870),a875),f330(a875)),a116)),x100551))),f328(f328(f7(a875,a875,a870),f243(a875)),x100552)))),f328(f37(a875),f328(f248(a875),f328(f328(f18(a875,a870,a870),f328(f328(f8(a870,f882(a870,a870),a875),a326),f328(f328(f7(a875,f882(a875,a870),a870),f330(a875)),x100551))),f328(f328(f7(a875,a875,a870),f243(a875)),f328(a116,x100552)))))) % 154.70/154.55 [7547]~P90(x75471)+E(f328(f328(f81(x75471),x75472),f328(f107(x75471),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),x75472) % 154.70/154.55 [7814]~P90(x78141)+E(f328(f328(f80(x78141),f328(f107(x78141),x78142)),f78(x78141)),f328(f107(x78141),f328(f328(f80(a1),x78142),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))) % 154.70/154.55 [7959]P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x79592)))+E(f328(f328(f253(a1),x79591),f328(f107(a875),f328(f328(f22(a1),f328(f328(f80(a1),x79592),x79592)),a101))),f78(a1)) % 154.70/154.55 [9382]~P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x93822)))+E(f328(f328(f253(a1),x93821),f328(f107(a875),f328(f328(f22(a1),f328(f328(f80(a1),x93822),x93822)),a101))),f328(f328(f86(a1,a1),f328(f328(f253(a1),x93821),f328(f107(a875),x93822))),f328(f328(f18(a1,a1,a1),f328(f328(f8(a1,f882(a1,a1),a1),f81(a1)),f328(f81(a1),x93821))),f5(a1)))) % 154.70/154.56 [9747]~P1(f328(f328(f242(a875),f669(x97472,x97471)),f328(x97471,f669(x97472,x97471))))+P1(f328(f61(a875),f328(f248(a875),f328(f328(f7(a875,a875,a870),f328(f328(f8(a875,f882(a875,a870),a875),f242(a875)),x97471)),x97472)))) % 154.70/154.56 [9897]~P1(f328(f328(f243(a875),f328(f107(a875),x98971)),f328(a116,x98972)))+P1(f328(f328(f86(a1,a870),f328(f107(a1),f328(f328(f80(a1),x98971),a101))),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a331),f328(f328(f8(a870,a870,a1),a323),a197))),f328(f328(f7(a1,a875,a870),f328(f328(f8(a875,f882(a875,a870),a1),f243(a875)),a108)),x98972)))) % 154.70/154.56 [9898]~P1(f328(f328(f242(a875),f328(f107(a875),x98981)),f328(a116,x98982)))+P1(f328(f328(f86(a1,a870),f328(f107(a1),f328(f328(f80(a1),x98981),a101))),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a331),f328(f328(f8(a870,a870,a1),a323),a197))),f328(f328(f7(a1,a875,a870),f328(f328(f8(a875,f882(a875,a870),a1),f242(a875)),a108)),x98982)))) % 154.70/154.56 [9947]P1(f328(f328(f243(a875),f328(f107(a875),x99471)),f328(a116,x99472)))+~P1(f328(f328(f86(a1,a870),f328(f107(a1),f328(f328(f80(a1),x99471),a101))),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a331),f328(f328(f8(a870,a870,a1),a323),a197))),f328(f328(f7(a1,a875,a870),f328(f328(f8(a875,f882(a875,a870),a1),f243(a875)),a108)),x99472)))) % 154.70/154.56 [9948]P1(f328(f328(f242(a875),f328(f107(a875),x99481)),f328(a116,x99482)))+~P1(f328(f328(f86(a1,a870),f328(f107(a1),f328(f328(f80(a1),x99481),a101))),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a331),f328(f328(f8(a870,a870,a1),a323),a197))),f328(f328(f7(a1,a875,a870),f328(f328(f8(a875,f882(a875,a870),a1),f242(a875)),a108)),x99482)))) % 154.70/154.56 [9978]~P1(f328(f328(f243(a875),f328(a116,x99782)),f328(f107(a875),x99781)))+P1(f328(f328(f86(a1,a870),f328(f107(a1),f328(f328(f80(a1),x99781),a101))),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a326),f328(f328(f8(a870,a870,a1),a323),a197))),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a331),f328(f328(f8(a870,a870,a1),a323),a197))),f328(f328(f8(a875,a870,a1),f328(f243(a875),x99782)),a108))))) % 154.70/154.56 [9979]~P1(f328(f328(f242(a875),f328(a116,x99792)),f328(f107(a875),x99791)))+P1(f328(f328(f86(a1,a870),f328(f107(a1),f328(f328(f80(a1),x99791),a101))),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a326),f328(f328(f8(a870,a870,a1),a323),a197))),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a331),f328(f328(f8(a870,a870,a1),a323),a197))),f328(f328(f8(a875,a870,a1),f328(f242(a875),x99792)),a108))))) % 154.70/154.56 [10022]P1(f328(f328(f243(a875),f328(a116,x100221)),f328(f107(a875),x100222)))+~P1(f328(f328(f86(a1,a870),f328(f107(a1),f328(f328(f80(a1),x100222),a101))),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a326),f328(f328(f8(a870,a870,a1),a323),a197))),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a331),f328(f328(f8(a870,a870,a1),a323),a197))),f328(f328(f8(a875,a870,a1),f328(f243(a875),x100221)),a108))))) % 154.70/154.56 [10023]P1(f328(f328(f242(a875),f328(a116,x100231)),f328(f107(a875),x100232)))+~P1(f328(f328(f86(a1,a870),f328(f107(a1),f328(f328(f80(a1),x100232),a101))),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a326),f328(f328(f8(a870,a870,a1),a323),a197))),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a331),f328(f328(f8(a870,a870,a1),a323),a197))),f328(f328(f8(a875,a870,a1),f328(f242(a875),x100231)),a108))))) % 154.70/154.56 [10095]~P1(f328(f328(f330(a875),f2(a875)),x100951))+E(f328(a116,f328(f37(a875),f328(f248(a875),f328(f328(f18(a875,a870,a870),f328(f328(f8(a870,f882(a870,a870),a875),a326),f328(f328(f7(a875,f882(a875,a870),a870),f328(f328(f8(a875,f882(f882(a875,a870),a870),a875),f330(a875)),a116)),x100951))),f328(f328(f7(a875,a875,a870),f243(a875)),x100952))))),f328(f37(a875),f328(f248(a875),f328(f328(f18(a875,a870,a870),f328(f328(f8(a870,f882(a870,a870),a875),a326),f328(f328(f7(a875,f882(a875,a870),a870),f330(a875)),x100951))),f328(f328(f7(a875,a875,a870),f243(a875)),f328(a116,x100952)))))) % 154.70/154.56 [8511]~P90(x85111)+E(f328(f328(f81(x85111),f328(f107(x85111),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),x85112),x85112) % 154.70/154.56 [8577]~P90(x85771)+E(f328(f328(f80(x85771),f78(x85771)),f328(f107(x85771),x85772)),f328(f107(x85771),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),x85772))) % 154.70/154.56 [8635]~P90(x86351)+E(f328(f328(f22(x86351),f328(f107(x86351),x86352)),f78(x86351)),f328(f107(x86351),f328(f328(f80(a1),x86352),f328(f79(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 154.70/154.56 [8776]~P1(f328(f328(f243(a875),f328(f107(a875),a83)),x87762))+E(f328(f328(f22(a875),x87761),f328(f328(f22(a875),x87762),f328(f107(a875),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(f328(f22(a875),f328(a116,x87761)),x87762)) % 154.70/154.56 [9421]~P109(x94211)+E(f328(f328(f81(x94211),x94212),x94212),f328(f328(f253(x94211),x94212),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 154.70/154.56 [9422]~P79(x94221)+E(f328(f328(f253(x94221),x94222),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(f328(f81(x94221),x94222),x94222)) % 154.70/154.56 [9424]~P90(x94241)+E(f328(f328(f81(x94241),x94242),f328(f107(x94241),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(f328(f80(x94241),x94242),x94242)) % 154.70/154.56 [9665]~P121(x96651)+E(f328(f328(f253(x96651),f328(f75(x96651),x96652)),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(f328(f253(x96651),x96652),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 154.70/154.56 [9666]~P135(x96661)+E(f328(f328(f253(x96661),f328(f79(x96661),x96662)),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(f328(f253(x96661),x96662),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 154.70/154.56 [9662]~P90(x96621)+E(f328(f328(f81(x96621),f328(f107(x96621),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x96622),f328(f328(f80(x96621),x96622),x96622)) % 154.70/154.56 [9787]~P121(x97871)+E(f328(f75(x97871),f328(f328(f253(x97871),x97872),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x97871),x97872),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 154.70/154.56 [9849]~P121(x98491)+P1(f328(f328(f242(x98491),f2(x98491)),f328(f328(f253(x98491),x98492),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))) % 154.70/154.56 [10013]~E(f328(a116,x100132),f328(f107(a875),x100131))+P1(f328(f328(f86(a1,a870),f328(f107(a1),f328(f328(f80(a1),x100131),a101))),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a326),f328(f328(f8(a870,a870,a1),a323),a197))),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a331),f328(f328(f8(a870,a870,a1),a323),a197))),f328(f328(f7(a1,a875,a870),f328(f328(f8(a875,f882(a875,a870),a1),a325),a108)),x100132))))) % 154.70/154.56 [10014]~E(f328(f107(a875),x100141),f328(a116,x100142))+P1(f328(f328(f86(a1,a870),f328(f107(a1),f328(f328(f80(a1),x100141),a101))),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a326),f328(f328(f8(a870,a870,a1),a323),a197))),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a331),f328(f328(f8(a870,a870,a1),a323),a197))),f328(f328(f7(a1,a875,a870),f328(f328(f8(a875,f882(a875,a870),a1),a325),a108)),x100142))))) % 154.70/154.56 [10058]E(f328(a116,x100581),f328(f107(a875),x100582))+~P1(f328(f328(f86(a1,a870),f328(f107(a1),f328(f328(f80(a1),x100582),a101))),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a326),f328(f328(f8(a870,a870,a1),a323),a197))),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a331),f328(f328(f8(a870,a870,a1),a323),a197))),f328(f328(f7(a1,a875,a870),f328(f328(f8(a875,f882(a875,a870),a1),a325),a108)),x100581))))) % 154.70/154.56 [10059]E(f328(f107(a875),x100591),f328(a116,x100592))+~P1(f328(f328(f86(a1,a870),f328(f107(a1),f328(f328(f80(a1),x100591),a101))),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a326),f328(f328(f8(a870,a870,a1),a323),a197))),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a331),f328(f328(f8(a870,a870,a1),a323),a197))),f328(f328(f7(a1,a875,a870),f328(f328(f8(a875,f882(a875,a870),a1),a325),a108)),x100592))))) % 154.70/154.56 [9846]~P90(x98461)+E(f328(f328(f253(x98461),f328(f107(x98461),a101)),f328(f328(f81(a875),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x98462)),f78(x98461)) % 154.70/154.56 [9847]~P135(x98471)+E(f328(f328(f253(x98471),f328(f79(x98471),f78(x98471))),f328(f328(f81(a875),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x98472)),f78(x98471)) % 154.70/154.56 [9851]~P79(x98511)+E(f328(f328(f253(x98511),x98512),f328(f107(a875),f328(f328(f22(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),a101))),f328(f328(f81(x98511),f328(f328(f81(x98511),x98512),x98512)),x98512)) % 154.70/154.56 [10037]~P1(f328(f328(f242(a1),f2(a1)),x100372))+E(f44(a1,f328(f328(f80(a1),f78(a1)),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x100371)),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x100372)),f328(f328(f80(a1),f78(a1)),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f44(a1,x100371,x100372)))) % 154.70/154.56 [10061]~P1(f328(f328(f242(a1),f2(a1)),x100612))+E(f328(f328(f38(a1),f328(f328(f80(a1),f78(a1)),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x100611))),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x100612)),f328(f328(f38(a1),x100611),x100612)) % 154.70/154.56 [10063]~P1(f328(f328(f242(a1),x100632),f2(a1)))+E(f328(f328(f38(a1),f328(f328(f80(a1),f78(a1)),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x100631))),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x100632)),f328(f328(f38(a1),f328(f328(f80(a1),x100631),f78(a1))),x100632)) % 154.70/154.56 [10064]~P1(f328(f328(f242(a1),x100642),f2(a1)))+E(f44(a1,f328(f328(f80(a1),f78(a1)),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x100641)),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x100642)),f328(f328(f22(a1),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f44(a1,f328(f328(f80(a1),x100641),f78(a1)),x100642))),f78(a1))) % 154.70/154.56 [9938]~P90(x99381)+E(f328(f328(f253(x99381),f328(f107(x99381),a101)),f328(a116,f328(f328(f81(a875),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x99382))),f328(f107(x99381),a101)) % 154.70/154.56 [9940]~P135(x99401)+E(f328(f328(f253(x99401),f328(f79(x99401),f78(x99401))),f328(a116,f328(f328(f81(a875),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x99402))),f328(f79(x99401),f78(x99401))) % 154.70/154.56 [5096]~P26(x50961,x50962,x50963)+P30(x50961,x50962,x50963) % 154.70/154.56 [8024]~E(x80242,x80243)+P36(x80241,x80241,a325,x80242,x80243) % 154.70/154.56 [8590]E(x85901,x85902)+~P36(x85903,x85903,a325,x85901,x85902) % 154.70/154.56 [5101]~P39(x51011,x51013)+P39(x51011,f322(x51011,x51012,x51013)) % 154.70/154.56 [5273]P29(x52731,x52732,x52733)+~P29(x52731,f328(a116,x52732),x52733) % 154.70/154.56 [5359]~P8(x53591,x53592,x53593)+P8(f876(x53591),f158(x53591,x53592),f155(x53591,x53593)) % 154.70/154.56 [5360]~P41(x53601,x53602,x53603)+P41(f876(x53601),f158(x53601,x53602),f155(x53601,x53603)) % 154.70/154.56 [5472]P51(x54721,x54722,x54723)+~E(f612(x54723,x54722,x54721),f613(x54723,x54722,x54721)) % 154.70/154.56 [5473]P52(x54731,x54732,x54733)+~E(f628(x54733,x54732,x54731),f629(x54733,x54732,x54731)) % 154.70/154.56 [6408]P30(x64081,x64082,x64083)+~P29(x64081,f599(x64083,x64082,x64081),f606(x64083,x64082,x64081)) % 154.70/154.56 [4649]~E(x46491,f205(x46492))+~E(x46491,f328(f235(x46492),x46493)) % 154.70/154.56 [4698]~E(f328(f166(x46982),x46981),x46983)+E(x46981,f328(f166(x46982),x46983)) % 154.70/154.56 [4699]~E(x46992,f328(f166(x46991),x46993))+E(f328(f166(x46991),x46992),x46993) % 154.70/154.56 [4746]E(x47461,x47462)+~E(f328(f235(x47463),x47461),f328(f235(x47463),x47462)) % 154.70/154.56 [4747]E(x47471,x47472)+~E(f328(f166(x47473),x47471),f328(f166(x47473),x47472)) % 154.70/154.56 [4952]~P7(x49523,x49521)+P1(f328(f328(x49521,x49522),x49522)) % 154.70/154.56 [4953]~P50(x49533,x49531)+P1(f328(f328(x49531,x49532),x49532)) % 154.70/154.56 [4955]~P56(x49551,x49552)+P1(f328(f316(x49551,x49552),x49553)) % 154.70/154.56 [5018]~P39(x50181,x50182)+P39(f876(x50181),f328(f140(x50181,x50182),x50183)) % 154.70/154.56 [5023]~P1(f328(x50232,x50233))+~E(f328(f248(x50231),x50232),f192(f882(x50231,a870))) % 154.70/154.56 [5024]~P1(f328(x50242,x50243))+~E(f192(f882(x50241,a870)),f328(f248(x50241),x50242)) % 154.70/154.56 [5038]E(x50381,f2(a875))+E(f141(x50382,f168(x50382,x50381,x50383)),x50383) % 154.70/154.56 [5056]~P1(f328(x50561,x50563))+P1(f328(x50561,f90(x50562,x50561))) % 154.70/154.56 [5068]E(x50681,f2(a875))+E(f328(f138(x50682),f168(x50682,x50681,x50683)),x50683) % 154.70/154.56 [5181]~E(x51812,x51813)+P1(f328(f328(f330(x51811),x51812),f328(a325,x51813))) % 154.70/154.56 [5193]P1(f328(x51931,x51932))+~P1(f328(x51931,f569(x51931,x51933))) % 154.70/154.56 [5239]E(f328(f166(x52391),x52392),f328(f328(f148(x52391),x52393),f117(x52391)))+~E(x52392,f328(f328(f148(x52391),x52393),f117(x52391))) % 154.70/154.56 [5240]~E(x52403,f328(f328(f148(x52401),x52402),f117(x52401)))+E(f328(f328(f148(x52401),x52402),f117(x52401)),f328(f166(x52401),x52403)) % 154.70/154.56 [5266]~E(x52663,f328(f16(f879(x52662),x52661),f205(x52662)))+E(f182(x52661,x52662,x52663),f192(f882(x52661,a870))) % 154.70/154.56 [5288]~P35(x52881,x52882,x52883)+P35(x52881,x52882,f328(f166(x52881),x52883)) % 154.70/154.56 [5289]~P33(x52891,x52892,x52893)+P33(x52891,x52892,f328(f166(x52891),x52893)) % 154.70/154.56 [5292]E(f328(f37(x52921),f778(x52922,x52923,x52921)),x52922)+~E(f328(f37(x52921),x52923),f328(a116,x52922)) % 154.70/154.56 [5298]~P39(x52981,x52983)+P1(f328(f328(f330(x52981),x52982),f317(x52981,x52983))) % 154.70/154.56 [5301]~E(f328(f166(x53012),x53011),f328(f328(f148(x53012),x53013),f117(x53012)))+E(x53011,f328(f328(f148(x53012),x53013),f117(x53012))) % 154.70/154.56 [5302]~E(f328(f328(f148(x53022),x53023),f117(x53022)),f328(f166(x53022),x53021))+E(x53021,f328(f328(f148(x53022),x53023),f117(x53022))) % 154.70/154.56 [5317]E(x53171,f328(f16(f879(x53172),x53173),f205(x53172)))+~E(f182(x53173,x53172,x53171),f192(f882(x53173,a870))) % 154.70/154.56 [5323]E(f85(f881(a875,a875),f47(x53231,x53232)),x53233)+~P1(f328(f47(x53231,x53232),x53233)) % 154.70/154.56 [5331]~E(x53313,f328(f235(x53311),x53312))+P1(f328(f328(f330(x53311),x53312),f234(x53311,x53313))) % 154.70/154.56 [5363]P35(x53631,x53632,x53633)+~P35(x53631,x53632,f328(f166(x53631),x53633)) % 154.70/154.56 [5364]P33(x53641,x53642,x53643)+~P33(x53641,x53642,f328(f166(x53641),x53643)) % 154.70/154.56 [5426]~E(x54262,f117(x54261))+P1(f328(f328(f330(f876(x54261)),x54262),f158(x54261,x54263))) % 154.70/154.56 [5433]~P41(x54331,x54332,x54333)+P41(x54331,x54332,f328(f283(x54331,x54331),x54333)) % 154.70/154.56 [5434]~P52(x54341,x54342,x54343)+P52(x54341,x54342,f328(f283(x54341,x54341),x54343)) % 154.70/154.56 [5453]~P57(x54531)+E(f44(x54531,f44(x54531,x54532,x54533),x54533),f44(x54531,x54532,x54533)) % 154.70/154.56 [5548]E(x55481,x55482)+~P1(f328(f328(f330(x55483),x55481),f328(a325,x55482))) % 154.70/154.56 [5594]~P140(x55941)+E(f194(x55941,x55942,f2(a875),x55943),x55943) % 154.70/154.56 [5614]P41(x56141,x56142,x56143)+~P41(x56141,x56142,f328(f283(x56141,x56141),x56143)) % 154.70/154.56 [5615]P52(x56151,x56152,x56153)+~P52(x56151,x56152,f328(f283(x56151,x56151),x56153)) % 154.70/154.56 [5619]~P105(x56192)+E(f147(x56191,x56192,x56193,f117(x56191)),f117(x56191)) % 154.70/154.56 [5632]E(f167(x56321,x56322,f149(x56321,x56323)),f149(x56321,f167(x56321,x56322,x56323)))+~P1(f328(f134(x56321),x56323)) % 154.70/154.56 [5638]E(x56381,f328(f235(x56382),x56383))+~P1(f328(f328(f330(x56382),x56383),f234(x56382,x56381))) % 154.70/154.56 [5724]~P1(f328(a25,x57243))+P1(f328(a25,f29(x57241,x57242,x57243))) % 154.70/154.56 [5735]E(f328(f133(x57351,x57352),x57353),f117(x57351))+P1(f328(x57352,f732(x57353,x57352,x57351))) % 154.70/154.56 [5878]~P1(f328(f134(x58781),x58782))+P1(f328(f134(x58781),f174(x58781,x58782,x58783))) % 154.70/154.56 [5879]~P1(f328(f134(x58791),x58793))+P1(f328(f134(x58791),f167(x58791,x58792,x58793))) % 154.70/154.56 [5880]~P1(f328(f134(x58801),x58803))+P1(f328(f134(x58801),f175(x58801,x58802,x58803))) % 154.70/154.56 [5881]~P1(f328(f134(x58811),x58813))+P1(f328(f134(x58811),f137(x58811,x58812,x58813))) % 154.70/154.56 [5882]~P143(x58821,x58823,x58822)+P1(f328(x58821,f44(a1,x58822,x58823))) % 154.70/154.56 [5901]~P35(x59013,x59011,x59012)+P1(f328(x59011,f781(x59012,x59011,x59013))) % 154.70/154.56 [5902]~P37(x59023,x59021,x59022)+P1(f328(x59021,f810(x59022,x59021,x59023))) % 154.70/154.56 [5923]E(f328(f133(x59231,x59232),x59233),f175(x59231,x59232,x59233))+P1(f328(x59232,f758(x59233,x59232,x59231))) % 154.70/154.56 [5963]~P1(f328(f134(x59631),x59633))+P1(f328(f134(f876(x59631)),f54(x59631,x59632,x59633))) % 154.70/154.56 [5994]~P107(x59941)+E(f328(f328(f105(f882(x59941,a870)),f328(f249(x59941),x59942)),f299(x59941,x59942,x59943)),f192(f882(x59941,a870))) % 154.70/154.56 [5995]~P107(x59951)+E(f328(f328(f105(f882(x59951,a870)),f328(f297(x59951),x59952)),f302(x59951,x59952,x59953)),f192(f882(x59951,a870))) % 154.70/154.56 [5996]~P107(x59961)+E(f328(f328(f105(f882(x59961,a870)),f328(f297(x59961),x59962)),f301(x59961,x59962,x59963)),f192(f882(x59961,a870))) % 154.70/154.56 [6143]P1(f328(a25,x61431))+~P1(f328(a25,f29(x61432,x61433,x61431))) % 154.70/154.56 [6145]P1(f328(a25,x61451))+~P1(f328(a25,f30(x61452,x61453,x61451))) % 154.70/154.56 [6147]P1(f328(a25,x61471))+~P1(f328(a25,f30(x61472,x61471,x61473))) % 154.70/154.56 [6230]E(f328(f133(x62301,x62302),x62303),x62303)+~P1(f328(x62302,f733(x62303,x62302,x62301))) % 154.70/154.56 [6232]E(f328(f328(f306(x62321),f858(x62322,x62323,x62321)),f778(x62322,x62323,x62321)),x62323)+~E(f328(f37(x62321),x62323),f328(a116,x62322)) % 154.70/154.56 [6248]P143(x62481,x62482,x62483)+~P1(f328(x62481,f44(a1,x62483,x62482))) % 154.70/154.56 [6295]P33(x62951,x62952,x62953)+~P1(f328(x62952,f796(x62952,x62953,x62951))) % 154.70/154.56 [6296]P33(x62961,x62962,x62963)+~P1(f328(x62962,f803(x62963,x62962,x62961))) % 154.70/154.56 [6297]P33(x62971,x62972,x62973)+~P1(f328(x62972,f804(x62973,x62972,x62971))) % 154.70/154.56 [6299]E(f175(x62991,x62992,x62993),x62993)+~P1(f328(x62992,f753(x62993,x62992,x62991))) % 154.70/154.56 [6377]~P1(f328(x63772,f594(x63773,x63772,x63771)))+P1(f328(f256(x63771,x63772),x63773)) % 154.70/154.56 [6378]~P1(f328(x63782,f723(x63783,x63782,x63781)))+P1(f328(f157(x63781,x63782),x63783)) % 154.70/154.56 [6623]~P1(f328(f316(x66231,x66232),f520(x66233,x66232,x66231)))+P1(f328(f316(x66231,x66232),x66233)) % 154.70/154.56 [6624]~P1(f328(f316(x66241,x66242),f538(x66243,x66242,x66241)))+P1(f328(f316(x66241,x66242),x66243)) % 154.70/154.56 [7233]~P57(x72331)+E(f328(f328(f80(x72331),f328(f328(f81(x72331),x72332),f328(f328(f38(x72331),x72333),x72332))),f44(x72331,x72333,x72332)),x72333) % 154.70/154.56 [7703]E(f328(f328(f263(x77031,x77031),f557(x77032,x77033,x77031)),f557(x77032,x77033,x77031)),x77033)+~P1(f328(f328(f330(f881(x77031,x77031)),x77033),f260(x77031,x77032))) % 154.70/154.56 [7822]~P1(f328(f328(f330(x78221),f558(x78223,x78222,x78221)),f317(x78221,x78223)))+P1(f328(f328(f330(x78221),x78222),f317(x78221,x78223))) % 154.70/154.56 [7823]~P1(f328(f328(f330(x78231),f615(x78233,x78232,x78231)),f317(x78231,x78233)))+P1(f328(f328(f330(x78231),x78232),f317(x78231,x78233))) % 154.70/154.56 [7824]~P1(f328(f328(f330(x78241),f617(x78243,x78242,x78241)),f317(x78241,x78243)))+P1(f328(f328(f330(x78241),x78242),f317(x78241,x78243))) % 154.70/154.56 [8005]~P57(x80051)+E(f328(f328(f80(x80051),f328(f328(f81(x80051),f328(f328(f38(x80051),x80052),x80053)),x80053)),f44(x80051,x80052,x80053)),x80052) % 154.70/154.56 [8050]~E(f328(f37(x80501),x80502),f328(a116,x80503))+~P1(f328(f328(f330(x80501),f858(x80503,x80502,x80501)),f778(x80503,x80502,x80501))) % 154.70/154.56 [8688]P1(f328(f328(f242(f882(f881(x86881,x86881),a870)),f304(x86881,x86882)),f304(x86881,x86883)))+~P1(f328(f328(f242(f882(f881(x86881,x86881),a870)),x86882),f304(x86881,x86883))) % 154.70/154.56 [8962]E(x89621,f117(x89622))+~P1(f328(f328(f330(f881(f876(x89622),f876(x89622))),f328(f328(f263(f876(x89622),f876(x89622)),x89621),f117(x89622))),f155(x89622,x89623))) % 154.70/154.56 [8988]E(x89881,f117(x89882))+~P1(f328(f328(f330(f881(f876(x89882),f876(x89882))),f328(f328(f263(f876(x89882),f876(x89882)),f117(x89882)),x89881)),f155(x89882,x89883))) % 154.70/154.56 [9113]E(f328(f328(f148(x91131),f708(x91132,x91133,x91131)),f709(x91132,x91133,x91131)),x91133)+~P1(f328(f328(f330(f881(f876(x91131),f876(x91131))),f328(f328(f263(f876(x91131),f876(x91131)),f117(x91131)),x91133)),f144(x91131,x91132))) % 154.70/154.56 [9350]~P120(x93501)+~P1(f328(f328(f243(x93501),f328(f328(f80(x93501),f328(f328(f81(x93501),x93502),x93502)),f328(f328(f81(x93501),x93503),x93503))),f2(x93501))) % 154.70/154.56 [9399]P1(f328(f61(x93991),x93992))+~P1(f328(f328(f330(f881(f882(x93991,a870),f882(x93991,a870))),f328(f328(f263(f882(x93991,a870),f882(x93991,a870)),x93993),x93992)),f303(x93991))) % 154.70/154.56 [9688]~P48(x96881,x96882,x96883)+P1(f328(f328(f243(a1),f328(f328(f73(f881(a1,a1),a1,x96881,f262(a1,a1)),f219(x96881)),f230(x96881,x96882,f227(x96881,x96883)))),f2(a1))) % 154.70/154.56 [9689]~P49(x96891,x96892,x96893)+P1(f328(f328(f242(a1),f328(f328(f73(f881(a1,a1),a1,x96891,f262(a1,a1)),f219(x96891)),f230(x96891,x96892,f227(x96891,x96893)))),f2(a1))) % 154.70/154.56 [9816]P48(x98161,x98162,x98163)+~P1(f328(f328(f243(a1),f328(f328(f73(f881(a1,a1),a1,x98161,f262(a1,a1)),f219(x98161)),f230(x98161,x98162,f227(x98161,x98163)))),f2(a1))) % 154.70/154.56 [9817]P49(x98171,x98172,x98173)+~P1(f328(f328(f242(a1),f328(f328(f73(f881(a1,a1),a1,x98171,f262(a1,a1)),f219(x98171)),f230(x98171,x98172,f227(x98171,x98173)))),f2(a1))) % 154.70/154.56 [10139]~P121(x101391)+~P1(f328(f328(f243(x101391),f328(f328(f80(x101391),f328(f328(f253(x101391),x101392),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x101391),x101393),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))),f2(x101391))) % 154.70/154.56 [4729]~E(x47293,f117(x47291))+E(f328(f328(f125(x47291),x47292),x47293),x47292) % 154.70/154.56 [4730]~E(x47302,f117(x47301))+E(f328(f328(f125(x47301),x47302),x47303),x47303) % 154.70/154.56 [4737]~E(x47372,f2(a875))+E(f328(f328(f173(x47371),x47372),x47373),f117(x47371)) % 154.70/154.56 [4741]~E(x47413,f117(x47411))+E(f328(f328(f173(x47411),x47412),x47413),f117(x47411)) % 154.70/154.56 [4781]~E(x47811,x47813)+E(x47811,f328(f328(f125(x47812),f117(x47812)),x47813)) % 154.70/154.56 [4869]~P98(x48692)+E(f328(f192(f882(x48691,x48692)),x48693),f192(x48692)) % 154.70/154.56 [4870]~P104(x48702)+E(f328(f251(f882(x48701,x48702)),x48703),f251(x48702)) % 154.70/154.56 [4889]E(x48891,f117(x48892))+~E(f328(f328(f125(x48892),x48893),x48891),x48893) % 154.70/154.56 [4890]E(x48901,f117(x48902))+~E(f328(f328(f125(x48902),x48901),x48903),x48903) % 154.70/154.56 [4898]E(x48981,f117(x48982))+~E(f328(f328(f125(x48982),x48983),x48981),f117(x48982)) % 154.70/154.56 [4899]E(x48991,f117(x48992))+~E(f328(f328(f125(x48992),x48991),x48993),f117(x48992)) % 154.70/154.56 [4922]~E(x49222,f2(a875))+E(f328(f328(f81(a875),x49221),x49222),f328(f328(f81(a875),x49223),x49222)) % 154.70/154.56 [4924]~E(x49241,f2(a875))+E(f328(f328(f81(a875),x49241),x49242),f328(f328(f81(a875),x49241),x49243)) % 154.70/154.56 [4977]~P2(x49771)+E(f328(f328(f114(x49771),x49772),x49773),f328(f328(f114(x49771),x49773),x49772)) % 154.70/154.56 [4979]~P99(x49791)+E(f328(f328(f114(x49791),x49792),x49793),f328(f328(f114(x49791),x49793),x49792)) % 154.70/154.56 [4980]~P2(x49801)+E(f328(f328(f105(x49801),x49802),x49803),f328(f328(f105(x49801),x49803),x49802)) % 154.70/154.56 [4982]~P100(x49821)+E(f328(f328(f105(x49821),x49822),x49823),f328(f328(f105(x49821),x49823),x49822)) % 154.70/154.56 [4983]~P109(x49831)+E(f328(f328(f80(x49831),x49832),x49833),f328(f328(f80(x49831),x49833),x49832)) % 154.70/154.56 [4984]~P109(x49841)+E(f328(f328(f81(x49841),x49842),x49843),f328(f328(f81(x49841),x49843),x49842)) % 154.70/154.56 [4986]~P105(x49861)+E(f328(f328(f240(x49861),x49862),x49863),f328(f328(f240(x49861),x49863),x49862)) % 154.70/154.56 [4988]~P105(x49881)+E(f328(f328(f241(x49881),x49882),x49883),f328(f328(f241(x49881),x49883),x49882)) % 154.70/154.56 [5051]E(f44(a875,x50511,x50512),f2(a875))+~E(x50511,f328(f328(f81(a875),x50512),x50513)) % 154.70/154.56 [5052]E(f44(a1,x50521,x50522),f2(a1))+~E(x50521,f328(f328(f81(a1),x50522),x50523)) % 154.70/154.56 [5113]E(x51131,x51132)+~E(f328(f328(f80(a875),x51133),x51131),f328(f328(f80(a875),x51133),x51132)) % 154.70/154.56 [5114]E(x51141,x51142)+~E(f328(f328(f80(a875),x51141),x51143),f328(f328(f80(a875),x51142),x51143)) % 154.70/154.56 [5124]~P93(x51241)+E(f328(f328(f105(x51241),x51242),f328(f79(x51241),x51243)),f328(f328(f22(x51241),x51242),x51243)) % 154.70/154.56 [5125]~P65(x51251)+E(f328(f328(f80(x51251),x51252),f328(f79(x51251),x51253)),f328(f328(f22(x51251),x51252),x51253)) % 154.70/154.56 [5126]~P72(x51261)+E(f328(f328(f80(x51261),x51262),f328(f79(x51261),x51263)),f328(f328(f22(x51261),x51262),x51263)) % 154.70/154.56 [5127]~P111(x51271)+E(f328(f328(f80(x51271),x51272),f328(f79(x51271),x51273)),f328(f328(f22(x51271),x51272),x51273)) % 154.70/154.56 [5128]~P72(x51281)+E(f328(f328(f22(x51281),x51282),f328(f79(x51281),x51283)),f328(f328(f80(x51281),x51282),x51283)) % 154.70/154.56 [5174]~P1(f328(x51743,x51742))+P1(f328(f328(f330(x51741),x51742),x51743)) % 154.70/154.56 [5176]~P66(x51762)+E(f328(f328(f6(x51761,x51762),x51763),f192(f882(x51761,a870))),f2(x51762)) % 154.70/154.56 [5178]~P73(x51782)+E(f328(f328(f9(x51781,x51782),x51783),f192(f882(x51781,a870))),f78(x51782)) % 154.70/154.56 [5227]~E(x52272,f328(f328(f80(a875),x52271),x52273))+P1(f328(f328(f242(a875),x52271),x52272)) % 154.70/154.56 [5230]~E(x52302,f192(f882(x52301,a870)))+E(f328(f328(f60(x52301),x52302),x52303),f192(f882(f882(x52301,a870),a870))) % 154.70/154.56 [5231]~E(x52312,f192(f882(x52311,a870)))+E(f192(f882(f882(x52311,a870),a870)),f328(f328(f60(x52311),x52312),x52313)) % 154.70/154.56 [5306]~E(f328(f259(x53062,x53063),x53061),f192(f882(x53063,a870)))+E(x53061,f192(f882(f881(x53062,x53063),a870))) % 154.70/154.56 [5307]~E(f328(f261(x53072,x53073),x53071),f192(f882(x53072,a870)))+E(x53071,f192(f882(f881(x53072,x53073),a870))) % 154.70/154.56 [5337]E(f328(f259(x53371,x53372),x53373),f192(f882(x53372,a870)))+~E(x53373,f192(f882(f881(x53371,x53372),a870))) % 154.70/154.56 [5338]E(f328(f261(x53381,x53382),x53383),f192(f882(x53381,a870)))+~E(x53383,f192(f882(f881(x53381,x53382),a870))) % 154.70/154.56 [5341]E(f278(x53411,x53412,x53413),f328(f328(f22(a103),x53412),x53413))+P1(f328(f328(f243(a103),x53412),x53413)) % 154.70/154.56 [5357]P1(f328(x53571,x53572))+~P1(f328(f328(f330(x53573),x53572),x53571)) % 154.70/154.56 [5396]E(x53961,x53962)+~E(f328(f79(f882(x53963,a870)),x53961),f328(f79(f882(x53963,a870)),x53962)) % 154.70/154.56 [5401]E(f310(x54011,x54012,x54013),f205(f876(a324)))+~P1(f328(f328(f243(a1),x54012),x54013)) % 154.70/154.56 [5406]~E(x54061,f192(f882(x54062,a870)))+~P1(f328(f328(f330(x54062),x54063),x54061)) % 154.70/154.56 [5435]~E(x54352,f328(f328(f80(a1),x54351),f328(f104(a1),x54353)))+P1(f328(f328(f242(a1),x54351),x54352)) % 154.70/154.56 [5451]E(f328(f328(f306(x54511),x54512),x54513),x54513)+~P1(f328(f328(f330(x54511),x54512),x54513)) % 154.70/154.56 [5462]E(x54621,f192(f882(x54622,a870)))+~E(f328(f328(f60(x54622),x54621),x54623),f192(f882(f882(x54622,a870),a870))) % 154.70/154.56 [5463]E(x54631,f192(f882(x54632,a870)))+~E(f192(f882(f882(x54632,a870),a870)),f328(f328(f60(x54632),x54631),x54633)) % 154.70/154.56 [5470]~P103(x54701)+E(f328(f328(f81(x54701),f328(f79(x54701),x54702)),f328(f79(x54701),x54703)),f328(f328(f81(x54701),x54702),x54703)) % 154.70/154.56 [5471]~P60(x54711)+E(f328(f328(f286(x54711),f328(f79(x54711),x54712)),f328(f79(x54711),x54713)),f328(f328(f286(x54711),x54712),x54713)) % 154.70/154.56 [5503]~P1(f328(x55033,x55032))+P1(f328(f328(f330(x55031),x55032),f328(f248(x55031),x55033))) % 154.70/154.56 [5541]E(f167(x55411,x55412,x55413),x55413)+P1(f328(f328(f330(x55411),x55412),f328(f170(x55411),x55413))) % 154.70/154.56 [5623]~P1(f328(f134(x56231),x56233))+P1(f328(f134(x56231),f328(f133(x56231,x56232),x56233))) % 154.70/154.56 [5668]~P57(x56681)+E(f328(f328(f38(x56681),f44(x56681,x56682,x56683)),x56683),f2(x56681)) % 154.70/154.56 [5687]E(f174(x56871,f328(f328(f148(x56871),x56872),f117(x56871)),x56873),f117(x56871))+P1(f328(f328(f330(a875),f2(a875)),x56873)) % 154.70/154.56 [5693]E(x56931,f2(a875))+E(f328(f169(x56932),f168(x56932,x56931,x56933)),f168(x56932,f328(f328(f22(a875),x56931),f78(a875)),x56933)) % 154.70/154.56 [5745]E(f328(f328(f148(x57451),x57452),x57453),f137(x57451,x57452,x57453))+P1(f328(f328(f330(x57451),x57452),f328(f170(x57451),x57453))) % 154.70/154.56 [5754]E(x57541,x57542)+~E(f328(f328(f81(a875),f328(a116,x57543)),x57541),f328(f328(f81(a875),f328(a116,x57543)),x57542)) % 154.70/154.56 [5755]~E(x57552,f328(f328(f80(a1),x57551),f328(f104(a1),f328(a116,x57553))))+P1(f328(f328(f243(a1),x57551),x57552)) % 154.70/154.56 [5860]~E(x58603,f117(x58601))+E(f328(f328(f328(f187(f876(x58601),f876(x58601)),x58602),f165(x58601)),x58603),f117(x58601)) % 154.70/154.56 [5864]P1(f328(x58641,x58642))+~P1(f328(f328(f330(x58643),x58642),f328(f248(x58643),x58641))) % 154.70/154.56 [5896]E(x58961,x58962)+~E(f328(f328(f306(x58963),x58961),f192(f882(x58963,a870))),f328(f328(f306(x58963),x58962),f192(f882(x58963,a870)))) % 154.70/154.56 [5907]~P107(x59071)+E(f328(f328(f105(f882(x59071,a870)),f328(f249(x59071),x59072)),f328(f298(x59071,x59072),x59073)),f192(f882(x59071,a870))) % 154.70/154.56 [5949]E(f137(x59491,x59492,x59493),x59493)+~P1(f328(f328(f330(x59491),x59492),f328(f170(x59491),x59493))) % 154.70/154.56 [5970]~P81(x59701)+E(f328(f307(x59701,x59701,f79(x59701)),f328(f298(x59701,x59702),x59703)),f301(x59701,f328(f79(x59701),x59703),f328(f79(x59701),x59702))) % 154.70/154.56 [5978]E(f328(f193(f876(x59781)),f167(x59781,x59782,x59783)),f328(f193(f876(x59781)),x59783))+P1(f328(f328(f330(x59781),x59782),f328(f170(x59781),x59783))) % 154.70/154.56 [6030]~P107(x60301)+E(f328(f328(f105(f882(x60301,a870)),f328(f298(x60301,x60302),x60303)),f328(f250(x60301),x60303)),f192(f882(x60301,a870))) % 154.70/154.56 [6053]~P81(x60531)+E(f328(f307(x60531,x60531,f79(x60531)),f302(x60531,x60532,x60533)),f302(x60531,f328(f79(x60531),x60533),f328(f79(x60531),x60532))) % 154.70/154.56 [6054]~P81(x60541)+E(f328(f307(x60541,x60541,f79(x60541)),f299(x60541,x60542,x60543)),f299(x60541,f328(f79(x60541),x60543),f328(f79(x60541),x60542))) % 154.70/154.56 [6111]E(f174(x61111,f328(f328(f148(x61111),x61112),f117(x61111)),x61113),f328(f328(f148(x61111),x61112),f117(x61111)))+~P1(f328(f328(f330(a875),f2(a875)),x61113)) % 154.70/154.56 [6118]~P81(x61181)+E(f328(f307(x61181,x61181,f79(x61181)),f301(x61181,x61182,x61183)),f328(f298(x61181,f328(f79(x61181),x61183)),f328(f79(x61181),x61182))) % 154.70/154.56 [6138]~P58(x61381)+E(f44(x61381,f328(f79(x61381),f44(x61381,x61382,x61383)),x61383),f44(x61381,f328(f79(x61381),x61382),x61383)) % 154.70/154.56 [6245]~P1(f328(f61(f881(x62452,x62451)),x62453))+P1(f328(f61(x62451),f328(f259(x62452,x62451),x62453))) % 154.70/154.56 [6246]~P1(f328(f61(f881(x62461,x62462)),x62463))+P1(f328(f61(x62461),f328(f261(x62461,x62462),x62463))) % 154.70/154.56 [6252]~P107(x62521)+E(f328(f328(f105(f882(x62521,a870)),f302(x62521,x62522,x62523)),f328(f250(x62521),x62523)),f192(f882(x62521,a870))) % 154.70/154.56 [6253]~P107(x62531)+E(f328(f328(f105(f882(x62531,a870)),f301(x62531,x62532,x62533)),f328(f300(x62531),x62533)),f192(f882(x62531,a870))) % 154.70/154.56 [6254]~P107(x62541)+E(f328(f328(f105(f882(x62541,a870)),f299(x62541,x62542,x62543)),f328(f300(x62541),x62543)),f192(f882(x62541,a870))) % 154.70/154.56 [6320]E(f328(f328(f162(x63201),x63202),f665(x63202,x63203,x63201)),x63203)+~P1(f328(f328(f330(x63201),x63203),f328(f170(x63201),x63202))) % 154.70/154.56 [6459]E(x64591,f117(x64592))+~E(f328(f328(f328(f187(f876(x64592),f876(x64592)),x64593),f165(x64592)),x64591),f117(x64592)) % 154.70/154.56 [6560]~P1(f328(f61(f881(x65602,x65601)),x65603))+P1(f328(f61(f881(x65601,x65602)),f328(f283(x65602,x65601),x65603))) % 154.70/154.56 [6712]P52(x67121,x67122,x67123)+P1(f328(f328(f330(x67121),f629(x67123,x67122,x67121)),x67122)) % 154.70/154.56 [6713]P52(x67131,x67132,x67133)+P1(f328(f328(f330(x67131),f628(x67133,x67132,x67131)),x67132)) % 154.70/154.56 [6725]P1(f328(f316(x67251,x67252),x67253))+P1(f328(f328(x67252,f520(x67253,x67252,x67251)),x67253)) % 154.70/154.56 [6726]P1(f328(f316(x67261,x67262),x67263))+P1(f328(f328(x67262,f538(x67263,x67262,x67261)),x67263)) % 154.70/154.56 [6757]E(f328(f193(f876(x67571)),f167(x67571,x67572,x67573)),f328(f328(f22(a875),f328(f193(f876(x67571)),x67573)),f78(a875)))+~P1(f328(f328(f330(x67571),x67572),f328(f170(x67571),x67573))) % 154.70/154.56 [6797]P1(f328(f256(x67971,x67972),x67973))+P1(f328(f328(f330(x67971),f594(x67973,x67972,x67971)),x67973)) % 154.70/154.56 [6808]~P1(f328(f61(f881(x68082,x68081)),f328(f283(x68081,x68082),x68083)))+P1(f328(f61(f881(x68081,x68082)),x68083)) % 154.70/154.56 [6865]~P1(f328(f328(f330(x68651),x68652),f328(f170(x68651),f118(x68651,x68653))))+P1(f328(f328(f330(x68651),x68652),f328(f170(x68651),x68653))) % 154.70/154.56 [6870]P30(x68701,x68702,x68703)+P1(f328(f328(f330(f874(x68701)),f606(x68703,x68702,x68701)),x68703)) % 154.70/154.56 [6898]E(f328(f133(x68981,x68982),x68983),x68983)+P1(f328(f328(f330(x68981),f733(x68983,x68982,x68981)),f328(f170(x68981),x68983))) % 154.70/154.56 [6913]E(f328(f133(x69131,x69132),x69133),f117(x69131))+P1(f328(f328(f330(x69131),f732(x69133,x69132,x69131)),f328(f170(x69131),x69133))) % 154.70/154.56 [6936]P33(x69361,x69362,x69363)+P1(f328(f328(f330(x69361),f803(x69363,x69362,x69361)),f328(f170(x69361),x69363))) % 154.70/154.56 [6937]P33(x69371,x69372,x69373)+P1(f328(f328(f330(x69371),f804(x69373,x69372,x69371)),f328(f170(x69371),x69373))) % 154.70/154.56 [6938]P33(x69381,x69382,x69383)+P1(f328(f328(f330(x69381),f796(x69382,x69383,x69381)),f328(f170(x69381),x69383))) % 154.70/154.56 [6941]E(f175(x69411,x69412,x69413),x69413)+P1(f328(f328(f330(x69411),f753(x69413,x69412,x69411)),f328(f170(x69411),x69413))) % 154.70/154.56 [7020]P1(f328(f157(x70201,x70202),x70203))+P1(f328(f328(f330(x70201),f723(x70203,x70202,x70201)),f328(f170(x70201),x70203))) % 154.70/154.56 [7029]~P35(x70291,x70293,x70292)+P1(f328(f328(f330(x70291),f781(x70292,x70293,x70291)),f328(f170(x70291),x70292))) % 154.70/154.56 [7030]~P37(x70301,x70303,x70302)+P1(f328(f328(f330(x70301),f810(x70302,x70303,x70301)),f328(f170(x70301),x70302))) % 154.70/154.56 [7065]P1(f328(f328(f330(x70651),x70652),f827(x70653,x70652,x70651)))+~P1(f328(f328(f330(x70651),x70652),f39(f882(x70651,a870),x70653))) % 154.70/154.56 [7066]~P66(x70661)+E(f328(f328(f80(x70661),f328(f328(f6(a875,x70661),x70662),f328(f249(a875),x70663))),f328(x70662,x70663)),f328(f328(f6(a875,x70661),x70662),f328(f249(a875),f328(a116,x70663)))) % 154.70/154.56 [7155]~P35(x71552,x71551,x71553)+P1(f328(x71551,f328(f328(f162(x71552),x71553),f793(x71553,x71551,x71552)))) % 154.70/154.56 [7168]~P1(f328(f328(f330(x71681),x71682),f521(x71682,x71683,x71681)))+P1(f328(f328(f330(x71681),x71682),f40(f882(x71681,a870),x71683))) % 154.70/154.56 [7200]~P66(x72001)+E(f328(f328(f80(x72001),f328(f328(f6(a875,x72001),x72002),f328(f297(a875),x72003))),f328(x72002,f328(a116,x72003))),f328(f328(f6(a875,x72001),x72002),f328(f297(a875),f328(a116,x72003)))) % 154.70/154.56 [7335]P1(f328(f328(f330(f876(x73351)),x73352),f158(x73351,x73353)))+P1(f328(f328(f330(x73351),f676(x73353,x73352,x73351)),f328(f170(x73351),x73352))) % 154.70/154.56 [7352]~P1(f328(f328(f330(f876(x73521)),x73522),f158(x73521,f317(x73521,x73523))))+P1(f328(f328(f330(f876(x73521)),x73522),f317(f876(x73521),f154(x73521,x73523)))) % 154.70/154.56 [7377]~P1(f328(f328(f330(f876(x73771)),x73772),f317(f876(x73771),f154(x73771,x73773))))+P1(f328(f328(f330(f876(x73771)),x73772),f158(x73771,f317(x73771,x73773)))) % 154.70/154.56 [7413]E(f328(f328(f328(f187(f876(x74131),f876(x74131)),x74132),f165(x74131)),x74133),x74133)+~P1(f328(f328(f242(a875),f328(f193(f876(x74131)),x74133)),f78(a875))) % 154.70/154.56 [7448]E(f328(f328(f125(x74481),f798(x74482,x74483,x74481)),f328(f328(f148(x74481),x74483),f799(x74482,x74483,x74481))),x74482)+~P1(f328(f328(f330(x74481),x74483),f328(f170(x74481),x74482))) % 154.70/154.56 [7449]E(f328(f328(f125(x74491),f794(x74492,x74493,x74491)),f328(f328(f148(x74491),x74493),f795(x74492,x74493,x74491))),x74492)+~P1(f328(f328(f330(x74491),x74493),f328(f170(x74491),x74492))) % 154.70/154.56 [7450]E(f328(f328(f125(x74501),f800(x74502,x74503,x74501)),f328(f328(f148(x74501),x74503),f802(x74502,x74503,x74501))),x74502)+~P1(f328(f328(f330(x74501),x74503),f328(f170(x74501),x74502))) % 154.70/154.56 [7474]~P27(x74741,x74742,x74743,f251(f882(x74741,a870)))+P27(f876(x74741),f876(x74742),f328(f151(x74741,x74742),x74743),f251(f882(f876(x74741),a870))) % 154.70/154.56 [7624]E(x76241,f328(f328(f80(a875),f328(f328(f81(a875),f328(f262(a875,a875),x76242)),x76243)),f328(f266(a875,a875),x76242)))+~P1(f328(f47(x76241,x76243),x76242)) % 154.70/154.56 [7632]P27(x76321,x76322,x76323,f251(f882(x76321,a870)))+~P27(f876(x76321),f876(x76322),f328(f151(x76321,x76322),x76323),f251(f882(f876(x76321),a870))) % 154.70/154.56 [7675]P1(f328(f328(f330(f882(x76751,a870)),f521(x76752,x76753,x76751)),x76753))+P1(f328(f328(f330(x76751),x76752),f40(f882(x76751,a870),x76753))) % 154.70/154.56 [7769]P1(f328(f328(f330(f876(x77691)),x77692),f158(x77691,x77693)))+~P1(f328(f328(f330(x77691),f676(x77693,x77692,x77691)),x77693)) % 154.70/154.56 [7811]P1(f328(f328(f328(f328(a200,x78111),x78112),f863(x78113,x78112,x78111)),x78113))+~P1(f328(f328(f328(a198,x78111),x78112),x78113)) % 154.70/154.56 [7871]P33(x78711,x78712,x78713)+~P1(f328(x78712,f328(f328(f162(x78711),x78713),f801(x78713,x78712,x78711)))) % 154.70/154.56 [7896]E(x78961,x78962)+~E(f328(f328(f7(x78963,f882(x78963,a870),a870),f330(x78963)),x78961),f328(f328(f7(x78963,f882(x78963,a870),a870),f330(x78963)),x78962)) % 154.70/154.56 [7902]~P1(f328(f328(f330(f881(x79021,x79021)),x79023),f260(x79021,x79022)))+P1(f328(f328(f330(x79021),f557(x79022,x79023,x79021)),x79022)) % 154.70/154.56 [7904]~P1(f328(f328(f330(x79041),x79043),f39(f882(x79041,a870),x79042)))+P1(f328(f328(f330(f882(x79041,a870)),f827(x79042,x79043,x79041)),x79042)) % 154.70/154.56 [8078]~P1(f328(f328(f330(x80781),x80782),f328(f170(x80781),f794(x80783,x80782,x80781))))+~P1(f328(f328(f330(x80781),x80782),f328(f170(x80781),x80783))) % 154.70/154.56 [8079]~P1(f328(f328(f330(x80791),x80792),f328(f170(x80791),f802(x80793,x80792,x80791))))+~P1(f328(f328(f330(x80791),x80792),f328(f170(x80791),x80793))) % 154.70/154.56 [8173]E(f328(f237(f879(f876(a324)),f876(a324),f310(x81731,x81732,f328(f328(f80(a1),x81733),f78(a1))),f235(f876(a324))),f328(x81731,x81733)),f310(x81731,x81732,x81733))+P1(f328(f328(f243(a1),x81732),x81733)) % 154.70/154.56 [8280]E(x82801,f117(x82802))+P1(f328(f328(f330(x82802),f328(f262(x82802,f881(a103,a103)),f328(f279(x82802,x82801),x82803))),f328(f170(x82802),x82801))) % 154.70/154.56 [8377]~P67(x83771)+E(f328(f139(x83771,x83771,f328(f7(x83771,x83771,x83771),f80(x83771)),x83772),f328(f166(x83771),x83773)),f328(f139(x83771,x83771,f80(x83771),x83772),x83773)) % 154.70/154.56 [8871]~P105(x88711)+E(f328(f170(x88711),f146(x88711,x88711,f5(x88711),x88712,x88713)),f328(f328(f306(x88711),x88712),f328(f170(x88711),x88713))) % 154.70/154.56 [8882]P1(f328(f328(f243(a875),f2(a875)),f638(x88821,x88822,x88823)))+~P1(f328(f328(f330(f881(x88823,x88823)),x88822),f328(f328(f285(x88823,x88823,x88823),x88821),f304(x88823,x88821)))) % 154.70/154.56 [9173]~P54(x91731,x91732)+~P1(f328(f328(f330(f881(x91731,x91731)),f328(f328(f263(x91731,x91731),x91733),x91733)),f328(f328(f285(x91731,x91731,x91731),x91732),f304(x91731,x91732)))) % 154.70/154.56 [9305]~E(f328(f328(f105(f882(f881(x93051,x93051),a870)),f328(f283(x93051,x93051),x93052)),f304(x93051,x93052)),f192(f882(f881(x93051,x93051),a870)))+~P1(f328(f328(f330(f881(x93051,x93051)),f328(f328(f263(x93051,x93051),x93053),x93053)),f328(f328(f285(x93051,x93051,x93051),x93052),f304(x93051,x93052)))) % 154.70/154.56 [9484]~P1(f328(f61(x94841),x94842))+P1(f328(f328(f242(a875),f328(f37(x94841),f328(f328(f22(f882(x94841,a870)),x94842),f328(f328(f306(x94841),x94843),f192(f882(x94841,a870)))))),f328(f37(x94841),x94842))) % 154.70/154.56 [5040]~E(x50403,f117(x50401))+E(f141(x50401,f328(f328(f148(x50401),x50402),x50403)),x50402) % 154.70/154.56 [5048]~E(x50483,f117(x50481))+E(f118(x50481,f328(f328(f148(x50481),x50482),x50483)),f117(x50481)) % 154.70/154.56 [5077]E(x50771,f117(x50772))+E(f141(x50772,f328(f328(f148(x50772),x50773),x50771)),f141(x50772,x50771)) % 154.70/154.56 [5079]E(x50791,f117(x50792))+E(f141(x50792,f328(f328(f125(x50792),x50793),x50791)),f141(x50792,x50791)) % 154.70/154.56 [5084]~E(x50843,f117(x50841))+E(f118(x50841,f328(f328(f125(x50841),x50842),x50843)),f118(x50841,x50842)) % 154.70/154.56 [5086]~E(x50863,f117(x50861))+E(f141(x50861,f328(f328(f125(x50861),x50862),x50863)),f141(x50861,x50862)) % 154.70/154.56 [5118]E(x51181,f117(x51182))+E(f328(f138(x51182),f328(f328(f125(x51182),x51181),x51183)),f328(f138(x51182),x51181)) % 154.70/154.56 [5148]~E(x51482,f117(x51481))+E(f328(f138(x51481),f328(f328(f125(x51481),x51482),x51483)),f328(f138(x51481),x51483)) % 154.70/154.56 [5203]~P2(x52031)+E(f328(f328(f114(x52031),x52032),f328(f328(f105(x52031),x52032),x52033)),x52032) % 154.70/154.56 [5204]~P2(x52041)+E(f328(f328(f105(x52041),x52042),f328(f328(f114(x52041),x52042),x52043)),x52042) % 154.70/154.56 [5205]~P105(x52051)+E(f328(f328(f240(x52051),x52052),f328(f328(f241(x52051),x52052),x52053)),x52052) % 154.70/154.56 [5206]~P105(x52061)+E(f328(f328(f241(x52061),x52062),f328(f328(f240(x52061),x52062),x52063)),x52062) % 154.70/154.56 [5225]~P57(x52251)+E(f44(x52251,f328(f328(f81(x52251),x52252),x52253),x52253),f2(x52251)) % 154.70/154.56 [5226]~P57(x52261)+E(f44(x52261,f328(f328(f81(x52261),x52262),x52263),x52262),f2(x52261)) % 154.70/154.56 [5300]~P65(x53001)+E(f328(f79(x53001),f328(f328(f22(x53001),x53002),x53003)),f328(f328(f22(x53001),x53003),x53002)) % 154.70/154.56 [5361]E(x53611,f117(x53612))+E(f118(x53612,f328(f328(f148(x53612),x53613),x53611)),f328(f328(f148(x53612),x53613),f118(x53612,x53611))) % 154.70/154.56 [5362]E(x53621,f117(x53622))+E(f118(x53622,f328(f328(f125(x53622),x53623),x53621)),f328(f328(f125(x53622),x53623),f118(x53622,x53621))) % 154.70/154.56 [5365]~P5(x53651)+E(f39(x53651,f328(f328(f306(x53651),x53652),x53653)),f328(f328(f114(x53651),x53652),f39(x53651,x53653))) % 154.70/154.56 [5366]~P5(x53661)+E(f40(x53661,f328(f328(f306(x53661),x53662),x53663)),f328(f328(f105(x53661),x53662),f40(x53661,x53663))) % 154.70/154.56 [5411]~P2(x54111)+E(f328(f328(f114(x54111),x54112),f328(f328(f114(x54111),x54112),x54113)),f328(f328(f114(x54111),x54112),x54113)) % 154.70/154.56 [5413]~P99(x54131)+E(f328(f328(f114(x54131),x54132),f328(f328(f114(x54131),x54132),x54133)),f328(f328(f114(x54131),x54132),x54133)) % 154.70/154.56 [5414]~P2(x54141)+E(f328(f328(f105(x54141),x54142),f328(f328(f105(x54141),x54142),x54143)),f328(f328(f105(x54141),x54142),x54143)) % 154.70/154.56 [5416]~P100(x54161)+E(f328(f328(f105(x54161),x54162),f328(f328(f105(x54161),x54162),x54163)),f328(f328(f105(x54161),x54162),x54163)) % 154.70/154.56 [5417]~P94(x54171)+E(f328(f328(f81(x54171),x54172),f328(f328(f81(x54171),x54172),x54173)),f328(f328(f81(x54171),x54172),x54173)) % 154.70/154.56 [5419]~P105(x54191)+E(f328(f328(f240(x54191),x54192),f328(f328(f240(x54191),x54192),x54193)),f328(f328(f240(x54191),x54192),x54193)) % 154.70/154.56 [5421]~P105(x54211)+E(f328(f328(f241(x54211),x54212),f328(f328(f241(x54211),x54212),x54213)),f328(f328(f241(x54211),x54212),x54213)) % 154.70/154.56 [5429]~P57(x54291)+E(f44(x54291,f328(f328(f80(x54291),x54292),x54293),x54293),f44(x54291,x54292,x54293)) % 154.70/154.56 [5430]~P57(x54301)+E(f44(x54301,f328(f328(f80(x54301),x54302),x54303),x54302),f44(x54301,x54303,x54302)) % 154.70/154.56 [5436]~P103(x54361)+E(f328(f328(f81(x54361),x54362),f328(f79(x54361),x54363)),f328(f79(x54361),f328(f328(f81(x54361),x54362),x54363))) % 154.70/154.56 [5437]~P60(x54371)+E(f328(f328(f286(x54371),x54372),f328(f79(x54371),x54373)),f328(f79(x54371),f328(f328(f286(x54371),x54372),x54373))) % 154.70/154.56 [5438]~P77(x54381)+E(f328(f328(f80(x54381),x54382),f328(f163(x54381),x54383)),f328(f163(x54381),f328(f328(f148(x54381),x54382),x54383))) % 154.70/154.56 [5468]~P103(x54681)+E(f328(f328(f81(x54681),f328(f79(x54681),x54682)),x54683),f328(f328(f81(x54681),x54682),f328(f79(x54681),x54683))) % 154.70/154.56 [5474]~P8(x54741,x54742,x54743)+E(f39(f882(x54741,a870),f328(f328(f60(x54741),x54742),x54743)),x54742) % 154.70/154.56 [5533]~P112(x55331)+E(f328(f328(f81(x55331),x55332),f328(f328(f253(x55331),x55332),x55333)),f328(f328(f253(x55331),x55332),f328(a116,x55333))) % 154.70/154.56 [5534]~P109(x55341)+E(f328(f328(f81(x55341),x55342),f328(f328(f253(x55341),x55342),x55343)),f328(f328(f253(x55341),x55342),f328(a116,x55343))) % 154.70/154.56 [5544]~P72(x55441)+E(f328(f328(f80(x55441),f328(f79(x55441),x55442)),f328(f328(f80(x55441),x55442),x55443)),x55443) % 154.70/154.56 [5567]~P140(x55671)+E(f328(f328(f253(x55671),f328(f104(x55671),x55672)),x55673),f328(f104(x55671),f328(f328(f253(a875),x55672),x55673))) % 154.70/154.56 [5568]~P135(x55681)+E(f328(f328(f253(x55681),f328(f106(x55681),x55682)),x55683),f328(f106(x55681),f328(f328(f253(a1),x55682),x55683))) % 154.70/154.56 [5573]~P83(x55731)+E(f328(f75(x55731),f328(f328(f22(x55731),x55732),x55733)),f328(f75(x55731),f328(f328(f22(x55731),x55733),x55732))) % 154.70/154.56 [5575]~P121(x55751)+E(f328(f328(f81(x55751),f82(x55751,x55752)),f82(x55751,x55753)),f82(x55751,f328(f328(f81(x55751),x55752),x55753))) % 154.70/154.56 [5579]E(x55791,f117(x55792))+E(f328(f328(f125(x55792),f328(f169(x55792),x55791)),x55793),f328(f169(x55792),f328(f328(f125(x55792),x55791),x55793))) % 154.70/154.56 [5585]~E(x55852,f328(a116,f328(f328(f80(a875),x55851),x55853)))+P1(f328(f328(f243(a875),x55851),x55852)) % 154.70/154.56 [5586]~P121(x55861)+E(f328(f328(f253(x55861),f328(f75(x55861),x55862)),x55863),f328(f75(x55861),f328(f328(f253(x55861),x55862),x55863))) % 154.70/154.56 [5587]~P103(x55871)+E(f328(f328(f81(x55871),f328(f79(x55871),x55872)),x55873),f328(f79(x55871),f328(f328(f81(x55871),x55872),x55873))) % 154.70/154.56 [5588]~P117(x55881)+E(f328(f328(f286(x55881),f328(f79(x55881),x55882)),x55883),f328(f79(x55881),f328(f328(f286(x55881),x55882),x55883))) % 154.70/154.56 [5686]E(f598(x56861,x56862,x56863),f614(x56861,x56862,x56863))+E(f328(f328(f105(f882(x56863,a870)),x56862),x56861),f192(f882(x56863,a870))) % 154.70/154.56 [5701]~P66(x57012)+E(f328(f328(f6(x57011,x57012),f328(f16(x57012,x57011),f2(x57012))),x57013),f2(x57012)) % 154.70/154.56 [5702]~P73(x57022)+E(f328(f328(f9(x57021,x57022),f328(f16(x57022,x57021),f78(x57022))),x57023),f78(x57022)) % 154.70/154.56 [5704]~P140(x57041)+E(f328(f328(f80(x57041),f328(f104(x57041),x57042)),f328(f104(x57041),x57043)),f328(f104(x57041),f328(f328(f80(a875),x57042),x57043))) % 154.70/154.56 [5705]~P140(x57051)+E(f328(f328(f81(x57051),f328(f104(x57051),x57052)),f328(f104(x57051),x57053)),f328(f104(x57051),f328(f328(f81(a875),x57052),x57053))) % 154.70/154.56 [5706]~P135(x57061)+E(f328(f328(f22(x57061),f328(f106(x57061),x57062)),f328(f106(x57061),x57063)),f328(f106(x57061),f328(f328(f22(a1),x57062),x57063))) % 154.70/154.56 [5707]~P135(x57071)+E(f328(f328(f80(x57071),f328(f106(x57071),x57072)),f328(f106(x57071),x57073)),f328(f106(x57071),f328(f328(f80(a1),x57072),x57073))) % 154.70/154.56 [5708]~P135(x57081)+E(f328(f328(f81(x57081),f328(f106(x57081),x57082)),f328(f106(x57081),x57083)),f328(f106(x57081),f328(f328(f81(a1),x57082),x57083))) % 154.70/154.56 [5709]~P90(x57091)+E(f328(f328(f22(x57091),f328(f107(x57091),x57092)),f328(f107(x57091),x57093)),f328(f107(x57091),f328(f328(f22(a1),x57092),x57093))) % 154.70/154.56 [5712]~P90(x57121)+E(f328(f328(f80(x57121),f328(f107(x57121),x57122)),f328(f107(x57121),x57123)),f328(f107(x57121),f328(f328(f80(a1),x57122),x57123))) % 154.70/154.56 [5713]~P90(x57131)+E(f328(f328(f81(x57131),f328(f107(x57131),x57132)),f328(f107(x57131),x57133)),f328(f107(x57131),f328(f328(f81(a1),x57132),x57133))) % 154.70/154.56 [5762]~E(x57623,x57622)+P1(f328(f328(f242(f882(x57621,a870)),x57622),x57623)) % 154.70/154.56 [5768]~E(x57682,x57683)+P1(f328(f328(f242(f882(x57681,a870)),x57682),x57683)) % 154.70/154.56 [5773]~P121(x57731)+E(f328(f328(f81(x57731),f328(f75(x57731),x57732)),f328(f75(x57731),x57733)),f328(f75(x57731),f328(f328(f81(x57731),x57732),x57733))) % 154.70/154.56 [5774]~P62(x57741)+E(f328(f328(f286(x57741),f328(f75(x57741),x57742)),f328(f75(x57741),x57743)),f328(f75(x57741),f328(f328(f286(x57741),x57742),x57743))) % 154.70/154.56 [5775]~P93(x57751)+E(f328(f328(f105(x57751),f328(f79(x57751),x57752)),f328(f79(x57751),x57753)),f328(f79(x57751),f328(f328(f114(x57751),x57752),x57753))) % 154.70/154.56 [5776]~P93(x57761)+E(f328(f328(f114(x57761),f328(f79(x57761),x57762)),f328(f79(x57761),x57763)),f328(f79(x57761),f328(f328(f105(x57761),x57762),x57763))) % 154.70/154.56 [5777]~P72(x57771)+E(f328(f328(f80(x57771),f328(f79(x57771),x57772)),f328(f79(x57771),x57773)),f328(f79(x57771),f328(f328(f80(x57771),x57773),x57772))) % 154.70/154.56 [5778]~P65(x57781)+E(f328(f328(f80(x57781),f328(f79(x57781),x57782)),f328(f79(x57781),x57783)),f328(f79(x57781),f328(f328(f80(x57781),x57782),x57783))) % 154.70/154.56 [5779]~P74(x57791)+E(f328(f328(f241(x57791),f328(f79(x57791),x57792)),f328(f79(x57791),x57793)),f328(f79(x57791),f328(f328(f240(x57791),x57792),x57793))) % 154.70/154.56 [5780]~P74(x57801)+E(f328(f328(f240(x57801),f328(f79(x57801),x57802)),f328(f79(x57801),x57803)),f328(f79(x57801),f328(f328(f241(x57801),x57802),x57803))) % 154.70/154.56 [5781]~P77(x57811)+E(f328(f328(f80(x57811),f328(f163(x57811),x57812)),f328(f163(x57811),x57813)),f328(f163(x57811),f328(f328(f125(x57811),x57812),x57813))) % 154.70/154.56 [5782]E(x57821,f192(f882(x57822,a870)))+~E(f328(f328(f114(f882(x57822,a870)),x57823),x57821),f192(f882(x57822,a870))) % 154.70/154.56 [5783]E(x57831,f192(f882(x57832,a870)))+~E(f328(f328(f114(f882(x57832,a870)),x57831),x57833),f192(f882(x57832,a870))) % 154.70/154.56 [5784]~P144(x57841,x57843,x57842)+P1(f328(x57841,f328(f328(f38(a1),x57842),x57843))) % 154.70/154.56 [5834]~P1(f328(f61(x58341),x58343))+P1(f328(f61(x58341),f328(f328(f306(x58341),x58342),x58343))) % 154.70/154.56 [5835]~P1(f328(f134(x58351),x58353))+P1(f328(f134(x58351),f328(f328(f173(x58351),x58352),x58353))) % 154.70/154.56 [5836]~P1(f328(f134(x58361),x58363))+P1(f328(f134(x58361),f328(f328(f135(x58361),x58362),x58363))) % 154.70/154.56 [5865]~P2(x58651)+P1(f328(f328(f242(x58651),x58652),f328(f328(f114(x58651),x58653),x58652))) % 154.70/154.56 [5866]~P99(x58661)+P1(f328(f328(f242(x58661),x58662),f328(f328(f114(x58661),x58663),x58662))) % 154.70/154.56 [5867]~P2(x58671)+P1(f328(f328(f242(x58671),x58672),f328(f328(f114(x58671),x58672),x58673))) % 154.70/154.56 [5868]~P99(x58681)+P1(f328(f328(f242(x58681),x58682),f328(f328(f114(x58681),x58682),x58683))) % 154.70/154.56 [5869]~P105(x58691)+P1(f328(f328(f242(x58691),x58692),f328(f328(f241(x58691),x58693),x58692))) % 154.70/154.56 [5870]~P105(x58701)+P1(f328(f328(f242(x58701),x58702),f328(f328(f241(x58701),x58702),x58703))) % 154.70/154.56 [5884]~E(x58841,f2(a875))+E(f328(f328(f38(a875),f328(f328(f81(a875),x58841),x58842)),f328(f328(f81(a875),x58841),x58843)),f2(a875)) % 154.70/154.56 [5965]~P90(x59651)+E(f328(f328(f22(x59651),f328(f107(x59651),x59652)),f328(f107(x59651),x59653)),f328(f107(x59651),f328(f328(f80(a1),x59652),f328(f79(a1),x59653)))) % 154.70/154.56 [6017]E(x60171,f2(a875))+E(f328(f328(f38(a875),f328(f328(f81(a875),x60171),x60172)),f328(f328(f81(a875),x60171),x60173)),f328(f328(f38(a875),x60172),x60173)) % 154.70/154.56 [6051]E(f149(x60511,f328(f328(f148(x60511),x60512),x60513)),f328(f328(f148(x60511),x60512),f149(x60511,x60513)))+P1(f328(f328(f330(x60511),x60512),f328(f170(x60511),x60513))) % 154.70/154.56 [6085]P144(x60851,x60852,x60853)+~P1(f328(x60851,f328(f328(f38(a1),x60853),x60852))) % 154.70/154.56 [6160]E(x61601,f117(x61602))+E(f328(f328(f148(x61602),f328(f138(x61602),x61601)),f328(f328(f173(x61602),x61603),f328(f169(x61602),x61601))),f328(f328(f173(x61602),f328(a116,x61603)),x61601)) % 154.70/154.56 [6165]P1(f328(x61651,x61652))+P1(f328(f328(f328(a198,f32(x61651,x61653)),x61652),x61652)) % 154.70/154.56 [6168]E(f328(f328(f22(f882(x61681,a870)),x61682),x61683),x61682)+~E(f328(f328(f105(f882(x61681,a870)),x61682),x61683),f192(f882(x61681,a870))) % 154.70/154.56 [6183]E(f149(x61831,f328(f328(f148(x61831),x61832),x61833)),f149(x61831,x61833))+~P1(f328(f328(f330(x61831),x61832),f328(f170(x61831),x61833))) % 154.70/154.56 [6215]~P1(f328(f328(f243(a875),x62151),x62153))+P1(f328(f328(f243(a875),x62151),f328(f328(f80(a875),x62152),x62153))) % 154.70/154.56 [6217]~P1(f328(f328(f243(a875),x62171),x62172))+P1(f328(f328(f243(a875),x62171),f328(f328(f80(a875),x62172),x62173))) % 154.70/154.56 [6219]~P1(f328(f328(f242(a875),x62191),x62193))+P1(f328(f328(f242(a875),x62191),f328(f328(f80(a875),x62192),x62193))) % 154.70/154.56 [6221]~P1(f328(f328(f242(a875),x62211),x62212))+P1(f328(f328(f242(a875),x62211),f328(f328(f80(a875),x62212),x62213))) % 154.70/154.56 [6260]P1(f328(f61(x62601),x62602))+~P1(f328(f61(x62601),f328(f328(f306(x62601),x62603),x62602))) % 154.70/154.56 [6261]P1(f328(f134(x62611),x62612))+~P1(f328(f134(x62611),f328(f328(f148(x62611),x62613),x62612))) % 154.70/154.56 [6262]P1(f328(f134(x62621),x62622))+~P1(f328(f134(x62621),f328(f328(f125(x62621),x62623),x62622))) % 154.70/154.56 [6263]P1(f328(f134(x62631),x62632))+~P1(f328(f134(x62631),f328(f328(f125(x62631),x62632),x62633))) % 154.70/154.56 [6309]~P109(x63091)+E(f328(f328(f80(x63091),x63092),f328(f328(f81(x63091),x63093),x63092)),f328(f328(f81(x63091),f328(f328(f80(x63091),x63093),f78(x63091))),x63092)) % 154.70/154.56 [6355]~E(x63551,x63552)+~P1(f328(f328(f243(f882(x63553,a870)),x63551),x63552)) % 154.70/154.56 [6399]P1(f328(f328(f330(x63991),x63992),x63993))+P1(f328(f328(f330(x63991),x63992),f328(f79(f882(x63991,a870)),x63993))) % 154.70/154.56 [6405]E(f141(x64051,f328(f328(f135(x64051),x64052),x64053)),f141(x64051,x64053))+~P1(f328(f328(f243(a875),x64052),f328(f193(f876(x64051)),x64053))) % 154.70/154.56 [6406]E(f328(f328(f173(x64061),x64062),f118(x64061,x64063)),f328(f328(f173(x64061),x64062),x64063))+~P1(f328(f328(f243(a875),x64062),f328(f193(f876(x64061)),x64063))) % 154.70/154.56 [6461]E(f328(f328(f328(f187(f876(x64611),f876(x64611)),x64612),f165(x64611)),x64613),x64613)+~E(f44(a875,x64612,f328(f193(f876(x64611)),x64613)),f2(a875)) % 154.70/154.56 [6468]~P8(x64681,x64683,x64682)+E(f328(f328(f285(x64681,x64681,x64681),f328(f283(x64681,x64681),x64682)),x64682),x64682) % 154.70/154.56 [6510]~E(f328(f328(f114(f882(x65101,a870)),x65102),x65103),x65103)+P1(f328(f328(f242(f882(x65101,a870)),x65102),x65103)) % 154.70/154.56 [6515]~P51(x65151,x65151,x65153)+P51(x65151,x65151,f328(f328(f187(f881(x65151,x65151),a870),x65152),x65153)) % 154.70/154.56 [6517]~P1(f328(f328(f330(x65171),x65173),f328(f170(x65171),x65172)))+P1(f328(f328(f243(a875),f2(a875)),f328(f193(f876(x65171)),x65172))) % 154.70/154.56 [6543]~P83(x65431)+E(f328(f75(x65431),f328(f328(f80(x65431),f328(f75(x65431),x65432)),f328(f75(x65431),x65433))),f328(f328(f80(x65431),f328(f75(x65431),x65432)),f328(f75(x65431),x65433))) % 154.70/154.56 [6553]E(f328(f328(f38(a875),f328(f328(f81(a875),x65531),x65532)),f328(f328(f81(a875),x65531),x65533)),f328(f328(f38(a875),x65532),x65533))+~P1(f328(f328(f243(a875),f2(a875)),x65531)) % 154.70/154.56 [6601]E(x66011,x66012)+~P1(f328(f328(f328(f328(a200,a24),x66011),x66013),x66012)) % 154.70/154.56 [6691]~P1(f328(f61(x66911),x66913))+E(f328(f328(f64(x66911,f882(x66911,a870),f306(x66911)),x66912),x66913),f328(f328(f114(f882(x66911,a870)),x66913),x66912)) % 154.70/154.56 [6750]E(f328(f328(f114(f882(x67501,a870)),x67502),x67503),x67502)+~P1(f328(f328(f242(f882(x67501,a870)),x67503),x67502)) % 154.70/154.56 [6752]E(f328(f328(f114(f882(x67521,a870)),x67522),x67523),x67523)+~P1(f328(f328(f242(f882(x67521,a870)),x67522),x67523)) % 154.70/154.56 [6753]E(f328(f328(f105(f882(x67531,a870)),x67532),x67533),x67533)+~P1(f328(f328(f242(f882(x67531,a870)),x67533),x67532)) % 154.70/154.56 [6754]E(f328(f328(f105(f882(x67541,a870)),x67542),x67543),x67542)+~P1(f328(f328(f242(f882(x67541,a870)),x67542),x67543)) % 154.70/154.56 [6806]~P1(f328(f134(x68061),x68062))+E(f328(f328(f22(f882(x68061,a870)),f328(f170(x68061),x68062)),f328(f328(f306(x68061),x68063),f192(f882(x68061,a870)))),f328(f170(x68061),f167(x68061,x68063,x68062))) % 154.70/154.56 [6859]P39(x68591,x68592)+~P39(x68591,f328(f328(f187(f881(x68591,x68591),a870),x68593),x68592)) % 154.70/154.56 [6924]P1(f328(f48(x69241,x69242),f328(a50,x69243)))+~P1(f328(f48(f328(f79(a1),x69241),f328(f79(a1),x69242)),x69243)) % 154.70/154.56 [6929]E(f328(f328(f22(f882(x69291,a870)),f328(f328(f306(x69291),x69292),x69293)),f328(f328(f306(x69291),x69292),f192(f882(x69291,a870)))),x69293)+P1(f328(f328(f330(x69291),x69292),x69293)) % 154.70/154.56 [6950]E(f328(f328(f105(f882(x69501,a870)),f328(f170(x69501),x69502)),f328(f170(x69501),x69503)),f192(f882(x69501,a870)))+~P1(f328(f134(x69501),f328(f328(f125(x69501),x69502),x69503))) % 154.70/154.56 [6966]~P1(f328(f328(f330(x69661),x69662),f328(f170(x69661),x69663)))+~P1(f328(f134(x69661),f328(f328(f148(x69661),x69662),x69663))) % 154.70/154.56 [7036]P33(x70361,x70362,x70363)+P1(f328(f328(f243(a875),f801(x70363,x70362,x70361)),f328(f193(f876(x70361)),x70363))) % 154.70/154.56 [7046]E(f328(f328(f105(f882(x70461,a870)),x70462),x70463),f192(f882(x70461,a870)))+P1(f328(f328(f330(x70461),f598(x70463,x70462,x70461)),x70462)) % 154.70/154.56 [7047]E(f328(f328(f105(f882(x70471,a870)),x70472),x70473),f192(f882(x70471,a870)))+P1(f328(f328(f330(x70471),f614(x70473,x70472,x70471)),x70473)) % 154.70/154.56 [7051]E(f118(x70511,f328(f328(f173(x70511),x70512),x70513)),f328(f328(f173(x70511),f328(f328(f22(a875),x70512),f78(a875))),x70513))+~P1(f328(f328(f242(a875),x70512),f328(f193(f876(x70511)),x70513))) % 154.70/154.56 [7110]~P35(x71103,x71102,x71101)+P1(f328(f328(f243(a875),f793(x71101,x71102,x71103)),f328(f193(f876(x71103)),x71101))) % 154.70/154.56 [7128]P1(f328(f328(f243(a875),f2(a875)),x71281))+P1(f328(f328(f242(a875),f328(f328(f81(a875),x71282),x71281)),f328(f328(f81(a875),x71283),x71281))) % 154.70/154.56 [7129]P1(f328(f328(f243(a875),f2(a875)),x71291))+P1(f328(f328(f242(a875),f328(f328(f81(a875),x71291),x71292)),f328(f328(f81(a875),x71291),x71293))) % 154.70/154.56 [7132]~P1(f328(f328(f330(x71321),x71322),x71323))+~P1(f328(f328(f330(x71321),x71322),f328(f79(f882(x71321,a870)),x71323))) % 154.70/154.56 [7139]~P1(f328(f328(f243(f882(x71391,a870)),x71392),x71393))+P1(f328(f328(f242(f882(x71391,a870)),x71392),x71393)) % 154.70/154.56 [7240]~P1(f328(f328(f243(a875),x72402),x72403))+P1(f328(f328(f243(a875),f328(f328(f80(a875),x72401),x72402)),f328(f328(f80(a875),x72401),x72403))) % 154.70/154.56 [7241]~P1(f328(f328(f243(a875),x72411),x72413))+P1(f328(f328(f243(a875),f328(f328(f80(a875),x72411),x72412)),f328(f328(f80(a875),x72413),x72412))) % 154.70/154.56 [7242]~P1(f328(f328(f243(a1),x72421),x72423))+P1(f328(f328(f243(a1),f328(f328(f80(a1),x72421),x72422)),f328(f328(f80(a1),x72423),x72422))) % 154.70/154.56 [7245]~P1(f328(f328(f242(a875),x72453),x72452))+P1(f328(f328(f242(a875),f328(f328(f22(a875),x72451),x72452)),f328(f328(f22(a875),x72451),x72453))) % 154.70/154.56 [7246]~P1(f328(f328(f242(a875),x72461),x72463))+P1(f328(f328(f242(a875),f328(f328(f22(a875),x72461),x72462)),f328(f328(f22(a875),x72463),x72462))) % 154.70/154.56 [7247]~P1(f328(f328(f242(a875),x72472),x72473))+P1(f328(f328(f242(a875),f328(f328(f80(a875),x72471),x72472)),f328(f328(f80(a875),x72471),x72473))) % 154.70/154.56 [7248]~P1(f328(f328(f242(a875),x72481),x72483))+P1(f328(f328(f242(a875),f328(f328(f80(a875),x72481),x72482)),f328(f328(f80(a875),x72483),x72482))) % 154.70/154.56 [7250]~P1(f328(f328(f242(a875),x72502),x72503))+P1(f328(f328(f242(a875),f328(f328(f81(a875),x72501),x72502)),f328(f328(f81(a875),x72501),x72503))) % 154.70/154.56 [7252]~P1(f328(f328(f242(a875),x72521),x72523))+P1(f328(f328(f242(a875),f328(f328(f81(a875),x72521),x72522)),f328(f328(f81(a875),x72523),x72522))) % 154.70/154.56 [7253]~P1(f328(f328(f242(a875),x72531),x72533))+P1(f328(f328(f242(a875),f328(f328(f38(a875),x72531),x72532)),f328(f328(f38(a875),x72533),x72532))) % 154.70/154.56 [7254]~P1(f328(f328(f242(a1),x72542),x72543))+P1(f328(f328(f242(a1),f328(f328(f80(a1),x72541),x72542)),f328(f328(f80(a1),x72541),x72543))) % 154.70/154.56 [7334]E(x73341,x73342)+~P1(f328(f328(f330(x73343),x73341),f328(f328(f306(x73343),x73342),f192(f882(x73343,a870))))) % 154.70/154.56 [7336]~E(f328(f328(f105(f882(x73361,a870)),x73362),x73363),f192(f882(x73361,a870)))+P1(f328(f328(f242(f882(x73361,a870)),x73362),f328(f79(f882(x73361,a870)),x73363))) % 154.70/154.56 [7344]P1(f328(f328(f330(f882(x73441,a870)),x73442),f328(f305(x73441),x73443)))+~P1(f328(f328(f242(f882(x73441,a870)),x73442),x73443)) % 154.70/154.56 [7397]E(f328(f328(f148(x73971),f328(f328(f162(x73971),x73972),x73973)),f328(f328(f135(x73971),f328(a116,x73973)),x73972)),f328(f328(f135(x73971),x73973),x73972))+~P1(f328(f328(f243(a875),x73973),f328(f193(f876(x73971)),x73972))) % 154.70/154.56 [7424]P1(f328(f328(f330(f881(x74241,x74241)),x74242),f304(x74241,x74243)))+~P1(f328(f328(f330(f881(x74241,x74241)),x74242),x74243)) % 154.70/154.56 [7434]~P1(f328(f328(f330(f882(x74341,a870)),x74342),f328(f305(x74341),x74343)))+P1(f328(f328(f242(f882(x74341,a870)),x74342),x74343)) % 154.70/154.56 [7480]P1(f328(f328(f242(f882(x74801,a870)),x74802),f39(f882(x74801,a870),x74803)))+~P1(f328(f328(f330(f882(x74801,a870)),x74802),x74803)) % 154.70/154.56 [7505]~P135(x75051)+E(f328(f328(f81(x75051),f328(f328(f253(x75051),f328(f79(x75051),f78(x75051))),x75052)),f328(f328(f253(x75051),x75053),x75052)),f328(f328(f253(x75051),f328(f79(x75051),x75053)),x75052)) % 154.70/154.56 [7526]E(f328(f328(f162(x75261),x75262),f328(f328(f22(a875),f328(f193(f876(x75261)),x75262)),f328(a116,x75263))),f328(f328(f162(x75261),f328(f166(x75261),x75262)),x75263))+~P1(f328(f328(f243(a875),x75263),f328(f193(f876(x75261)),x75262))) % 154.70/154.56 [7543]~E(f328(f328(f105(f882(x75431,a870)),f783(x75433,x75432,x75431)),x75433),f192(f882(x75431,a870)))+E(f328(f328(f105(f882(x75431,a870)),f39(f882(x75431,a870),x75432)),x75433),f192(f882(x75431,a870))) % 154.70/154.56 [7606]~P1(f328(f328(f330(x76063),x76062),f328(f170(x76063),x76061)))+P1(f328(f328(f243(a875),f665(x76061,x76062,x76063)),f328(f193(f876(x76063)),x76061))) % 154.70/154.56 [7614]P1(f328(f328(f330(x76141),f328(f328(f162(x76141),x76142),x76143)),f328(f170(x76141),x76142)))+~P1(f328(f328(f243(a875),x76143),f328(f193(f876(x76141)),x76142))) % 154.70/154.56 [7714]~P1(f328(x77142,f755(x77143,x77142,x77141)))+E(f328(f328(f135(x77141),f328(f193(f876(x77141)),f175(x77141,x77142,x77143))),x77143),f117(x77141)) % 154.70/154.56 [7725]P1(f328(f328(f242(f882(f876(x77251),a870)),f158(x77251,x77252)),f158(x77251,x77253)))+~P1(f328(f328(f242(f882(x77251,a870)),x77252),x77253)) % 154.70/154.56 [7726]P1(f328(f328(f242(f882(f876(x77261),a870)),f157(x77261,x77262)),f157(x77261,x77263)))+~P1(f328(f328(f242(f882(x77261,a870)),x77262),x77263)) % 154.70/154.56 [7753]E(f328(f328(f105(f882(x77531,a870)),f39(f882(x77531,a870),x77532)),x77533),f192(f882(x77531,a870)))+P1(f328(f328(f330(f882(x77531,a870)),f783(x77533,x77532,x77531)),x77532)) % 154.70/154.56 [7756]~P1(f328(f328(f330(f882(x77561,a870)),x77563),x77562))+P1(f328(f328(f242(f882(x77561,a870)),f40(f882(x77561,a870),x77562)),x77563)) % 154.70/154.56 [7758]E(f328(f328(f105(f882(x77581,a870)),x77582),x77583),f192(f882(x77581,a870)))+~P1(f328(f328(f242(f882(x77581,a870)),x77582),f328(f79(f882(x77581,a870)),x77583))) % 154.70/154.56 [7808]E(f328(f328(f22(a875),f328(f328(f80(a875),f328(f163(a875),x78081)),x78082)),f328(f328(f162(a875),x78081),x78083)),f328(f163(a875),f328(f328(f156(a875,x78081),x78083),x78082)))+~P1(f328(f328(f243(a875),x78083),f328(f193(f876(a875)),x78081))) % 154.70/154.56 [7859]P1(f328(f328(f243(a875),x78591),x78592))+~P1(f328(f328(f243(a875),f328(f328(f80(a875),x78593),x78591)),f328(f328(f80(a875),x78593),x78592))) % 154.70/154.56 [7860]P1(f328(f328(f243(a875),x78601),x78602))+~P1(f328(f328(f243(a875),f328(f328(f81(a875),x78603),x78601)),f328(f328(f81(a875),x78603),x78602))) % 154.70/154.56 [7861]P1(f328(f328(f243(a875),x78611),x78612))+~P1(f328(f328(f243(a875),f328(f328(f81(a875),x78611),x78613)),f328(f328(f81(a875),x78612),x78613))) % 154.70/154.56 [7864]P1(f328(f328(f242(a875),x78641),x78642))+~P1(f328(f328(f242(a875),f328(f328(f80(a875),x78643),x78641)),f328(f328(f80(a875),x78643),x78642))) % 154.70/154.56 [7894]P1(f328(f328(f243(a875),f2(a875)),x78941))+~P1(f328(f328(f243(a875),f328(f328(f81(a875),x78942),x78941)),f328(f328(f81(a875),x78943),x78941))) % 154.70/154.56 [7895]P1(f328(f328(f243(a875),f2(a875)),x78951))+~P1(f328(f328(f243(a875),f328(f328(f81(a875),x78951),x78952)),f328(f328(f81(a875),x78951),x78953))) % 154.70/154.56 [7968]E(f255(x79681,x79682,x79683),x79682)+~P1(f328(f328(f242(f882(x79681,a870)),x79683),f328(f328(f306(x79681),x79682),f192(f882(x79681,a870))))) % 154.70/154.56 [8018]~P1(f328(f134(x80181),x80183))+E(f328(f133(x80181,f328(f328(f8(a870,a870,x80181),a323),f328(a325,x80182))),x80183),f167(x80181,x80182,x80183)) % 154.70/154.56 [8041]E(f328(f328(f135(x80411),f328(f193(f876(x80411)),f175(x80411,x80412,x80413))),x80413),f117(x80411))+P1(f328(f328(f330(x80411),f755(x80413,x80412,x80411)),f328(f170(x80411),x80413))) % 154.70/154.56 [8045]E(f328(f328(f125(x80451),f328(f328(f173(x80451),x80452),x80453)),f328(f328(f148(x80451),f328(f328(f162(x80451),x80453),x80452)),f117(x80451))),f328(f328(f173(x80451),f328(a116,x80452)),x80453))+~P1(f328(f328(f243(a875),x80452),f328(f193(f876(x80451)),x80453))) % 154.70/154.56 [8108]E(f328(f133(x81081,f328(f328(f8(a870,a870,x81081),a323),f328(a325,x81082))),x81083),x81083)+P1(f328(f328(f330(x81081),x81082),f328(f170(x81081),x81083))) % 154.70/154.56 [8116]P1(f328(f328(f242(f882(f882(x81161,a870),a870)),f256(x81161,x81162)),f256(x81161,x81163)))+~P1(f328(f328(f242(f882(x81161,a870)),x81162),x81163)) % 154.70/154.56 [8161]~P1(f328(f134(x81611),x81613))+P1(f328(f134(x81611),f328(f328(f328(f187(f876(x81611),f876(x81611)),x81612),f165(x81611)),x81613))) % 154.70/154.56 [8169]~P1(f328(f328(f243(a875),x81692),x81693))+P1(f328(f328(f243(a875),f328(f328(f81(a875),f328(a116,x81691)),x81692)),f328(f328(f81(a875),f328(a116,x81691)),x81693))) % 154.70/154.56 [8192]P1(f328(f328(f242(f882(f882(x81921,a870),a870)),f328(f305(x81921),x81922)),f328(f305(x81921),x81923)))+~P1(f328(f328(f242(f882(x81921,a870)),x81922),x81923)) % 154.70/154.56 [8360]~P1(f328(f328(f242(f882(x83601,a870)),x83603),x83602))+P1(f328(f328(f242(f882(x83601,a870)),f328(f79(f882(x83601,a870)),x83602)),f328(f79(f882(x83601,a870)),x83603))) % 154.70/154.56 [8390]E(f328(f307(a875,a875,f328(f328(f7(a875,a875,a875),f22(a875)),x83901)),f328(f298(a875,x83902),x83903)),f328(f298(a875,f328(f328(f22(a875),x83902),x83901)),f328(f328(f22(a875),x83903),x83901)))+~P1(f328(f328(f243(a875),x83901),x83903)) % 154.70/154.56 [8420]~P77(x84201)+E(f328(f328(f80(x84201),x84202),f328(f139(x84201,x84201,f80(x84201),f2(x84201)),x84203)),f328(f139(x84201,x84201,f80(x84201),x84202),x84203)) % 154.70/154.56 [8495]~P83(x84951)+P1(f328(f328(f242(x84951),f328(f75(x84951),f328(f328(f22(x84951),x84952),x84953))),f328(f328(f80(x84951),f328(f75(x84951),x84952)),f328(f75(x84951),x84953)))) % 154.70/154.56 [8496]~P83(x84961)+P1(f328(f328(f242(x84961),f328(f75(x84961),f328(f328(f80(x84961),x84962),x84963))),f328(f328(f80(x84961),f328(f75(x84961),x84962)),f328(f75(x84961),x84963)))) % 154.70/154.56 [8509]E(f328(f328(f80(a1),f328(f328(f81(a1),x85091),f44(a1,f328(f328(f38(a1),x85092),x85091),x85093))),f44(a1,x85092,x85091)),f44(a1,x85092,f328(f328(f81(a1),x85091),x85093)))+~P1(f328(f328(f243(a1),f2(a1)),x85093)) % 154.70/154.56 [8515]E(f328(f328(f125(x85151),f328(f328(f173(x85151),x85152),x85153)),f328(f328(f148(x85151),f328(f138(x85151),f328(f328(f135(x85151),x85152),x85153))),f117(x85151))),f328(f328(f173(x85151),f328(a116,x85152)),x85153))+~P1(f328(f328(f243(a875),x85152),f328(f193(f876(x85151)),x85153))) % 154.70/154.56 [8535]E(f328(f274(x85351,f328(f328(f151(x85351,f881(a103,x85351)),f328(f263(a103,x85351),f78(a103))),x85352)),f328(a3,x85353)),f328(f328(f162(x85351),x85352),x85353))+~P1(f328(f328(f243(a875),x85353),f328(f193(f876(x85351)),x85352))) % 154.70/154.56 [8606]P1(f328(f328(f330(f881(x86061,x86061)),x86062),f328(f328(f285(x86061,x86061,x86061),x86063),f304(x86061,x86063))))+~P1(f328(f328(f330(f881(x86061,x86061)),x86062),x86063)) % 154.70/154.56 [8626]P1(f328(f328(f242(a875),x86261),x86262))+~P1(f328(f328(f242(a875),f328(f328(f81(a875),f328(a116,x86263)),x86261)),f328(f328(f81(a875),f328(a116,x86263)),x86262))) % 154.70/154.56 [8643]P1(f328(f328(f242(f882(x86431,a870)),x86432),x86433))+~P1(f328(f328(f242(f882(x86431,a870)),f328(f79(f882(x86431,a870)),x86433)),f328(f79(f882(x86431,a870)),x86432))) % 154.70/154.56 [8661]P1(f328(f134(x86611),x86612))+~P1(f328(f134(x86611),f328(f328(f328(f187(f876(x86611),f876(x86611)),x86613),f165(x86611)),x86612))) % 154.70/154.56 [8721]E(f328(f307(f881(x87211,x87212),x87212,f266(x87211,x87212)),f328(f170(f881(x87211,x87212)),x87213)),f184(x87211,x87212,f328(f176(x87211,x87212),x87213)))+~P1(f328(f134(x87211),f328(f328(f151(f881(x87211,x87212),x87211),f262(x87211,x87212)),x87213))) % 154.70/154.56 [8730]E(f328(f282(x87301,x87301,f304(x87301,x87302)),x87303),x87303)+~P1(f328(f328(f242(f882(x87301,a870)),f328(f282(x87301,x87301,x87302),x87303)),x87303)) % 154.70/154.56 [8772]~P105(x87721)+P16(x87721,f328(f133(x87721,f328(f328(f7(x87721,x87721,a870),a325),f328(x87722,x87723))),x87723)) % 154.70/154.56 [8778]~P1(f328(f328(f242(a875),x87781),x87782))+P1(f328(f328(f242(a875),x87781),f328(f139(a875,a875,f80(a875),x87782),x87783))) % 154.70/154.56 [8855]~P1(f328(f328(f330(f881(x88551,x88551)),x88552),f304(x88551,x88553)))+P1(f328(f328(f330(f881(x88551,x88551)),x88552),f328(f328(f187(f881(x88551,x88551),a870),f635(x88553,x88552,x88551)),x88553))) % 154.70/154.56 [8948]~P77(x89481)+E(f328(f328(f80(x89481),x89482),f328(f139(x89481,x89481,f328(f7(x89481,x89481,x89481),f80(x89481)),f2(x89481)),f328(f166(x89481),x89483))),f328(f139(x89481,x89481,f80(x89481),x89482),x89483)) % 154.70/154.56 [9219]P51(x92191,x92192,x92193)+P1(f328(f328(f330(f881(x92191,x92192)),f328(f328(f263(x92191,x92192),f626(x92193,x92192,x92191)),f613(x92193,x92192,x92191))),x92193)) % 154.70/154.56 [9220]P51(x92201,x92202,x92203)+P1(f328(f328(f330(f881(x92201,x92202)),f328(f328(f263(x92201,x92202),f626(x92203,x92202,x92201)),f612(x92203,x92202,x92201))),x92203)) % 154.70/154.56 [9290]~P1(f328(f328(f330(f881(x92901,x92901)),x92902),f328(f328(f285(x92901,x92901,x92901),x92903),f304(x92901,x92903))))+P1(f328(f328(f330(f881(x92901,x92901)),x92902),f328(f328(f187(f881(x92901,x92901),a870),f638(x92903,x92902,x92901)),x92903))) % 154.70/154.56 [9291]~P1(f328(x92911,f328(f328(f162(x92912),x92913),f328(f193(f876(x92912)),f175(x92912,x92911,x92913)))))+~P1(f328(f328(f243(a875),f328(f193(f876(x92912)),f175(x92912,x92911,x92913))),f328(f193(f876(x92912)),x92913))) % 154.70/154.56 [9380]~P1(f328(f328(f242(f882(x93801,a870)),x93802),x93803))+P1(f328(f328(f242(f882(x93801,a870)),f328(f328(f7(x93801,f882(x93801,a870),a870),f330(x93801)),x93802)),f328(f328(f7(x93801,f882(x93801,a870),a870),f330(x93801)),x93803))) % 154.70/154.56 [9433]~P1(f328(f328(f330(f881(f882(x94331,a870),f882(x94331,a870))),f328(f328(f263(f882(x94331,a870),f882(x94331,a870)),x94332),x94333)),f303(x94331)))+P1(f328(f328(f243(f882(x94331,a870)),x94332),x94333)) % 154.70/154.56 [9458]P52(x94581,x94582,x94583)+~P1(f328(f328(f330(f881(x94581,x94581)),f328(f328(f263(x94581,x94581),f629(x94583,x94582,x94581)),f628(x94583,x94582,x94581))),x94583)) % 154.70/154.56 [9459]P52(x94591,x94592,x94593)+~P1(f328(f328(f330(f881(x94591,x94591)),f328(f328(f263(x94591,x94591),f628(x94593,x94592,x94591)),f629(x94593,x94592,x94591))),x94593)) % 154.70/154.56 [9495]~P1(f328(f328(f330(f881(f876(x94951),f876(x94951))),f328(f328(f263(f876(x94951),f876(x94951)),x94952),x94952)),f144(x94951,x94953)))+P1(f328(f328(f330(f881(x94951,x94951)),f328(f328(f263(x94951,x94951),f668(x94952,x94953,x94951)),f668(x94952,x94953,x94951))),x94953)) % 154.70/154.56 [9547]P1(f328(f328(f242(f882(x95471,a870)),x95472),x95473))+~P1(f328(f328(f242(f882(x95471,a870)),f328(f328(f7(x95471,f882(x95471,a870),a870),f330(x95471)),x95472)),f328(f328(f7(x95471,f882(x95471,a870),a870),f330(x95471)),x95473))) % 154.70/154.56 [9628]E(f328(f328(f22(a875),f328(f328(f6(a875,a875),x96281),f328(f249(a875),x96282))),f328(f328(f6(a875,a875),x96283),f328(f249(a875),x96282))),f328(f328(f6(a875,a875),f328(f328(f18(a875,a875,a875),f328(f328(f8(a875,f882(a875,a875),a875),f22(a875)),x96281)),x96283)),f328(f249(a875),x96282)))+~P1(f328(f328(f242(a875),f328(x96283,f377(x96282,x96281,x96283))),f328(x96281,f377(x96282,x96281,x96283)))) % 154.70/154.56 [9932]E(f328(f248(f881(x99321,x99322)),f328(f267(x99321,x99322,a870),f328(f328(f7(x99321,f882(x99322,f879(x99322)),f882(x99322,a870)),f328(f328(f8(f882(f879(x99322),a870),f882(f882(x99322,f879(x99322)),f882(x99322,a870)),x99321),f8(f879(x99322),a870,x99322)),f328(f328(f8(f879(x99322),f882(f879(x99322),a870),x99321),a325),f328(f176(x99321,x99322),x99323)))),f235(x99322)))),f328(f170(f881(x99321,x99322)),x99323))+~P1(f328(f134(x99321),f328(f328(f151(f881(x99321,x99322),x99321),f262(x99321,x99322)),x99323))) % 154.70/154.56 [5620]~P72(x56201)+E(f328(f328(f22(x56201),f328(f328(f80(x56201),x56202),x56203)),x56203),x56202) % 154.70/154.56 [5621]~P72(x56211)+E(f328(f328(f80(x56211),f328(f328(f22(x56211),x56212),x56213)),x56213),x56212) % 154.70/154.56 [5842]~P72(x58421)+E(f328(f328(f80(x58421),x58422),f328(f328(f80(x58421),f328(f79(x58421),x58422)),x58423)),x58423) % 154.70/154.56 [5926]~P79(x59261)+E(f328(f328(f81(x59261),f328(f328(f253(x59261),x59262),x59263)),x59262),f328(f328(f253(x59261),x59262),f328(a116,x59263))) % 154.70/154.56 [5927]~P109(x59271)+E(f328(f328(f81(x59271),f328(f328(f253(x59271),x59272),x59273)),x59272),f328(f328(f253(x59271),x59272),f328(a116,x59273))) % 154.70/154.56 [6135]~P121(x61351)+E(f328(f75(x61351),f328(f328(f253(x61351),f328(f79(x61351),x61352)),x61353)),f328(f75(x61351),f328(f328(f253(x61351),x61352),x61353))) % 154.70/154.56 [6197]~P79(x61971)+E(f328(f328(f81(x61971),f328(f328(f253(x61971),x61972),x61973)),x61972),f328(f328(f81(x61971),x61972),f328(f328(f253(x61971),x61972),x61973))) % 154.70/154.56 [6251]E(f328(f328(f22(a103),f328(f328(f80(a103),x62511),x62512)),x62513),f278(x62511,x62512,x62513))+~P1(f328(f328(f243(a103),x62512),x62513)) % 154.70/154.56 [6272]~E(f328(f328(f135(x62721),x62723),x62722),f117(x62721))+P1(f328(f328(f242(a875),f328(f193(f876(x62721)),x62722)),x62723)) % 154.70/154.56 [6404]E(f328(f328(f81(a875),f328(f107(a875),x64041)),f328(f328(f81(a875),f328(f107(a875),x64042)),x64043)),f2(a875))+~P1(f328(f328(f243(a1),x64041),a83)) % 154.70/154.56 [6420]~P60(x64201)+E(f328(f328(f253(x64201),f328(f328(f286(x64201),f78(x64201)),x64202)),x64203),f328(f328(f286(x64201),f78(x64201)),f328(f328(f253(x64201),x64202),x64203))) % 154.70/154.56 [6497]E(f328(f328(f22(a875),f328(f328(f80(a875),x64971),x64972)),x64973),f328(f328(f22(a875),x64971),f328(f328(f22(a875),x64973),x64972)))+~P1(f328(f328(f242(a875),x64972),x64973)) % 154.70/154.56 [6499]E(f328(f328(f22(a875),f328(f328(f80(a875),x64991),x64992)),x64993),f328(f328(f80(a875),x64991),f328(f328(f22(a875),x64992),x64993)))+~P1(f328(f328(f242(a875),x64993),x64992)) % 154.70/154.56 [6534]~P2(x65341)+P1(f328(f328(f242(x65341),f328(f328(f105(x65341),x65342),x65343)),x65343)) % 154.70/154.56 [6535]~P100(x65351)+P1(f328(f328(f242(x65351),f328(f328(f105(x65351),x65352),x65353)),x65353)) % 154.70/154.56 [6536]~P2(x65361)+P1(f328(f328(f242(x65361),f328(f328(f105(x65361),x65362),x65363)),x65362)) % 154.70/154.56 [6537]~P100(x65371)+P1(f328(f328(f242(x65371),f328(f328(f105(x65371),x65372),x65373)),x65372)) % 154.70/154.56 [6538]~P105(x65381)+P1(f328(f328(f242(x65381),f328(f328(f240(x65381),x65382),x65383)),x65383)) % 154.70/154.56 [6539]~P105(x65391)+P1(f328(f328(f242(x65391),f328(f328(f240(x65391),x65392),x65393)),x65392)) % 154.70/154.56 [6552]E(f328(f328(f38(a1),f328(f328(f38(a1),x65521),x65522)),x65523),f328(f328(f38(a1),x65521),f328(f328(f81(a1),x65522),x65523)))+~P1(f328(f328(f243(a1),f2(a1)),x65523)) % 154.70/154.56 [6604]~P109(x66041)+E(f328(f328(f80(x66041),f328(f328(f81(x66041),x66042),x66043)),x66043),f328(f328(f81(x66041),f328(f328(f80(x66041),x66042),f78(x66041))),x66043)) % 154.70/154.56 [6605]~P90(x66051)+E(f328(f328(f81(x66051),f328(f79(x66051),f328(f107(x66051),x66052))),x66053),f328(f328(f81(x66051),f328(f107(x66051),f328(f79(a1),x66052))),x66053)) % 154.70/154.56 [6678]~P77(x66781)+E(f328(f163(x66781),f328(f328(f151(x66782,x66781),f328(f16(x66781,x66782),f2(x66781))),x66783)),f2(x66781)) % 154.70/154.56 [6694]E(f328(f328(f80(a875),f328(f107(a875),x66941)),f328(f328(f80(a875),f328(f107(a875),x66942)),x66943)),f328(f328(f80(a875),f328(f107(a875),x66942)),x66943))+~P1(f328(a197,f328(f107(a1),x66941))) % 154.70/154.56 [6708]~P5(x67081)+E(f39(x67081,f328(f328(f306(x67081),x67082),f328(f328(f306(x67081),x67083),f192(f882(x67081,a870))))),f328(f328(f114(x67081),x67082),x67083)) % 154.70/154.56 [6709]~P5(x67091)+E(f40(x67091,f328(f328(f306(x67091),x67092),f328(f328(f306(x67091),x67093),f192(f882(x67091,a870))))),f328(f328(f105(x67091),x67092),x67093)) % 154.70/154.56 [6732]E(f328(f328(f173(x67321),x67322),x67323),x67323)+~P1(f328(f328(f242(a875),f328(f193(f876(x67321)),x67323)),x67322)) % 154.70/154.56 [6745]E(f328(f328(f135(x67451),x67452),x67453),f117(x67451))+~P1(f328(f328(f242(a875),f328(f193(f876(x67451)),x67453)),x67452)) % 154.70/154.56 [6756]E(f328(f328(f80(a875),f328(f328(f22(a875),x67561),x67562)),x67563),f328(f328(f22(a875),f328(f328(f80(a875),x67561),x67563)),x67562))+~P1(f328(f328(f242(a875),x67562),x67561)) % 154.70/154.56 [6770]~P1(f328(f328(f243(a875),x67701),x67703))+P1(f328(f328(f243(a875),f328(f328(f22(a875),x67701),x67702)),x67703)) % 154.70/154.56 [6798]~P105(x67981)+E(f167(x67981,x67982,f328(f328(f145(x67981,x67981,f5(x67981)),x67982),x67983)),x67983) % 154.70/154.56 [6888]E(f328(f328(f22(a875),f328(f328(f80(a875),x68881),x68882)),f328(a116,x68883)),f328(f328(f22(a875),x68881),f328(a116,f328(f328(f22(a875),x68883),x68882))))+~P1(f328(f328(f242(a875),x68882),x68883)) % 154.70/154.56 [6889]~P121(x68891)+P1(f328(f328(f242(x68891),f2(x68891)),f328(f328(f253(x68891),f328(f75(x68891),x68892)),x68893))) % 154.70/154.56 [6934]P26(x69341,x69342,x69343)+~P1(f328(f328(f242(f882(f874(x69341),a870)),x69343),x69342)) % 154.70/154.56 [6977]~P1(f328(f61(x69771),x69772))+P1(f328(f61(x69771),f328(f328(f22(f882(x69771,a870)),x69772),x69773))) % 154.70/154.56 [6978]~P1(f328(f61(x69781),x69783))+P1(f328(f61(x69781),f328(f328(f105(f882(x69781,a870)),x69782),x69783))) % 154.70/154.56 [6979]~P1(f328(f61(x69791),x69792))+P1(f328(f61(x69791),f328(f328(f105(f882(x69791,a870)),x69792),x69793))) % 154.70/154.56 [7118]~P39(x71181,x71183)+P39(x71181,f328(f328(f105(f882(f881(x71181,x71181),a870)),x71182),x71183)) % 154.70/154.56 [7119]~P39(x71191,x71192)+P39(x71191,f328(f328(f105(f882(f881(x71191,x71191),a870)),x71192),x71193)) % 154.70/154.56 [7236]~P2(x72361)+E(f10(x72361,f328(f170(x72361),f328(f328(f148(x72361),x72362),x72363))),f328(f139(x72361,x72361,f114(x72361),x72362),x72363)) % 154.70/154.56 [7237]~P2(x72371)+E(f11(x72371,f328(f170(x72371),f328(f328(f148(x72371),x72372),x72373))),f328(f139(x72371,x72371,f105(x72371),x72372),x72373)) % 154.70/154.56 [7238]~P105(x72381)+E(f14(x72381,f328(f170(x72381),f328(f328(f148(x72381),x72382),x72383))),f328(f139(x72381,x72381,f240(x72381),x72382),x72383)) % 154.70/154.56 [7239]~P105(x72391)+E(f15(x72391,f328(f170(x72391),f328(f328(f148(x72391),x72392),x72393))),f328(f139(x72391,x72391,f241(x72391),x72392),x72393)) % 154.70/154.56 [7299]~P1(f328(f61(x72991),x72992))+P1(f328(f328(f242(a875),f328(f37(x72991),x72992)),f328(f37(x72991),f328(f328(f306(x72991),x72993),x72992)))) % 154.70/154.56 [7307]E(f328(f328(f114(f882(a875,a870)),f328(f298(a875,x73071),x73072)),f328(f298(a875,x73072),f328(f328(f80(a875),x73072),x73073))),f328(f298(a875,x73071),f328(f328(f80(a875),x73072),x73073)))+~P1(f328(f328(f242(a875),x73071),x73072)) % 154.70/154.56 [7315]P1(f328(f328(f243(a875),x73151),x73152))+~P1(f328(f328(f243(a875),f328(f328(f80(a875),x73151),x73153)),x73152)) % 154.70/154.56 [7318]P1(f328(f328(f242(a875),x73181),x73182))+~P1(f328(f328(f242(a875),f328(f328(f80(a875),x73183),x73181)),x73182)) % 154.70/154.56 [7319]P1(f328(f328(f242(a875),x73191),x73192))+~P1(f328(f328(f242(a875),f328(f328(f80(a875),x73191),x73193)),x73192)) % 154.70/154.56 [7361]~P105(x73611)+E(f12(x73611,f241(x73611),f328(f170(x73611),f328(f328(f148(x73611),x73612),x73613))),f328(f139(x73611,x73611,f241(x73611),x73612),x73613)) % 154.70/154.56 [7362]~P105(x73621)+E(f13(x73621,f240(x73621),f328(f170(x73621),f328(f328(f148(x73621),x73622),x73623))),f328(f139(x73621,x73621,f240(x73621),x73622),x73623)) % 154.70/154.56 [7366]~E(x73662,f192(f882(f881(x73661,x73661),a870)))+P1(f328(f328(f242(f882(f881(x73661,x73661),a870)),x73662),x73663)) % 154.70/154.56 [7475]E(f328(f328(f114(f882(x74751,a870)),x74752),f328(f328(f22(f882(x74751,a870)),x74753),x74752)),x74753)+~P1(f328(f328(f242(f882(x74751,a870)),x74752),x74753)) % 154.70/154.56 [7476]~P1(f328(f328(f243(a875),x74761),f328(f328(f22(a875),x74763),x74762)))+P1(f328(f328(f243(a875),f328(f328(f80(a875),x74761),x74762)),x74763)) % 154.70/154.56 [7477]~P1(f328(f328(f242(a875),x74771),f328(f328(f80(a875),x74773),x74772)))+P1(f328(f328(f242(a875),f328(f328(f22(a875),x74771),x74772)),x74773)) % 154.70/154.56 [7533]E(x75331,f117(x75332))+E(f328(f138(x75332),f328(f328(f328(f187(f876(x75332),f876(x75332)),x75333),f165(x75332)),x75331)),f328(f328(f162(x75332),x75331),f44(a875,x75333,f328(f193(f876(x75332)),x75331)))) % 154.70/154.56 [7542]E(f328(f328(f306(x75421),x75422),f328(f328(f22(f882(x75421,a870)),x75423),f328(f328(f306(x75421),x75422),f192(f882(x75421,a870))))),x75423)+~P1(f328(f328(f330(x75421),x75422),x75423)) % 154.70/154.56 [7705]P1(f328(f328(f243(a875),x77051),f328(f328(f22(a875),x77052),x77053)))+~P1(f328(f328(f243(a875),f328(f328(f80(a875),x77051),x77053)),x77052)) % 154.70/154.56 [7706]P1(f328(f328(f242(a875),x77061),f328(f328(f80(a875),x77062),x77063)))+~P1(f328(f328(f242(a875),f328(f328(f22(a875),x77061),x77063)),x77062)) % 154.70/154.56 [7729]P1(f328(f61(x77291),x77292))+~P1(f328(f61(x77291),f328(f328(f114(f882(x77291,a870)),x77293),x77292))) % 154.70/154.56 [7730]P1(f328(f61(x77301),x77302))+~P1(f328(f61(x77301),f328(f328(f114(f882(x77301,a870)),x77302),x77303))) % 154.70/154.56 [7807]~P47(x78071,x78073)+P1(f328(f328(f330(f881(x78071,x78071)),f328(f328(f263(x78071,x78071),x78072),x78072)),x78073)) % 154.70/154.56 [7942]E(f328(f328(f162(a875),f136(a875,f328(f298(a875,x79421),x79422))),x79423),f328(f328(f80(a875),x79421),x79423))+~P1(f328(f328(f243(a875),f328(f328(f80(a875),x79421),x79423)),x79422)) % 154.70/154.56 [8007]E(f328(f328(f173(a875),x80071),f136(a875,f328(f298(a875,x80072),x80073))),f136(a875,f328(f298(a875,x80072),f328(f328(f80(a875),x80072),x80071))))+~P1(f328(f328(f242(a875),f328(f328(f80(a875),x80072),x80071)),x80073)) % 154.70/154.56 [8060]~P90(x80601)+E(f328(f328(f253(x80601),x80602),f328(f107(a875),f328(f328(f80(a1),x80603),x80603))),f328(f328(f86(x80601,x80601),f328(f328(f253(x80601),x80602),f328(f107(a875),x80603))),f328(f328(f18(x80601,x80601,x80601),f81(x80601)),f5(x80601)))) % 154.70/154.56 [8214]~P1(f328(f328(f328(a198,f328(a26,x82141)),x82142),x82143))+P1(f328(f328(f328(a198,f328(f239(a871),f328(a28,x82141))),x82142),x82143)) % 154.70/154.56 [8340]E(f328(f328(f125(x83401),f328(f328(f173(x83401),x83402),x83403)),f328(f328(f148(x83401),f328(f328(f162(x83401),x83403),x83402)),f328(f328(f135(x83401),f328(a116,x83402)),x83403))),x83403)+~P1(f328(f328(f243(a875),x83402),f328(f193(f876(x83401)),x83403))) % 154.70/154.56 [8347]P1(f328(f328(f242(f882(x83471,a870)),f316(x83471,x83472)),f316(x83471,x83473)))+~P1(f328(f328(f242(f882(x83471,f882(x83471,a870))),x83473),x83472)) % 154.70/154.56 [8349]~P52(x83491,x83492,x83493)+P52(x83491,x83492,f328(f328(f22(f882(f881(x83491,x83491),a870)),x83493),f304(x83491,f192(f882(f881(x83491,x83491),a870))))) % 154.70/154.56 [8366]P1(f328(f328(f242(f882(x83661,a870)),f317(x83661,x83662)),f317(x83661,x83663)))+~P1(f328(f328(f242(f882(f881(x83661,x83661),a870)),x83663),x83662)) % 154.70/154.56 [8373]~P120(x83731)+P1(f328(f328(f242(x83731),f2(x83731)),f328(f328(f80(x83731),f328(f328(f81(x83731),x83732),x83732)),f328(f328(f81(x83731),x83733),x83733)))) % 154.70/154.56 [8394]P1(f328(f328(f328(a198,f328(a26,x83941)),x83942),x83943))+~P1(f328(f328(f328(a198,f328(f239(a871),f328(a28,x83941))),x83942),x83943)) % 154.70/154.56 [8408]P1(f328(f328(f242(f882(x84081,a870)),f328(f281(x84081),x84082)),f328(f281(x84081),x84083)))+~P1(f328(f328(f242(f882(f881(x84081,x84081),a870)),x84082),x84083)) % 154.70/154.56 [8438]~P43(x84381,x84382)+~P1(f328(f328(f330(f881(x84381,x84381)),f328(f328(f263(x84381,x84381),x84383),x84383)),x84382)) % 154.70/154.56 [8440]~P39(x84401,x84402)+~P1(f328(f328(f330(f881(x84401,x84401)),f328(f328(f263(x84401,x84401),x84403),x84403)),x84402)) % 154.70/154.56 [8497]P1(f328(f328(f242(f882(x84971,a870)),f39(f882(x84971,a870),x84972)),f39(f882(x84971,a870),x84973)))+~P1(f328(f328(f242(f882(f882(x84971,a870),a870)),x84972),x84973)) % 154.70/154.56 [8498]P1(f328(f328(f242(f882(x84981,a870)),f40(f882(x84981,a870),x84982)),f40(f882(x84981,a870),x84983)))+~P1(f328(f328(f242(f882(f882(x84981,a870),a870)),x84983),x84982)) % 154.70/154.56 [8557]~P8(x85571,x85573,x85572)+P1(f328(f328(f242(f882(f881(x85571,x85571),a870)),x85572),f328(f328(f265(x85571,x85571),x85573),f328(f16(f882(x85571,a870),x85571),x85573)))) % 154.70/154.56 [8558]~P41(x85581,x85583,x85582)+P1(f328(f328(f242(f882(f881(x85581,x85581),a870)),x85582),f328(f328(f265(x85581,x85581),x85583),f328(f16(f882(x85581,a870),x85581),x85583)))) % 154.70/154.56 [8607]~P83(x86071)+P1(f328(f328(f242(x86071),f328(f328(f22(x86071),f328(f75(x86071),x86072)),f328(f75(x86071),x86073))),f328(f75(x86071),f328(f328(f22(x86071),x86073),x86072)))) % 154.70/154.56 [8608]~P83(x86081)+P1(f328(f328(f242(x86081),f328(f328(f22(x86081),f328(f75(x86081),x86082)),f328(f75(x86081),x86083))),f328(f75(x86081),f328(f328(f22(x86081),x86082),x86083)))) % 154.70/154.56 [8641]P1(f328(f328(f242(f882(f881(x86411,x86411),a870)),f304(x86411,x86412)),f304(x86411,x86413)))+~P1(f328(f328(f242(f882(f881(x86411,x86411),a870)),x86412),x86413)) % 154.70/154.56 [8796]P52(x87961,x87962,x87963)+~P52(x87961,x87962,f328(f328(f22(f882(f881(x87961,x87961),a870)),x87963),f304(x87961,f192(f882(f881(x87961,x87961),a870))))) % 154.70/154.56 [8814]P1(f328(f328(f242(f882(f881(f876(x88141),f876(x88141)),a870)),f154(x88141,x88142)),f154(x88141,x88143)))+~P1(f328(f328(f242(f882(f881(x88141,x88141),a870)),x88142),x88143)) % 154.70/154.56 [8815]P1(f328(f328(f242(f882(f881(f876(x88151),f876(x88151)),a870)),f155(x88151,x88152)),f155(x88151,x88153)))+~P1(f328(f328(f242(f882(f881(x88151,x88151),a870)),x88152),x88153)) % 154.70/154.56 [8834]~P41(x88341,x88343,x88342)+P1(f328(f328(f242(f882(f881(x88341,x88341),a870)),x88342),f328(f328(f285(x88341,x88341,x88341),f328(f283(x88341,x88341),x88342)),x88342))) % 154.70/154.56 [8883]~P1(f328(f134(x88831),x88832))+E(f328(f133(x88831,f328(f328(f7(x88831,f882(x88831,a870),a870),f330(x88831)),f328(f170(x88831),f174(x88831,x88832,x88833)))),x88832),f174(x88831,x88832,x88833)) % 154.70/154.56 [8946]E(x89461,x89462)+~P1(f328(f328(f330(f881(x89463,x89463)),f328(f328(f263(x89463,x89463),x89461),x89462)),f304(x89463,f192(f882(f881(x89463,x89463),a870))))) % 154.70/154.56 [9031]P1(f328(f328(f330(x90311),x90312),f317(x90311,x90313)))+P1(f328(f328(f330(f881(x90311,x90311)),f328(f328(f263(x90311,x90311),f558(x90313,x90312,x90311)),x90312)),x90313)) % 154.70/154.56 [9032]P1(f328(f328(f330(x90321),x90322),f317(x90321,x90323)))+P1(f328(f328(f330(f881(x90321,x90321)),f328(f328(f263(x90321,x90321),f615(x90323,x90322,x90321)),x90322)),x90323)) % 154.70/154.56 [9033]P1(f328(f328(f330(x90331),x90332),f317(x90331,x90333)))+P1(f328(f328(f330(f881(x90331,x90331)),f328(f328(f263(x90331,x90331),f617(x90333,x90332,x90331)),x90332)),x90333)) % 154.70/154.56 [9122]~P1(f328(f328(f330(f876(x91221)),x91223),f158(x91221,x91222)))+P1(f328(f157(x91221,f328(f328(f7(x91221,f882(x91221,a870),a870),f330(x91221)),x91222)),x91223)) % 154.70/154.56 [9143]P1(f328(x91433,x91432))+E(f328(f248(x91431),f328(f328(f18(x91431,a870,a870),f328(f328(f8(a870,f882(a870,a870),x91431),a326),f328(a325,x91432))),x91433)),f192(f882(x91431,a870))) % 154.70/154.56 [9164]~P83(x91641)+P1(f328(f328(f242(x91641),f328(f75(x91641),f328(f328(f22(x91641),f328(f75(x91641),x91642)),f328(f75(x91641),x91643)))),f328(f75(x91641),f328(f328(f22(x91641),x91642),x91643)))) % 154.70/154.56 [9178]~P1(f328(x91783,x91782))+E(f328(f248(x91781),f328(f328(f18(x91781,a870,a870),f328(f328(f8(a870,f882(a870,a870),x91781),a326),f328(a325,x91782))),x91783)),f328(f328(f306(x91781),x91782),f192(f882(x91781,a870)))) % 154.70/154.56 [9185]~P1(f328(f328(f330(f882(x91851,a870)),x91853),f328(f305(x91851),x91852)))+P1(f328(f256(x91851,f328(f328(f7(x91851,f882(x91851,a870),a870),f330(x91851)),x91852)),x91853)) % 154.70/154.56 [9218]P39(x92181,x92182)+P1(f328(f328(f330(f881(x92181,x92181)),f328(f328(f263(x92181,x92181),f328(f565(x92182,x92181),f328(a116,x92183))),f328(f565(x92182,x92181),x92183))),x92182)) % 154.70/154.56 [9359]P1(f328(f328(f330(f876(x93591)),x93592),f158(x93591,x93593)))+~P1(f328(f157(x93591,f328(f328(f7(x93591,f882(x93591,a870),a870),f330(x93591)),x93593)),x93592)) % 154.70/154.56 [9372]P1(f328(f328(f330(f882(x93721,a870)),x93722),f328(f305(x93721),x93723)))+~P1(f328(f256(x93721,f328(f328(f7(x93721,f882(x93721,a870),a870),f330(x93721)),x93723)),x93722)) % 154.70/154.56 [9429]P1(f328(f328(f330(x94291),f328(f274(x94291,x94292),x94293)),f328(f170(x94291),f328(f328(f151(f881(a103,x94291),x94291),f266(a103,x94291)),x94292))))+~P1(f328(f328(f243(a103),x94293),f328(f163(a103),f328(f328(f151(f881(a103,x94291),a103),f262(a103,x94291)),x94292)))) % 154.70/154.56 [9477]P1(f328(f328(f242(f882(f881(f876(x94771),f876(x94771)),a870)),f155(x94771,x94772)),f328(f328(f265(f876(x94771),f876(x94771)),f158(x94771,x94773)),f328(f16(f882(f876(x94771),a870),f876(x94771)),f158(x94771,x94773)))))+~P1(f328(f328(f242(f882(f881(x94771,x94771),a870)),x94772),f328(f328(f265(x94771,x94771),x94773),f328(f16(f882(x94771,a870),x94771),x94773)))) % 154.70/154.56 [9498]P1(f328(f328(f330(x94981),f328(f262(x94981,f881(a103,a103)),f328(f272(x94981,x94982),x94983))),f328(f170(x94981),f328(f328(f151(f881(a103,x94981),x94981),f266(a103,x94981)),x94982))))+~P1(f328(f328(f243(a103),f2(a103)),f328(f163(a103),f328(f328(f151(f881(a103,x94981),a103),f262(a103,x94981)),x94982)))) % 154.70/154.56 [9515]~P1(f328(f328(f242(f882(f881(x95151,x95151),a870)),x95152),f328(f328(f265(x95151,x95151),x95153),f328(f16(f882(x95151,a870),x95151),x95153))))+P1(f328(f328(f242(f882(f881(x95151,x95151),a870)),f328(f328(f285(x95151,x95151,x95151),x95152),f304(x95151,x95152))),f328(f328(f265(x95151,x95151),x95153),f328(f16(f882(x95151,a870),x95151),x95153)))) % 154.70/154.56 [9819]~P39(x98191,x98192)+~P1(f328(f328(f330(f881(x98191,x98191)),f328(f328(f263(x98191,x98191),f328(x98193,f328(a116,f566(x98192,x98191,x98193)))),f328(x98193,f566(x98192,x98191,x98193)))),x98192)) % 154.70/154.56 [9820]~P39(x98201,x98202)+~P1(f328(f328(f330(f881(x98201,x98201)),f328(f328(f263(x98201,x98201),f328(x98203,f328(a116,f620(x98203,x98202,x98201)))),f328(x98203,f620(x98203,x98202,x98201)))),x98202)) % 154.70/154.56 [10072]P1(f328(f328(f242(f882(f881(f882(x100721,a870),f882(x100721,a870)),a870)),f328(f328(f285(f882(x100721,a870),f882(x100721,a870),f882(x100721,a870)),f321(x100721,x100722)),f328(f328(f114(f882(f881(f882(x100721,a870),f882(x100721,a870)),a870)),f321(x100721,x100723)),f328(f328(f306(f881(f882(x100721,a870),f882(x100721,a870))),f328(f328(f263(f882(x100721,a870),f882(x100721,a870)),f192(f882(x100721,a870))),f192(f882(x100721,a870)))),f192(f882(f881(f882(x100721,a870),f882(x100721,a870)),a870)))))),f321(x100721,x100722)))+~P1(f328(f328(f242(f882(f881(x100721,x100721),a870)),f328(f328(f285(x100721,x100721,x100721),x100722),x100723)),x100722)) % 154.70/154.56 [10073]P1(f328(f328(f242(f882(f881(f882(x100731,a870),f882(x100731,a870)),a870)),f328(f328(f285(f882(x100731,a870),f882(x100731,a870),f882(x100731,a870)),f319(x100731,x100732)),f328(f328(f114(f882(f881(f882(x100731,a870),f882(x100731,a870)),a870)),f319(x100731,x100733)),f328(f328(f306(f881(f882(x100731,a870),f882(x100731,a870))),f328(f328(f263(f882(x100731,a870),f882(x100731,a870)),f192(f882(x100731,a870))),f192(f882(x100731,a870)))),f192(f882(f881(f882(x100731,a870),f882(x100731,a870)),a870)))))),f319(x100731,x100732)))+~P1(f328(f328(f242(f882(f881(x100731,x100731),a870)),f328(f328(f285(x100731,x100731,x100731),x100732),x100733)),x100732)) % 154.70/154.56 [7235]~P1(f328(f328(f242(a875),x72352),x72351))+E(f328(f328(f22(a875),f328(a116,f328(f328(f22(a875),x72351),x72352))),x72353),f328(f328(f22(a875),f328(a116,x72351)),f328(f328(f80(a875),x72352),x72353))) % 154.70/154.56 [7274]~P57(x72741)+E(f328(f328(f80(x72741),f44(x72741,x72742,x72743)),f328(f328(f81(x72741),f328(f328(f38(x72741),x72742),x72743)),x72743)),x72742) % 154.70/154.56 [7481]E(f328(f328(f81(a875),f328(f107(a875),x74811)),f328(f328(f81(a875),f328(f107(a875),x74812)),x74813)),f328(f328(f81(a875),f328(f107(a875),f328(f328(f81(a1),x74811),x74812))),x74813))+P1(f328(f328(f243(a1),x74811),a83)) % 154.70/154.56 [7951]~P1(f328(f328(f242(a875),x79513),x79512))+P1(f328(f328(f242(a875),x79511),f328(f328(f22(a875),f328(f328(f80(a875),x79512),x79511)),x79513))) % 154.70/154.56 [8151]~P1(f328(f328(f242(a875),x81511),x81512))+E(f328(f328(f125(a875),f136(a875,f328(f298(a875,x81511),x81512))),f136(a875,f328(f298(a875,x81512),f328(f328(f80(a875),x81512),x81513)))),f136(a875,f328(f298(a875,x81511),f328(f328(f80(a875),x81512),x81513)))) % 154.70/154.56 [8417]~P1(f328(f61(x84171),x84172))+E(f328(a116,f328(f37(x84171),f328(f328(f22(f882(x84171,a870)),x84172),f328(f328(f306(x84171),x84173),f192(f882(x84171,a870)))))),f328(f37(x84171),f328(f328(f306(x84171),x84173),x84172))) % 154.70/154.56 [8459]~P1(f328(f61(x84591),x84592))+E(f328(f328(f80(a875),f78(a875)),f328(f37(x84591),f328(f328(f22(f882(x84591,a870)),x84592),f328(f328(f306(x84591),x84593),f192(f882(x84591,a870)))))),f328(f37(x84591),f328(f328(f306(x84591),x84593),x84592))) % 154.70/154.56 [8650]E(f328(f328(f22(a875),f328(f37(x86501),x86502)),f328(f37(x86501),f328(f328(f105(f882(x86501,a870)),x86502),x86503))),f328(f37(x86501),f328(f328(f22(f882(x86501,a870)),x86502),x86503)))+~P1(f328(f61(x86501),f328(f328(f105(f882(x86501,a870)),x86502),x86503))) % 154.70/154.56 [8879]~P6(f328(x88792,f426(x88792,x88793,x88791)))+E(f328(f104(a1),f328(f328(f6(x88791,a875),f328(f328(f8(a1,a875,x88791),a108),x88792)),x88793)),f328(f328(f6(x88791,a1),x88792),x88793)) % 154.70/154.56 [8880]~P6(f328(x88802,f476(x88802,x88803,x88801)))+E(f328(f104(a1),f328(f328(f9(x88801,a875),f328(f328(f8(a1,a875,x88801),a108),x88802)),x88803)),f328(f328(f9(x88801,a1),x88802),x88803)) % 154.70/154.56 [8928]~P1(f328(f61(x89281),x89283))+P1(f328(f328(f242(a875),f328(f328(f22(a875),f328(f37(x89281),x89282)),f328(f37(x89281),x89283))),f328(f37(x89281),f328(f328(f22(f882(x89281,a870)),x89282),x89283)))) % 154.70/154.56 [8954]P1(f328(f328(f330(x89541),f426(x89542,x89543,x89541)),x89543))+E(f328(f104(a1),f328(f328(f6(x89541,a875),f328(f328(f8(a1,a875,x89541),a108),x89542)),x89543)),f328(f328(f6(x89541,a1),x89542),x89543)) % 154.70/154.56 [8955]P1(f328(f328(f330(x89551),f476(x89552,x89553,x89551)),x89553))+E(f328(f104(a1),f328(f328(f9(x89551,a875),f328(f328(f8(a1,a875,x89551),a108),x89552)),x89553)),f328(f328(f9(x89551,a1),x89552),x89553)) % 154.70/154.56 [9023]E(f85(x90231,f328(f328(f7(x90231,f882(x90231,a870),a870),f330(x90231)),f328(f328(f22(f882(x90231,a870)),x90232),f328(f328(f306(x90231),x90233),f192(f882(x90231,a870)))))),f255(x90231,x90233,x90232))+P1(f328(f328(f242(f882(x90231,a870)),x90232),f328(f328(f306(x90231),x90233),f192(f882(x90231,a870))))) % 154.70/154.56 [9373]E(f328(f328(f151(f876(x93731),x93731),f328(f328(f7(f876(x93731),a875,x93731),f162(x93731)),x93732)),f328(f133(f876(x93731),f328(f328(f8(a875,a870,f876(x93731)),f328(f243(a875),x93732)),f193(f876(x93731)))),x93733)),f328(f328(f162(f876(x93731)),f178(x93731,x93733)),x93732))+~P1(f328(f328(f243(a875),x93732),f328(f193(f876(f876(x93731))),f178(x93731,x93733)))) % 154.70/154.56 [9446]E(f328(f133(x94461,x94462),x94463),f175(x94461,x94462,x94463))+P1(f328(f328(f330(x94461),f758(x94463,x94462,x94461)),f328(f170(x94461),f328(f328(f135(x94461),f328(f193(f876(x94461)),f175(x94461,x94462,x94463))),x94463)))) % 154.70/154.56 [9587]E(f328(f328(f135(x95871),f328(f193(f876(x95871)),f175(x95871,x95872,x95873))),x95873),f117(x95871))+~P1(f328(x95872,f328(f138(x95871),f328(f328(f135(x95871),f328(f193(f876(x95871)),f175(x95871,x95872,x95873))),x95873)))) % 154.70/154.56 [9680]~P1(f328(f328(f330(f881(x96801,x96801)),x96802),f304(x96801,x96803)))+P1(f328(f328(f330(f881(x96801,x96801)),x96802),f328(f328(f41(a875,f882(f881(x96801,x96801),a870)),f251(f882(a875,a870))),f328(f328(f7(a875,f882(f881(x96801,x96801),a870),f882(f881(x96801,x96801),a870)),f187(f881(x96801,x96801),a870)),x96803)))) % 154.70/154.56 [9737]~P1(f328(f328(f242(f882(x97371,a870)),f328(f328(f41(a875,f882(x97371,a870)),f328(f298(a875,f2(a875)),f379(x97373,x97372,x97371))),x97372)),x97373))+P1(f328(f328(f242(f882(x97371,a870)),f328(f328(f41(a875,f882(x97371,a870)),f251(f882(a875,a870))),x97372)),x97373)) % 154.70/154.56 [9795]~P1(f328(f328(f243(a1),f2(a1)),x97953))+P1(f328(f328(f243(a1),x97951),f328(f328(f80(a1),x97952),f328(f328(f81(a1),f328(f328(f80(a1),f328(f75(a1),f328(f328(f22(a1),x97952),x97951))),f78(a1))),x97953)))) % 154.70/154.56 [9806]~P39(x98061,f328(f328(f114(f882(f881(x98061,x98061),a870)),x98062),x98063))+P39(x98061,f328(f328(f114(f882(f881(x98061,x98061),a870)),f328(f328(f114(f882(f881(x98061,x98061),a870)),f328(f328(f285(x98061,x98061,x98061),x98062),x98062)),f328(f328(f285(x98061,x98061,x98061),x98063),x98062))),x98063)) % 154.70/154.56 [9888]P39(x98881,f328(f328(f114(f882(f881(x98881,x98881),a870)),x98882),x98883))+~P39(x98881,f328(f328(f114(f882(f881(x98881,x98881),a870)),f328(f328(f114(f882(f881(x98881,x98881),a870)),f328(f328(f285(x98881,x98881,x98881),x98882),x98882)),f328(f328(f285(x98881,x98881,x98881),x98883),x98882))),x98883)) % 154.70/154.56 [9450]~P135(x94501)+E(f328(f106(x94501),f328(a89,f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),f328(f328(f263(a875,a875),x94502),x94503)),f192(f882(f881(a875,a875),a870)))))),f328(f328(f22(x94501),f328(f104(x94501),x94502)),f328(f104(x94501),x94503))) % 154.70/154.56 [9533]P1(f328(x95333,x95332))+E(f328(f248(x95331),f328(f328(f18(x95331,a870,a870),f328(f328(f8(a870,f882(a870,a870),x95331),a326),f328(f328(f7(x95331,x95331,a870),a325),x95332))),x95333)),f192(f882(x95331,a870))) % 154.70/154.56 [9536]~P1(f328(x95363,x95362))+E(f328(f248(x95361),f328(f328(f18(x95361,a870,a870),f328(f328(f8(a870,f882(a870,a870),x95361),a326),f328(f328(f7(x95361,x95361,a870),a325),x95362))),x95363)),f328(f328(f306(x95361),x95362),f192(f882(x95361,a870)))) % 154.70/154.56 [9773]E(x97731,x97732)+P1(f328(f328(f252(x97733,x97733,f328(f328(f8(f882(x97733,a870),f882(x97733,a870),x97733),f328(f8(a870,a870,x97733),a323)),a325)),x97731),x97732)) % 154.70/154.56 [9866]~E(x98661,x98662)+~P1(f328(f328(f252(x98663,x98663,f328(f328(f8(f882(x98663,a870),f882(x98663,a870),x98663),f328(f8(a870,a870,x98663),a323)),a325)),x98661),x98662)) % 154.70/154.56 [9880]~P1(f328(f61(x98801),x98803))+E(f328(f328(f64(x98801,f882(x98801,a870),f328(f328(f8(f882(x98801,a870),f882(f882(x98801,a870),f882(x98801,a870)),x98801),f328(f7(f882(x98801,a870),f882(x98801,a870),f882(x98801,a870)),f22(f882(x98801,a870)))),f328(f328(f7(x98801,f882(x98801,a870),f882(x98801,a870)),f306(x98801)),f192(f882(x98801,a870))))),x98802),x98803),f328(f328(f22(f882(x98801,a870)),x98802),x98803)) % 154.70/154.56 [9912]~P1(f328(f328(f243(a1),f2(a1)),x99123))+P1(f328(f328(f243(a1),f328(f328(f22(a1),x99121),f328(f328(f81(a1),f328(f328(f80(a1),f328(f75(a1),f328(f328(f22(a1),x99121),x99122))),f78(a1))),x99123))),x99122)) % 154.70/154.56 [10135]~P1(f328(f328(f330(x101351),x101353),f317(x101351,x101352)))+P1(f328(f316(x101351,f328(f328(f7(x101351,f882(f881(x101351,x101351),a870),f882(x101351,a870)),f328(f328(f8(f882(x101351,f882(f882(f881(x101351,x101351),a870),a870)),f882(f882(f881(x101351,x101351),a870),f882(x101351,a870)),x101351),f7(x101351,f882(f881(x101351,x101351),a870),a870)),f328(f328(f8(f882(x101351,f881(x101351,x101351)),f882(x101351,f882(f882(f881(x101351,x101351),a870),a870)),x101351),f328(f8(f881(x101351,x101351),f882(f882(f881(x101351,x101351),a870),a870),x101351),f330(f881(x101351,x101351)))),f263(x101351,x101351)))),x101352)),x101353)) % 154.70/154.56 [10148]P1(f328(f328(f330(x101481),x101482),f317(x101481,x101483)))+~P1(f328(f316(x101481,f328(f328(f7(x101481,f882(f881(x101481,x101481),a870),f882(x101481,a870)),f328(f328(f8(f882(x101481,f882(f882(f881(x101481,x101481),a870),a870)),f882(f882(f881(x101481,x101481),a870),f882(x101481,a870)),x101481),f7(x101481,f882(f881(x101481,x101481),a870),a870)),f328(f328(f8(f882(x101481,f881(x101481,x101481)),f882(x101481,f882(f882(f881(x101481,x101481),a870),a870)),x101481),f328(f8(f881(x101481,x101481),f882(f882(f881(x101481,x101481),a870),a870),x101481),f330(f881(x101481,x101481)))),f263(x101481,x101481)))),x101483)),x101482)) % 154.70/154.56 [9735]~P1(f328(f61(x97351),f328(f248(x97351),x97353)))+P1(f328(f61(x97351),f328(f248(x97351),f328(f328(f18(x97351,a870,a870),f328(f328(f8(a870,f882(a870,a870),x97351),a326),x97352)),x97353)))) % 154.70/154.56 [9736]~P1(f328(f61(x97361),f328(f248(x97361),x97362)))+P1(f328(f61(x97361),f328(f248(x97361),f328(f328(f18(x97361,a870,a870),f328(f328(f8(a870,f882(a870,a870),x97361),a326),x97362)),x97363)))) % 154.70/154.56 [9838]P1(f328(f61(x98381),f328(f248(x98381),x98382)))+~P1(f328(f61(x98381),f328(f248(x98381),f328(f328(f18(x98381,a870,a870),f328(f328(f8(a870,f882(a870,a870),x98381),a327),x98383)),x98382)))) % 154.70/154.56 [9839]P1(f328(f61(x98391),f328(f248(x98391),x98392)))+~P1(f328(f61(x98391),f328(f248(x98391),f328(f328(f18(x98391,a870,a870),f328(f328(f8(a870,f882(a870,a870),x98391),a327),x98392)),x98393)))) % 154.70/154.56 [10122]~P1(f328(f61(x101221),x101222))+P1(f328(f61(f876(x101221)),f328(f248(f876(x101221)),f328(f328(f18(f876(x101221),a870,a870),f328(f328(f8(a870,f882(a870,a870),f876(x101221)),a326),f328(f328(f7(f876(x101221),f882(x101221,a870),a870),f328(f328(f8(f882(x101221,a870),f882(f882(x101221,a870),a870),f876(x101221)),f242(f882(x101221,a870))),f170(x101221))),x101222))),f328(f328(f7(f876(x101221),a875,a870),f328(f328(f8(a875,f882(a875,a870),f876(x101221)),a325),f193(f876(x101221)))),x101223))))) % 154.70/154.56 [10123]~P1(f328(f61(x101231),x101232))+P1(f328(f61(f876(x101231)),f328(f248(f876(x101231)),f328(f328(f18(f876(x101231),a870,a870),f328(f328(f8(a870,f882(a870,a870),f876(x101231)),a326),f328(f328(f7(f876(x101231),f882(x101231,a870),a870),f328(f328(f8(f882(x101231,a870),f882(f882(x101231,a870),a870),f876(x101231)),f242(f882(x101231,a870))),f170(x101231))),x101232))),f328(f328(f7(f876(x101231),a875,a870),f328(f328(f8(a875,f882(a875,a870),f876(x101231)),f242(a875)),f193(f876(x101231)))),x101233))))) % 154.70/154.56 [9853]~P109(x98531)+E(f328(f328(f253(x98531),x98532),f328(f328(f81(a875),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x98533)),f328(f328(f81(x98531),f328(f328(f253(x98531),x98532),x98533)),f328(f328(f253(x98531),x98532),x98533))) % 154.70/154.56 [9893]~P79(x98931)+E(f328(f328(f253(x98931),f328(f328(f253(x98931),x98932),x98933)),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(f328(f253(x98931),x98932),f328(f328(f81(a875),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x98933))) % 154.70/154.56 [9939]~P135(x99391)+E(f328(f328(f253(x99391),f328(f79(x99391),x99392)),f328(f328(f81(a875),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x99393)),f328(f328(f253(x99391),x99392),f328(f328(f81(a875),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x99393))) % 154.70/154.56 [10079]~P121(x100791)+P1(f328(f328(f242(x100791),f2(x100791)),f328(f328(f80(x100791),f328(f328(f253(x100791),x100792),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x100791),x100793),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))))) % 154.70/154.56 [9949]~P109(x99491)+E(f328(f328(f253(x99491),x99492),f328(a116,f328(f328(f81(a875),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x99493))),f328(f328(f81(x99491),x99492),f328(f328(f81(x99491),f328(f328(f253(x99491),x99492),x99493)),f328(f328(f253(x99491),x99492),x99493)))) % 154.70/154.56 [9998]~P79(x99981)+E(f328(f328(f81(x99981),x99982),f328(f328(f253(x99981),f328(f328(f253(x99981),x99982),x99983)),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x99981),x99982),f328(a116,f328(f328(f81(a875),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x99983)))) % 154.70/154.56 [10036]~P121(x100361)+P1(f328(f328(f242(x100361),f2(x100361)),f328(f328(f253(x100361),x100362),f328(f328(f81(a875),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x100363)))) % 154.70/154.56 [10102]~P90(x101021)+E(f328(f328(f22(x101021),f328(f328(f80(x101021),f328(f328(f253(x101021),x101022),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x101021),x101023),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))),f328(f328(f81(x101021),f328(f328(f81(x101021),f328(f107(x101021),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x101022)),x101023)),f328(f328(f253(x101021),f328(f328(f22(x101021),x101022),x101023)),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 154.70/154.56 [10103]~P90(x101031)+E(f328(f328(f80(x101031),f328(f328(f80(x101031),f328(f328(f253(x101031),x101032),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x101031),x101033),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))),f328(f328(f81(x101031),f328(f328(f81(x101031),f328(f107(x101031),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x101032)),x101033)),f328(f328(f253(x101031),f328(f328(f80(x101031),x101032),x101033)),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 154.70/154.56 [10203]~P29(x102031,x102032,x102033)+P1(f98(x102031,a870,f328(f328(f8(f882(a871,f882(f882(x102031,f882(a872,a870)),f882(x102031,a870))),f882(a871,f882(f882(x102031,f882(a872,a870)),a870)),f882(x102031,f882(a872,a870))),f328(f8(f882(f882(x102031,f882(a872,a870)),f882(x102031,a870)),f882(f882(x102031,f882(a872,a870)),a870),a871),f328(f8(f882(x102031,a870),a870,f882(x102031,f882(a872,a870))),f88(x102031)))),f328(f328(f8(f882(a871,f882(f882(x102031,f882(a872,a870)),f882(x102031,f882(a872,a870)))),f882(a871,f882(f882(x102031,f882(a872,a870)),f882(x102031,a870))),f882(x102031,f882(a872,a870))),f328(f8(f882(f882(x102031,f882(a872,a870)),f882(x102031,f882(a872,a870))),f882(f882(x102031,f882(a872,a870)),f882(x102031,a870)),a871),f328(f8(f882(x102031,f882(a872,a870)),f882(x102031,a870),f882(x102031,f882(a872,a870))),f328(f8(f882(a872,a870),a870,x102031),f88(a872))))),f328(f328(f7(f882(x102031,f882(a872,a870)),f882(a871,f882(f882(x102031,f882(a872,a870)),f882(x102031,f882(a872,a870)))),f882(a871,f882(f882(x102031,f882(a872,a870)),f882(x102031,f882(a872,a870))))),f328(f328(f8(f882(f882(f882(x102031,f882(a872,a870)),f882(x102031,f882(a872,a870))),f882(f882(x102031,f882(a872,a870)),f882(x102031,f882(a872,a870)))),f882(f882(a871,f882(f882(x102031,f882(a872,a870)),f882(x102031,f882(a872,a870)))),f882(a871,f882(f882(x102031,f882(a872,a870)),f882(x102031,f882(a872,a870))))),f882(x102031,f882(a872,a870))),f8(f882(f882(x102031,f882(a872,a870)),f882(x102031,f882(a872,a870))),f882(f882(x102031,f882(a872,a870)),f882(x102031,f882(a872,a870))),a871)),f328(f328(f8(f882(f882(x102031,f882(a872,a870)),f882(x102031,f882(a872,a870))),f882(f882(f882(x102031,f882(a872,a870)),f882(x102031,f882(a872,a870))),f882(f882(x102031,f882(a872,a870)),f882(x102031,f882(a872,a870)))),f882(x102031,f882(a872,a870))),f8(f882(x102031,f882(a872,a870)),f882(x102031,f882(a872,a870)),f882(x102031,f882(a872,a870)))),f328(f328(f8(f882(x102031,f882(f882(a872,a870),f882(a872,a870))),f882(f882(x102031,f882(a872,a870)),f882(x102031,f882(a872,a870))),f882(x102031,f882(a872,a870))),f18(x102031,f882(a872,a870),f882(a872,a870))),f328(f328(f8(f882(x102031,f882(a872,f882(a870,a870))),f882(x102031,f882(f882(a872,a870),f882(a872,a870))),f882(x102031,f882(a872,a870))),f328(f8(f882(a872,f882(a870,a870)),f882(f882(a872,a870),f882(a872,a870)),x102031),f18(a872,a870,a870))),f328(f8(f882(a872,a870),f882(a872,f882(a870,a870)),x102031),f328(f8(a870,f882(a870,a870),a872),a331))))))),f328(f328(f8(f882(f882(x102031,f882(a872,a870)),f882(x102031,f882(a872,f882(a872,a870)))),f882(f882(x102031,f882(a872,a870)),f882(x102031,f882(a872,a870))),a871),f328(f8(f882(x102031,f882(a872,f882(a872,a870))),f882(x102031,f882(a872,a870)),f882(x102031,f882(a872,a870))),f328(f8(f882(a872,f882(a872,a870)),f882(a872,a870),x102031),f328(f8(f882(a872,a870),a870,a872),f88(a872))))),f328(f328(f8(f882(f882(a872,a870),f882(a872,f882(a872,a870))),f882(f882(x102031,f882(a872,a870)),f882(x102031,f882(a872,f882(a872,a870)))),a871),f8(f882(a872,a870),f882(a872,f882(a872,a870)),x102031)),f328(f328(f8(f882(a872,f882(f882(a872,a870),f882(a872,a870))),f882(f882(a872,a870),f882(a872,f882(a872,a870))),a871),f7(a872,f882(a872,a870),f882(a872,a870))),f328(f328(f8(f882(a872,f882(a872,f882(a870,a870))),f882(a872,f882(f882(a872,a870),f882(a872,a870))),a871),f328(f8(f882(a872,f882(a870,a870)),f882(f882(a872,a870),f882(a872,a870)),a872),f18(a872,a870,a870))),f328(f328(f8(f882(a872,f882(a872,a870)),f882(a872,f882(a872,f882(a870,a870))),a871),f328(f8(f882(a872,a870),f882(a872,f882(a870,a870)),a872),f328(f8(a870,f882(a870,a870),a872),a331))),f328(f328(f7(a871,a875,f882(a872,f882(a872,a870))),f328(f328(f8(f882(a872,f882(a875,f882(a872,a870))),f882(a875,f882(a872,f882(a872,a870))),a871),f7(a872,a875,f882(a872,a870))),a200)),x102032))))))))),x102033)) % 154.70/154.56 [10205]P29(x102051,x102052,x102053)+~P1(f98(x102051,a870,f328(f328(f8(f882(a871,f882(f882(x102051,f882(a872,a870)),f882(x102051,a870))),f882(a871,f882(f882(x102051,f882(a872,a870)),a870)),f882(x102051,f882(a872,a870))),f328(f8(f882(f882(x102051,f882(a872,a870)),f882(x102051,a870)),f882(f882(x102051,f882(a872,a870)),a870),a871),f328(f8(f882(x102051,a870),a870,f882(x102051,f882(a872,a870))),f88(x102051)))),f328(f328(f8(f882(a871,f882(f882(x102051,f882(a872,a870)),f882(x102051,f882(a872,a870)))),f882(a871,f882(f882(x102051,f882(a872,a870)),f882(x102051,a870))),f882(x102051,f882(a872,a870))),f328(f8(f882(f882(x102051,f882(a872,a870)),f882(x102051,f882(a872,a870))),f882(f882(x102051,f882(a872,a870)),f882(x102051,a870)),a871),f328(f8(f882(x102051,f882(a872,a870)),f882(x102051,a870),f882(x102051,f882(a872,a870))),f328(f8(f882(a872,a870),a870,x102051),f88(a872))))),f328(f328(f7(f882(x102051,f882(a872,a870)),f882(a871,f882(f882(x102051,f882(a872,a870)),f882(x102051,f882(a872,a870)))),f882(a871,f882(f882(x102051,f882(a872,a870)),f882(x102051,f882(a872,a870))))),f328(f328(f8(f882(f882(f882(x102051,f882(a872,a870)),f882(x102051,f882(a872,a870))),f882(f882(x102051,f882(a872,a870)),f882(x102051,f882(a872,a870)))),f882(f882(a871,f882(f882(x102051,f882(a872,a870)),f882(x102051,f882(a872,a870)))),f882(a871,f882(f882(x102051,f882(a872,a870)),f882(x102051,f882(a872,a870))))),f882(x102051,f882(a872,a870))),f8(f882(f882(x102051,f882(a872,a870)),f882(x102051,f882(a872,a870))),f882(f882(x102051,f882(a872,a870)),f882(x102051,f882(a872,a870))),a871)),f328(f328(f8(f882(f882(x102051,f882(a872,a870)),f882(x102051,f882(a872,a870))),f882(f882(f882(x102051,f882(a872,a870)),f882(x102051,f882(a872,a870))),f882(f882(x102051,f882(a872,a870)),f882(x102051,f882(a872,a870)))),f882(x102051,f882(a872,a870))),f8(f882(x102051,f882(a872,a870)),f882(x102051,f882(a872,a870)),f882(x102051,f882(a872,a870)))),f328(f328(f8(f882(x102051,f882(f882(a872,a870),f882(a872,a870))),f882(f882(x102051,f882(a872,a870)),f882(x102051,f882(a872,a870))),f882(x102051,f882(a872,a870))),f18(x102051,f882(a872,a870),f882(a872,a870))),f328(f328(f8(f882(x102051,f882(a872,f882(a870,a870))),f882(x102051,f882(f882(a872,a870),f882(a872,a870))),f882(x102051,f882(a872,a870))),f328(f8(f882(a872,f882(a870,a870)),f882(f882(a872,a870),f882(a872,a870)),x102051),f18(a872,a870,a870))),f328(f8(f882(a872,a870),f882(a872,f882(a870,a870)),x102051),f328(f8(a870,f882(a870,a870),a872),a331))))))),f328(f328(f8(f882(f882(x102051,f882(a872,a870)),f882(x102051,f882(a872,f882(a872,a870)))),f882(f882(x102051,f882(a872,a870)),f882(x102051,f882(a872,a870))),a871),f328(f8(f882(x102051,f882(a872,f882(a872,a870))),f882(x102051,f882(a872,a870)),f882(x102051,f882(a872,a870))),f328(f8(f882(a872,f882(a872,a870)),f882(a872,a870),x102051),f328(f8(f882(a872,a870),a870,a872),f88(a872))))),f328(f328(f8(f882(f882(a872,a870),f882(a872,f882(a872,a870))),f882(f882(x102051,f882(a872,a870)),f882(x102051,f882(a872,f882(a872,a870)))),a871),f8(f882(a872,a870),f882(a872,f882(a872,a870)),x102051)),f328(f328(f8(f882(a872,f882(f882(a872,a870),f882(a872,a870))),f882(f882(a872,a870),f882(a872,f882(a872,a870))),a871),f7(a872,f882(a872,a870),f882(a872,a870))),f328(f328(f8(f882(a872,f882(a872,f882(a870,a870))),f882(a872,f882(f882(a872,a870),f882(a872,a870))),a871),f328(f8(f882(a872,f882(a870,a870)),f882(f882(a872,a870),f882(a872,a870)),a872),f18(a872,a870,a870))),f328(f328(f8(f882(a872,f882(a872,a870)),f882(a872,f882(a872,f882(a870,a870))),a871),f328(f8(f882(a872,a870),f882(a872,f882(a870,a870)),a872),f328(f8(a870,f882(a870,a870),a872),a331))),f328(f328(f7(a871,a875,f882(a872,f882(a872,a870))),f328(f328(f8(f882(a872,f882(a875,f882(a872,a870))),f882(a875,f882(a872,f882(a872,a870))),a871),f7(a872,a875,f882(a872,a870))),a200)),x102052))))))))),x102053)) % 154.70/154.56 [4668]E(x46681,x46682)+~E(f33(x46683,x46681),f33(x46684,x46682)) % 154.70/154.56 [4669]E(x46691,x46692)+~E(f33(x46691,x46693),f33(x46692,x46694)) % 154.70/154.56 [4670]E(x46701,x46702)+~E(f32(x46703,x46701),f32(x46704,x46702)) % 154.70/154.56 [4671]E(x46711,x46712)+~E(f32(x46711,x46713),f32(x46712,x46714)) % 154.70/154.56 [7747]P27(x77471,x77472,x77473,x77474)+~E(f430(x77474,x77473,x77472,x77471),f435(x77474,x77473,x77472,x77471)) % 154.70/154.56 [8039]P36(x80391,x80392,x80393,x80394,f117(x80392))+~E(x80394,f117(x80391)) % 154.70/154.56 [8040]P36(x80401,x80402,x80403,f117(x80401),x80404)+~E(x80404,f117(x80402)) % 154.70/154.56 [8265]~P27(x82651,f879(x82652),x82654,f182(x82651,x82652,x82654))+P27(x82651,f879(x82652),f183(x82651,x82652,x82653,x82654),f182(x82651,x82652,x82654)) % 154.70/154.56 [8473]~P27(x84731,f879(x84732),f183(x84731,x84732,x84734,x84733),f182(x84731,x84732,x84733))+P27(x84731,f879(x84732),x84733,f182(x84731,x84732,x84733)) % 154.70/154.56 [8597]~P36(x85972,x85973,x85974,x85971,f117(x85973))+E(x85971,f117(x85972)) % 154.70/154.56 [8598]~P36(x85983,x85982,x85984,f117(x85983),x85981)+E(x85981,f117(x85982)) % 154.70/154.56 [5044]~P19(x50443,x50441,x50444)+E(f328(f328(x50441,x50442),x50442),x50442) % 154.70/154.56 [5334]~E(x53344,f192(f882(x53341,a870)))+E(f328(f307(x53341,x53342,x53343),x53344),f192(f882(x53342,a870))) % 154.70/154.56 [5601]~E(f328(f307(x56012,x56013,x56014),x56011),f192(f882(x56013,a870)))+E(x56011,f192(f882(x56012,a870))) % 154.70/154.56 [5885]~P105(x58852)+E(f328(f328(f145(x58851,x58852,x58853),x58854),f117(x58851)),f328(f328(f148(x58851),x58854),f117(x58851))) % 154.70/154.56 [5922]E(f328(x59221,x59222),f205(x59223))+P1(f328(f328(f330(x59224),x59222),f182(x59224,x59223,x59221))) % 154.70/154.56 [6244]~E(x62441,f192(f882(x62442,a870)))+~P1(f328(f62(x62442,x62443,x62441),x62444)) % 154.70/154.56 [6266]~P55(x62661,x62663,x62664,x62662)+P1(f328(f61(x62661),x62662)) % 154.70/154.56 [6267]~P55(x62671,x62673,x62672,x62674)+P1(f328(f61(x62671),x62672)) % 154.70/154.56 [6273]~P55(x62732,x62733,x62734,x62731)+~E(x62731,f192(f882(x62732,a870))) % 154.70/154.56 [6304]~P107(x63041)+E(f328(f328(f105(f882(x63041,a870)),f328(f298(x63041,x63042),x63043)),f299(x63041,x63043,x63044)),f192(f882(x63041,a870))) % 154.70/154.56 [6331]~P1(f328(f328(x63313,x63314),x63312))+P1(f328(f328(f330(x63311),x63312),f289(x63311,x63313,x63314))) % 154.70/154.56 [6332]~P1(f328(f328(x63323,x63324),x63322))+P1(f328(f328(f330(x63321),x63322),f290(x63321,x63323,x63324))) % 154.70/154.56 [6333]~P1(f328(f328(x63333,x63332),x63334))+P1(f328(f328(f330(x63331),x63332),f291(x63331,x63333,x63334))) % 154.70/154.56 [6334]~P1(f328(f328(x63343,x63342),x63344))+P1(f328(f328(f330(x63341),x63342),f294(x63341,x63343,x63344))) % 154.70/154.56 [6472]~P107(x64721)+E(f328(f328(f105(f882(x64721,a870)),f302(x64721,x64722,x64723)),f299(x64721,x64723,x64724)),f192(f882(x64721,a870))) % 154.70/154.56 [6473]~P107(x64731)+E(f328(f328(f105(f882(x64731,a870)),f301(x64731,x64732,x64733)),f302(x64731,x64733,x64734)),f192(f882(x64731,a870))) % 154.70/154.56 [6474]~P107(x64741)+E(f328(f328(f105(f882(x64741,a870)),f301(x64741,x64742,x64743)),f301(x64741,x64743,x64744)),f192(f882(x64741,a870))) % 154.70/154.56 [6475]~P107(x64751)+E(f328(f328(f105(f882(x64751,a870)),f299(x64751,x64752,x64753)),f302(x64751,x64753,x64754)),f192(f882(x64751,a870))) % 154.70/154.56 [6476]~P107(x64761)+E(f328(f328(f105(f882(x64761,a870)),f299(x64761,x64762,x64763)),f301(x64761,x64763,x64764)),f192(f882(x64761,a870))) % 154.70/154.56 [6513]P1(f328(f328(x65131,x65132),f578(x65132,x65131)))+~P1(f328(f257(x65133,x65134,x65131),x65132)) % 154.70/154.56 [6561]~E(f328(x65611,x65612),f205(x65613))+~P1(f328(f328(f330(x65614),x65612),f182(x65614,x65613,x65611))) % 154.70/154.56 [6590]~P105(x65902)+E(f328(f170(x65901),f147(x65901,x65902,x65903,x65904)),f328(f170(x65901),x65904)) % 154.70/154.56 [6643]~P140(x66431)+E(f194(x66431,x66432,f328(a116,x66433),x66434),f194(x66431,x66432,x66433,f328(x66432,x66434))) % 154.70/154.56 [6703]~P1(f328(f328(f330(x67034),x67033),f289(x67034,x67031,x67032)))+P1(f328(f328(x67031,x67032),x67033)) % 154.70/154.56 [6704]~P1(f328(f328(f330(x67044),x67043),f290(x67044,x67041,x67042)))+P1(f328(f328(x67041,x67042),x67043)) % 154.70/154.56 [6705]~P1(f328(f328(f330(x67054),x67052),f291(x67054,x67051,x67053)))+P1(f328(f328(x67051,x67052),x67053)) % 154.70/154.56 [6706]~P1(f328(f328(f330(x67064),x67062),f294(x67064,x67061,x67063)))+P1(f328(f328(x67061,x67062),x67063)) % 154.70/154.56 [6783]E(f328(f37(f880(x67831,x67832)),f315(x67831,x67832,x67833,x67834)),f2(a875))+P1(f328(f61(x67832),x67834)) % 154.70/154.56 [6784]E(f328(f37(f880(x67841,x67842)),f315(x67841,x67842,x67843,x67844)),f2(a875))+P1(f328(f61(x67841),x67843)) % 154.70/154.56 [6986]~P17(x69864,x69861,x69862)+E(f328(f73(x69861,x69861,x69861,f328(x69862,x69863)),f328(x69862,x69863)),f328(x69862,x69863)) % 154.70/154.56 [7787]~P1(f328(x77871,x77874))+P1(f328(x77871,f96(x77872,a875,x77873,x77871))) % 154.70/154.56 [7872]~E(x78722,x78723)+P1(f328(f328(f330(f881(x78721,x78721)),f328(f328(f263(x78721,x78721),x78722),x78723)),f304(x78721,x78724))) % 154.70/154.56 [7901]~P27(x79011,x79012,x79013,f251(f882(x79011,a870)))+E(f328(f77(x79011,x79012,f251(f882(x79011,a870)),x79013),f328(x79013,x79014)),x79014) % 154.70/154.56 [7990]~P1(f328(f328(f330(f876(x79901)),f328(f328(f148(x79901),x79904),x79902)),f158(x79901,x79903)))+P1(f328(f328(f330(f876(x79901)),x79902),f158(x79901,x79903))) % 154.70/154.56 [7991]~P1(f328(f328(f330(f876(x79911)),f328(f328(f125(x79911),x79914),x79912)),f158(x79911,x79913)))+P1(f328(f328(f330(f876(x79911)),x79912),f158(x79911,x79913))) % 154.70/154.56 [7992]~P1(f328(f328(f330(f876(x79921)),f328(f328(f125(x79921),x79922),x79924)),f158(x79921,x79923)))+P1(f328(f328(f330(f876(x79921)),x79922),f158(x79921,x79923))) % 154.70/154.56 [8003]~P105(x80031)+P16(x80031,f328(f328(f151(x80032,x80031),x80033),f147(x80032,x80031,x80033,x80034))) % 154.70/154.56 [8102]P27(x81024,x81023,x81021,x81022)+E(f328(x81021,f430(x81022,x81021,x81023,x81024)),f328(x81021,f435(x81022,x81021,x81023,x81024))) % 154.70/154.56 [8115]E(f183(x81151,x81152,x81153,x81154),f183(x81151,x81152,x81154,x81153))+~E(f328(f328(f105(f882(x81151,a870)),f182(x81151,x81152,x81153)),f182(x81151,x81152,x81154)),f192(f882(x81151,a870))) % 154.70/154.56 [8227]~P27(x82272,x82271,x82274,x82273)+P27(x82271,x82272,f77(x82272,x82271,x82273,x82274),f328(f307(x82272,x82271,x82274),x82273)) % 154.70/154.56 [8364]P39(f881(x83642,x83644),f280(x83642,x83644,x83641,x83643))+P1(f328(x83641,f564(x83642,x83643,x83644,x83641))) % 154.70/154.56 [8481]E(x84811,x84812)+~P1(f328(f328(f330(f881(x84813,x84813)),f328(f328(f263(x84813,x84813),x84811),x84812)),f260(x84813,x84814))) % 154.70/154.56 [8549]~P1(f328(f61(f880(x85493,x85491)),f315(x85493,x85491,x85494,x85492)))+P1(f328(f61(x85491),x85492)) % 154.70/154.56 [8550]~P1(f328(f61(f880(x85501,x85503)),f315(x85501,x85503,x85502,x85504)))+P1(f328(f61(x85501),x85502)) % 154.70/154.56 [8733]P39(f881(x87331,x87332),f280(x87331,x87332,x87333,x87334))+~P39(x87332,f328(x87334,f564(x87331,x87334,x87332,x87333))) % 154.70/154.56 [9295]E(f328(f328(f156(x92951,x92952),f688(x92953,x92954,x92952,x92951)),f689(x92953,x92954,x92952,x92951)),x92954)+~P1(f328(f328(f330(f881(f876(x92951),f876(x92951))),f328(f328(f263(f876(x92951),f876(x92951)),x92952),x92954)),f154(x92951,x92953))) % 154.70/154.56 [9296]~P1(f328(x92963,x92964))+P1(f328(f328(f242(a875),f328(x92961,f96(x92962,a875,x92961,x92963))),f328(x92961,x92964))) % 154.70/154.56 [9302]~P1(f328(f328(f330(f881(f876(x93021),f876(x93021))),f328(f328(f263(f876(x93021),f876(x93021)),x93022),x93023)),f142(x93021,x93024)))+P1(f328(f328(f330(f881(f876(x93021),f876(x93021))),f328(f328(f263(f876(x93021),f876(x93021)),x93022),x93023)),f144(x93021,x93024))) % 154.70/154.56 [9408]P1(f328(f61(x94081),x94082))+~P1(f328(f328(f330(f881(f882(x94081,a870),f882(x94081,a870))),f328(f328(f263(f882(x94081,a870),f882(x94081,a870)),x94083),x94082)),f319(x94081,x94084))) % 154.70/154.56 [9409]P1(f328(f61(x94091),x94092))+~P1(f328(f328(f330(f881(f882(x94091,a870),f882(x94091,a870))),f328(f328(f263(f882(x94091,a870),f882(x94091,a870)),x94092),x94093)),f319(x94091,x94094))) % 154.70/154.56 [9412]~E(x94121,f192(f882(x94122,a870)))+~P1(f328(f328(f330(f881(f882(x94122,a870),f882(x94122,a870))),f328(f328(f263(f882(x94122,a870),f882(x94122,a870)),x94123),x94121)),f319(x94122,x94124))) % 154.70/154.56 [10048]P14(x100481,x100482,x100483,x100484)+~P1(f328(f328(f267(x100481,x100481,a870),f328(f328(f7(x100481,f882(x100481,x100482),f882(x100481,a870)),f328(f328(f8(f882(x100482,a870),f882(f882(x100481,x100482),f882(x100481,a870)),x100481),f8(x100482,a870,x100481)),f328(f328(f8(x100482,f882(x100482,a870),x100481),a325),x100484))),x100484)),f595(x100484,x100483,x100482,x100481))) % 154.70/154.56 [4943]~E(x49432,f117(x49431))+E(f328(f328(f156(x49431,x49432),x49433),x49434),f117(x49431)) % 154.70/154.56 [4944]~E(x49444,f117(x49441))+E(f328(f328(f151(x49441,x49442),x49443),x49444),f117(x49442)) % 154.70/154.56 [4945]~E(x49454,f205(x49451))+E(f328(f328(f206(x49451,x49452),x49453),x49454),f205(x49452)) % 154.70/154.56 [5183]E(x51831,f117(x51832))+~E(f328(f328(f151(x51832,x51833),x51834),x51831),f117(x51833)) % 154.70/154.56 [5184]E(x51841,f205(x51842))+~E(f328(f328(f206(x51842,x51843),x51844),x51841),f205(x51843)) % 154.70/154.56 [5185]E(x51851,f117(x51852))+~E(f328(f328(f156(x51852,x51851),x51853),x51854),f117(x51852)) % 154.70/154.56 [5217]E(x52171,x52172)+~E(f328(f328(f125(x52173),x52174),x52171),f328(f328(f125(x52173),x52174),x52172)) % 154.70/154.56 [5218]E(x52181,x52182)+~E(f328(f328(f125(x52183),x52181),x52184),f328(f328(f125(x52183),x52182),x52184)) % 154.70/154.56 [5371]P1(f328(x53713,x53712))+E(f167(x53711,x53712,f328(f133(x53711,x53713),x53714)),f328(f133(x53711,x53713),x53714)) % 154.70/154.56 [5374]~P1(f328(x53742,x53743))+P35(x53741,x53742,f328(f328(f148(x53741),x53743),x53744)) % 154.70/154.56 [5383]E(x53831,x53832)+~E(f136(a875,f328(f298(a875,x53831),x53833)),f328(f328(f148(a875),x53832),x53834)) % 154.70/154.56 [5431]~P28(x54312,x54313)+P28(x54311,f328(f328(f74(x54312,x54311),x54313),x54314)) % 154.70/154.56 [5432]~P39(x54322,x54323)+P39(x54321,f328(f328(f284(x54322,x54321),x54323),x54324)) % 154.70/154.56 [5556]~P35(x55561,x55562,x55564)+P35(x55561,x55562,f328(f328(f148(x55561),x55563),x55564)) % 154.70/154.56 [5557]~P35(x55571,x55572,x55574)+P35(x55571,x55572,f328(f328(f125(x55571),x55573),x55574)) % 154.70/154.56 [5558]~P35(x55581,x55582,x55583)+P35(x55581,x55582,f328(f328(f125(x55581),x55583),x55584)) % 154.70/154.56 [5644]~E(x56441,f117(x56442))+~E(f328(f328(f125(x56442),x56443),f328(f328(f148(x56442),x56444),f117(x56442))),x56441) % 154.70/154.56 [5669]~P33(x56693,x56691,f328(f328(f148(x56693),x56692),x56694))+P1(f328(x56691,x56692)) % 154.70/154.56 [5679]E(f118(x56791,x56792),x56793)+~E(f328(f328(f125(x56791),x56793),f328(f328(f148(x56791),x56794),f117(x56791))),x56792) % 154.70/154.56 [5680]E(f141(x56801,x56802),x56803)+~E(f328(f328(f125(x56801),x56804),f328(f328(f148(x56801),x56803),f117(x56801))),x56802) % 154.70/154.56 [5790]~E(f136(a875,f328(f298(a875,x57901),x57902)),f328(f328(f148(a875),x57903),x57904))+P1(f328(f328(f243(a875),x57901),x57902)) % 154.70/154.56 [5798]P33(x57981,x57982,x57983)+~P33(x57981,x57982,f328(f328(f148(x57981),x57984),x57983)) % 154.70/154.56 [5799]P33(x57991,x57992,x57993)+~P33(x57991,x57992,f328(f328(f125(x57991),x57994),x57993)) % 154.70/154.56 [5800]P33(x58001,x58002,x58003)+~P33(x58001,x58002,f328(f328(f125(x58001),x58003),x58004)) % 154.70/154.56 [5985]E(x59851,f328(f328(f125(x59852),f328(f166(x59852),x59853)),f328(f328(f148(x59852),x59854),f117(x59852))))+~E(f328(f166(x59852),x59851),f328(f328(f148(x59852),x59854),x59853)) % 154.70/154.56 [6162]~P107(x61621)+E(f328(f328(f105(f882(x61621,a870)),f328(f298(x61621,x61622),x61623)),f328(f298(x61621,x61623),x61624)),f192(f882(x61621,a870))) % 154.70/154.56 [6175]E(f328(f328(f162(x61751),f168(x61751,x61752,x61753)),x61754),x61753)+~P1(f328(f328(f243(a875),x61754),x61752)) % 154.70/154.56 [6202]~P66(x62021)+E(f328(f163(x62021),f328(f328(f151(a1,x62021),x62022),f177(x62023,x62024))),f328(f328(f6(a1,x62021),x62022),f328(f170(a1),f177(x62023,x62024)))) % 154.70/154.56 [6203]~P66(x62031)+E(f328(f328(f6(a1,x62031),x62032),f328(f170(a1),f177(x62033,x62034))),f328(f163(x62031),f328(f328(f151(a1,x62031),x62032),f177(x62033,x62034)))) % 154.70/154.56 [6344]~E(x63442,f328(f328(f125(x63441),f328(f166(x63441),x63444)),f328(f328(f148(x63441),x63443),f117(x63441))))+E(f328(f166(x63441),x63442),f328(f328(f148(x63441),x63443),x63444)) % 154.70/154.56 [6359]~P21(x63592,x63593,x63594,x63591)+E(f328(x63591,f192(f882(x63592,a870))),f34(x63593)) % 154.70/154.56 [6385]~P107(x63851)+E(f328(f328(f105(f882(x63851,a870)),f302(x63851,x63852,x63853)),f328(f298(x63851,x63853),x63854)),f192(f882(x63851,a870))) % 154.70/154.56 [6591]E(x65911,f192(f882(x65912,a870)))+~E(f315(x65913,x65912,x65914,x65911),f192(f882(f880(x65913,x65912),a870))) % 154.70/154.56 [6592]E(x65921,f192(f882(x65922,a870)))+~E(f315(x65922,x65923,x65921,x65924),f192(f882(f880(x65922,x65923),a870))) % 154.70/154.56 [6662]~P105(x66622)+E(f328(f193(f876(x66621)),f147(x66621,x66622,x66623,x66624)),f328(f193(f876(x66621)),x66624)) % 154.70/154.56 [6674]~P1(f328(f258(x66743,x66744,x66741),x66742))+P1(f328(f328(x66741,f572(x66742,x66741)),x66742)) % 154.70/154.56 [6714]~P1(f328(f61(x67142),x67144))+P1(f328(f61(x67141),f328(f307(x67142,x67141,x67143),x67144))) % 154.70/154.56 [6946]~P27(x69462,x69461,x69463,x69464)+E(f328(f37(x69461),f328(f307(x69462,x69461,x69463),x69464)),f328(f37(x69462),x69464)) % 154.70/154.56 [6965]E(f328(f307(x69651,x69652,x69653),f328(f308(x69651,x69652,x69653),x69654)),x69654)+~E(f328(f307(x69651,x69652,x69653),f251(f882(x69651,a870))),f251(f882(x69652,a870))) % 154.70/154.56 [7375]~P27(x73751,x73752,x73753,f251(f882(x73751,a870)))+E(f328(f308(x73751,x73752,x73753),f328(f307(x73751,x73752,x73753),x73754)),x73754) % 154.70/154.56 [7663]E(x76631,x76632)+~P1(f328(f328(f330(x76633),x76631),f328(f170(x76633),f168(x76633,x76634,x76632)))) % 154.70/154.56 [7672]~E(x76721,f2(a875))+~P1(f328(f328(f330(x76722),x76723),f328(f170(x76722),f168(x76722,x76721,x76724)))) % 154.70/154.56 [7708]P1(f328(x77081,x77082))+~P1(f328(f328(f330(x77083),x77082),f328(f170(x77083),f175(x77083,x77081,x77084)))) % 154.70/154.56 [7819]~P1(f328(f328(f330(f876(x78191)),f328(f328(f148(x78191),x78192),x78194)),f158(x78191,x78193)))+P1(f328(f328(f330(x78191),x78192),x78193)) % 154.70/154.56 [7948]~P1(f328(f328(f330(x79481),x79482),f328(f170(x79481),f174(x79481,x79483,x79484))))+P1(f328(f328(f330(x79481),x79482),f328(f170(x79481),x79483))) % 154.70/154.56 [7949]~P1(f328(f328(f330(x79491),x79492),f328(f170(x79491),f167(x79491,x79494,x79493))))+P1(f328(f328(f330(x79491),x79492),f328(f170(x79491),x79493))) % 154.70/154.56 [7950]~P1(f328(f328(f330(x79501),x79502),f328(f170(x79501),f175(x79501,x79504,x79503))))+P1(f328(f328(f330(x79501),x79502),f328(f170(x79501),x79503))) % 154.70/154.56 [7960]E(f328(f193(f876(x79601)),x79602),x79603)+~P1(f328(f328(f330(f876(x79601)),x79602),f328(f170(f876(x79601)),f54(x79601,x79603,x79604)))) % 154.70/154.56 [8051]P1(f328(x80513,x80512))+E(f328(f133(x80511,f328(f328(f8(a870,a870,x80511),a323),f328(a325,x80512))),f328(f133(x80511,x80513),x80514)),f328(f133(x80511,x80513),x80514)) % 154.70/154.56 [8171]E(f328(f328(f162(x81711),f175(x81711,x81712,x81713)),x81714),f328(f328(f162(x81711),x81713),x81714))+~P1(f328(f328(f243(a875),x81714),f328(f193(f876(x81711)),f175(x81711,x81712,x81713)))) % 154.70/154.56 [8263]~P66(x82631)+E(f328(f328(f6(a875,x82631),f328(f328(f8(a875,x82631,a875),x82632),a116)),f328(f298(a875,x82633),x82634)),f328(f328(f6(a875,x82631),x82632),f328(f298(a875,f328(a116,x82633)),f328(a116,x82634)))) % 154.70/154.56 [8273]~P66(x82731)+E(f328(f328(f6(a875,x82731),f328(f328(f8(a875,x82731,a875),x82732),a116)),f299(a875,x82733,x82734)),f328(f328(f6(a875,x82731),x82732),f299(a875,f328(a116,x82733),f328(a116,x82734)))) % 154.70/154.56 [8401]~P27(x84011,x84013,x84014,f251(f882(x84011,a870)))+P27(x84011,f882(x84012,x84013),f328(f328(f8(x84013,f882(x84012,x84013),x84011),f16(x84013,x84012)),x84014),f251(f882(x84011,a870))) % 154.70/154.56 [8486]~P27(x84862,x84861,x84864,x84863)+E(f328(f307(x84861,x84862,f77(x84862,x84861,x84863,x84864)),f328(f307(x84862,x84861,x84864),x84863)),x84863) % 154.70/154.56 [8551]~P1(f328(f328(f330(f881(x85511,x85511)),f328(f328(f263(x85511,x85511),x85512),x85514)),f260(x85511,x85513)))+P1(f328(f328(f330(x85511),x85512),x85513)) % 154.70/154.56 [8646]E(f328(f328(f328(f72(x86461,f879(x86462)),f328(f16(f879(x86462),x86461),f205(x86462))),x86463),f328(f235(x86462),f724(x86463,x86464,x86462,x86461))),x86464)+~E(f182(x86461,x86462,x86464),f328(f328(f306(x86461),x86463),f192(f882(x86461,a870)))) % 154.70/154.56 [8768]~E(f328(f328(f6(x87681,a875),x87684),x87683),f328(a116,x87682))+P1(f328(f328(f330(x87681),f864(x87682,x87683,x87684,x87681)),x87683)) % 154.70/154.56 [8788]~E(f328(f328(f6(x87884,a875),x87881),x87883),f328(a116,x87882))+P1(f328(f328(f243(a875),f2(a875)),f328(x87881,f864(x87882,x87883,x87881,x87884)))) % 154.70/154.56 [8799]~P1(f328(f61(x87992),x87994))+P1(f328(f328(f242(a875),f328(f37(x87991),f328(f307(x87992,x87991,x87993),x87994))),f328(f37(x87992),x87994))) % 154.70/154.56 [8800]E(f328(f328(f263(x88001,x88002),f655(x88003,x88004,x88002,x88001)),f656(x88003,x88004,x88002,x88001)),x88004)+~P1(f328(f328(f330(f881(x88001,x88002)),x88004),f328(f283(x88002,x88001),x88003))) % 154.70/154.56 [8808]P27(x88081,x88082,x88083,x88084)+P1(f328(f328(f330(x88081),f430(x88084,x88083,x88082,x88081)),x88084)) % 154.70/154.56 [8809]P27(x88091,x88092,x88093,x88094)+P1(f328(f328(f330(x88091),f435(x88094,x88093,x88092,x88091)),x88094)) % 154.70/154.56 [8870]P14(x88701,x88702,x88703,x88704)+P1(f328(f328(f330(f881(x88701,x88701)),f595(x88704,x88703,x88702,x88701)),x88703)) % 154.70/154.56 [8932]P1(f328(x89321,x89322))+~P1(f328(x89321,f328(f328(f263(x89323,x89324),f532(x89324,x89323,x89321)),f533(x89324,x89323,x89321)))) % 154.70/154.56 [8949]E(f328(f193(f876(x89491)),x89492),f328(f193(f876(x89491)),x89493))+~P1(f328(f328(f330(f881(f876(x89491),f876(x89491))),f328(f328(f263(f876(x89491),f876(x89491)),x89492),x89493)),f142(x89491,x89494))) % 154.70/154.56 [8950]E(f328(f193(f876(x89501)),x89502),f328(f193(f876(x89501)),x89503))+~P1(f328(f328(f330(f881(f876(x89501),f876(x89501))),f328(f328(f263(f876(x89501),f876(x89501)),x89502),x89503)),f154(x89501,x89504))) % 154.70/154.56 [8953]E(f328(f193(f876(x89531)),x89532),f328(f193(f876(x89531)),x89533))+~P1(f328(f328(f330(f881(f876(x89531),f876(x89531))),f328(f328(f263(f876(x89531),f876(x89531)),x89532),x89533)),f155(x89531,x89534))) % 154.70/154.56 [9027]P1(f328(f328(f242(a875),f152(x90271,x90272,x90273)),f152(x90271,x90274,x90273)))+P1(f328(f328(f330(x90271),f686(x90274,x90272,x90273,x90271)),f328(f170(x90271),x90273))) % 154.70/154.56 [9030]E(f328(f193(f876(x90301)),x90302),f328(f193(f876(x90301)),x90303))+~P1(f328(f328(f330(f881(f876(x90301),f876(x90301))),f328(f328(f263(f876(x90301),f876(x90301)),x90302),x90303)),f304(f876(x90301),f154(x90301,x90304)))) % 154.70/154.56 [9267]~P27(x92671,x92672,x92673,x92674)+~P1(f328(f328(f243(a875),f328(f37(x92672),f328(f307(x92671,x92672,x92673),x92674))),f328(f37(x92671),x92674))) % 154.70/154.56 [9313]~P1(f328(f328(f330(f881(f876(x93131),f876(x93131))),f328(f328(f263(f876(x93131),f876(x93131)),x93132),x93133)),f154(x93131,x93134)))+P1(f328(f328(f330(f881(f876(x93131),f876(x93131))),f328(f328(f263(f876(x93131),f876(x93131)),x93132),x93133)),f155(x93131,f304(x93131,x93134)))) % 154.70/154.56 [9317]~P1(f328(f328(f330(f881(f876(x93171),f876(x93171))),f328(f328(f263(f876(x93171),f876(x93171)),x93172),x93173)),f155(x93171,x93174)))+P1(f328(f328(f330(f881(f876(x93171),f876(x93171))),f328(f328(f263(f876(x93171),f876(x93171)),x93172),x93173)),f304(f876(x93171),f154(x93171,x93174)))) % 154.70/154.56 [9334]P1(f328(f328(f330(f881(x93341,x93341)),f328(f328(f263(x93341,x93341),x93342),x93343)),f304(x93341,x93344)))+~P1(f328(f328(f330(f881(x93341,x93341)),f328(f328(f263(x93341,x93341),x93342),x93343)),f328(f328(f285(x93341,x93341,x93341),x93344),f304(x93341,x93344)))) % 154.70/154.56 [9516]E(f328(f328(f125(x95161),f700(x95162,x95163,x95164,x95161)),f328(f328(f148(x95161),f701(x95162,x95163,x95164,x95161)),f703(x95162,x95163,x95164,x95161))),x95164)+~P1(f328(f328(f330(f881(f876(x95161),f876(x95161))),f328(f328(f263(f876(x95161),f876(x95161)),x95164),x95163)),f154(x95161,x95162))) % 154.70/154.56 [9517]E(f328(f328(f125(x95171),f700(x95172,x95173,x95174,x95171)),f328(f328(f148(x95171),f702(x95172,x95173,x95174,x95171)),f703(x95172,x95173,x95174,x95171))),x95173)+~P1(f328(f328(f330(f881(f876(x95171),f876(x95171))),f328(f328(f263(f876(x95171),f876(x95171)),x95174),x95173)),f154(x95171,x95172))) % 154.70/154.56 [9594]P1(f328(f328(f330(f881(x95941,x95941)),f328(f328(f263(x95941,x95941),x95942),f648(x95943,x95944,x95942,x95941))),f304(x95941,x95943)))+~P1(f328(f328(f330(f881(x95941,x95941)),f328(f328(f263(x95941,x95941),x95942),x95944)),f328(f328(f285(x95941,x95941,x95941),x95943),f304(x95941,x95943)))) % 154.70/154.56 [9663]P1(f328(f328(f242(a875),f152(x96631,x96632,x96633)),f152(x96631,x96634,x96633)))+~P1(f328(f328(f243(a875),f328(x96632,f686(x96634,x96632,x96633,x96631))),f328(x96634,f686(x96634,x96632,x96633,x96631)))) % 154.70/154.56 [9731]P1(f328(f328(f330(f881(x97311,x97311)),f328(f328(f263(x97311,x97311),f647(x97312,x97313,x97314,x97311)),x97313)),f304(x97311,x97312)))+~P1(f328(f328(f330(f881(x97311,x97311)),f328(f328(f263(x97311,x97311),x97314),x97313)),f328(f328(f285(x97311,x97311,x97311),x97312),f304(x97311,x97312)))) % 154.70/154.56 [5199]~E(x51992,x51993)+E(f167(x51991,x51992,f328(f328(f148(x51991),x51993),x51994)),x51994) % 154.70/154.56 [5326]P1(f328(x53262,x53263))+E(f175(x53261,x53262,f328(f328(f148(x53261),x53263),x53264)),f117(x53261)) % 154.70/154.56 [5395]~P86(x53952)+E(f328(f328(f79(f882(x53951,x53952)),x53953),x53954),f328(f79(x53952),f328(x53953,x53954))) % 154.70/154.56 [5407]~E(x54072,f2(a875))+E(f328(f328(f135(x54071),x54072),f328(f328(f148(x54071),x54073),x54074)),f328(f328(f148(x54071),x54073),x54074)) % 154.70/154.56 [5408]P1(f328(x54082,x54083))+E(f328(f133(x54081,x54082),f328(f328(f148(x54081),x54083),x54084)),f328(f133(x54081,x54082),x54084)) % 154.70/154.56 [5539]~E(x55392,x55394)+P1(f328(f328(f328(f306(x55391),x55392),x55393),x55394)) % 154.70/154.56 [5547]E(x55471,f117(x55472))+E(f141(x55473,f328(f328(f151(x55472,x55473),x55474),x55471)),f328(x55474,f141(x55472,x55471))) % 154.70/154.56 [5561]~E(x55611,f63(x55612,x55614))+E(f328(x55611,f328(f328(f306(x55612),x55613),f192(f882(x55612,a870)))),x55613) % 154.70/154.56 [5596]E(x55961,f117(x55962))+E(f328(f138(x55963),f328(f328(f151(x55962,x55963),x55964),x55961)),f328(x55964,f328(f138(x55962),x55961))) % 154.70/154.56 [5699]~P1(f328(x56993,x56994))+P1(f328(f328(f328(f306(x56991),x56992),x56993),x56994)) % 154.70/154.56 [5815]~P20(x58152,x58154,x58151)+E(f328(x58151,f328(f328(f306(x58152),x58153),f192(f882(x58152,a870)))),x58153) % 154.70/154.56 [5839]~E(x58392,x58393)+P1(f328(f328(f330(x58391),x58392),f328(f328(f306(x58391),x58393),x58394))) % 154.70/154.56 [5843]~P2(x58431)+E(f328(f328(f114(x58431),x58432),f328(f328(f114(x58431),x58433),x58434)),f328(f328(f114(x58431),x58433),f328(f328(f114(x58431),x58432),x58434))) % 154.70/154.56 [5845]~P99(x58451)+E(f328(f328(f114(x58451),x58452),f328(f328(f114(x58451),x58453),x58454)),f328(f328(f114(x58451),x58453),f328(f328(f114(x58451),x58452),x58454))) % 154.70/154.56 [5846]~P2(x58461)+E(f328(f328(f105(x58461),x58462),f328(f328(f105(x58461),x58463),x58464)),f328(f328(f105(x58461),x58463),f328(f328(f105(x58461),x58462),x58464))) % 154.70/154.56 [5848]~P100(x58481)+E(f328(f328(f105(x58481),x58482),f328(f328(f105(x58481),x58483),x58484)),f328(f328(f105(x58481),x58483),f328(f328(f105(x58481),x58482),x58484))) % 154.70/154.56 [5849]~P109(x58491)+E(f328(f328(f80(x58491),x58492),f328(f328(f80(x58491),x58493),x58494)),f328(f328(f80(x58491),x58493),f328(f328(f80(x58491),x58492),x58494))) % 154.70/154.56 [5850]~P109(x58501)+E(f328(f328(f81(x58501),x58502),f328(f328(f81(x58501),x58503),x58504)),f328(f328(f81(x58501),x58503),f328(f328(f81(x58501),x58502),x58504))) % 154.70/154.56 [5852]~P105(x58521)+E(f328(f328(f240(x58521),x58522),f328(f328(f240(x58521),x58523),x58524)),f328(f328(f240(x58521),x58523),f328(f328(f240(x58521),x58522),x58524))) % 154.70/154.56 [5854]~P105(x58541)+E(f328(f328(f241(x58541),x58542),f328(f328(f241(x58541),x58543),x58544)),f328(f328(f241(x58541),x58543),f328(f328(f241(x58541),x58542),x58544))) % 154.70/154.56 [5859]E(x58591,x58592)+E(f167(x58593,x58591,f328(f328(f148(x58593),x58592),x58594)),f328(f328(f148(x58593),x58592),f167(x58593,x58591,x58594))) % 154.70/154.56 [5872]~P1(f328(x58722,x58723))+E(f328(f133(x58721,x58722),f328(f328(f148(x58721),x58723),x58724)),f328(f328(f148(x58721),x58723),f328(f133(x58721,x58722),x58724))) % 154.70/154.56 [6005]~P1(f328(x60052,x60053))+E(f175(x60051,x60052,f328(f328(f148(x60051),x60053),x60054)),f328(f328(f148(x60051),x60053),f175(x60051,x60052,x60054))) % 154.70/154.56 [6056]P26(x60561,x60562,x60563)+~P26(x60561,x60562,f328(f328(f306(f874(x60561)),x60564),x60563)) % 154.70/154.56 [6069]E(x60691,f192(f882(x60692,a870)))+E(f328(f328(f41(x60692,f882(x60693,a870)),x60691),f328(f16(f882(x60693,a870),x60692),x60694)),x60694) % 154.70/154.56 [6070]E(x60701,f192(f882(x60702,a870)))+E(f328(f328(f42(x60702,f882(x60703,a870)),x60701),f328(f16(f882(x60703,a870),x60702),x60704)),x60704) % 154.70/154.56 [6079]~E(x60794,f192(f882(x60792,a870)))+E(f328(f328(f265(x60791,x60792),x60793),f328(f16(f882(x60792,a870),x60791),x60794)),f192(f882(f881(x60791,x60792),a870))) % 154.70/154.56 [6080]~E(x60803,f192(f882(x60801,a870)))+E(f328(f328(f265(x60801,x60802),x60803),f328(f16(f882(x60802,a870),x60801),x60804)),f192(f882(f881(x60801,x60802),a870))) % 154.70/154.56 [6126]E(x61261,f2(a875))+E(f328(f328(f135(x61262),x61261),f328(f328(f148(x61262),x61263),x61264)),f328(f328(f135(x61262),f328(f328(f22(a875),x61261),f78(a875))),x61264)) % 154.70/154.56 [6156]E(x61561,f192(f882(x61562,a870)))+E(f328(f307(x61562,x61563,f328(f16(x61563,x61562),x61564)),x61561),f328(f328(f306(x61563),x61564),f192(f882(x61563,a870)))) % 154.70/154.56 [6159]E(f328(f308(x61591,x61592,f328(f16(x61592,x61591),x61593)),x61594),f192(f882(x61591,a870)))+P1(f328(f328(f330(x61592),x61593),x61594)) % 154.70/154.56 [6228]~E(x62283,f192(f882(x62281,a870)))+E(f328(f328(f41(x62281,f882(x62282,a870)),x62283),f328(f16(f882(x62282,a870),x62281),x62284)),f192(f882(x62282,a870))) % 154.70/154.56 [6229]~E(x62293,f192(f882(x62291,a870)))+E(f328(f328(f42(x62291,f882(x62292,a870)),x62293),f328(f16(f882(x62292,a870),x62291),x62294)),f251(f882(x62292,a870))) % 154.70/154.56 [6231]~P57(x62311)+E(f44(x62311,f328(f328(f81(x62311),x62312),x62313),f328(f328(f81(x62311),x62312),x62314)),f328(f328(f81(x62311),x62312),f44(x62311,x62313,x62314))) % 154.70/154.56 [6395]E(f328(f308(x63951,x63952,f328(f16(x63952,x63951),x63953)),x63954),f251(f882(x63951,a870)))+~P1(f328(f328(f330(x63952),x63953),x63954)) % 154.70/154.56 [6418]~P1(f328(f328(f330(x64181),x64182),x64184))+P1(f328(f328(f330(x64181),x64182),f328(f328(f306(x64181),x64183),x64184))) % 154.70/154.56 [6423]P1(f328(x64231,x64232))+~P1(f328(f157(x64233,x64231),f328(f328(f148(x64233),x64232),x64234))) % 154.70/154.56 [6432]~E(x64323,f328(f328(f22(a875),f328(f193(f876(x64321)),x64322)),f78(a875)))+E(f118(x64321,f328(f328(f156(x64321,x64322),x64323),x64324)),f118(x64321,x64322)) % 154.70/154.56 [6451]~P105(x64511)+E(f328(f328(f105(f882(x64511,a870)),f328(f297(x64511),x64512)),f299(x64511,x64513,x64514)),f299(x64511,x64513,f328(f328(f240(x64511),x64512),x64514))) % 154.70/154.56 [6452]~P105(x64521)+E(f328(f328(f105(f882(x64521,a870)),f328(f250(x64521),x64522)),f299(x64521,x64523,x64524)),f299(x64521,f328(f328(f241(x64521),x64522),x64523),x64524)) % 154.70/154.56 [6467]E(f328(f328(f105(f882(x64671,a870)),x64672),f328(f328(f306(x64671),x64673),x64674)),f328(f328(f105(f882(x64671,a870)),x64672),x64674))+P1(f328(f328(f330(x64671),x64673),x64672)) % 154.70/154.56 [6479]E(f167(x64791,x64792,f328(f328(f125(x64791),x64793),x64794)),f328(f328(f125(x64791),x64793),f167(x64791,x64792,x64794)))+P1(f328(f328(f330(x64791),x64792),f328(f170(x64791),x64793))) % 154.70/154.56 [6483]~P79(x64831)+E(f328(f328(f81(x64831),f328(f328(f253(x64831),x64832),x64833)),f328(f328(f253(x64831),x64832),x64834)),f328(f328(f253(x64831),x64832),f328(f328(f80(a875),x64833),x64834))) % 154.70/154.56 [6484]~P109(x64841)+E(f328(f328(f81(x64841),f328(f328(f253(x64841),x64842),x64843)),f328(f328(f253(x64841),x64842),x64844)),f328(f328(f253(x64841),x64842),f328(f328(f80(a875),x64843),x64844))) % 154.70/154.56 [6520]~P96(x65201)+E(f328(f328(f105(x65201),f328(f328(f114(x65201),x65202),x65203)),f328(f328(f114(x65201),x65202),x65204)),f328(f328(f114(x65201),x65202),f328(f328(f105(x65201),x65203),x65204))) % 154.70/154.56 [6521]~P96(x65211)+E(f328(f328(f114(x65211),f328(f328(f105(x65211),x65212),x65213)),f328(f328(f105(x65211),x65212),x65214)),f328(f328(f105(x65211),x65212),f328(f328(f114(x65211),x65213),x65214))) % 154.70/154.56 [6522]~P109(x65221)+E(f328(f328(f80(x65221),f328(f328(f81(x65221),x65222),x65223)),f328(f328(f81(x65221),x65222),x65224)),f328(f328(f81(x65221),x65222),f328(f328(f80(x65221),x65223),x65224))) % 154.70/154.56 [6523]~P105(x65231)+E(f328(f328(f241(x65231),f328(f328(f240(x65231),x65232),x65233)),f328(f328(f240(x65231),x65232),x65234)),f328(f328(f240(x65231),x65232),f328(f328(f241(x65231),x65233),x65234))) % 154.70/154.56 [6524]~P105(x65241)+E(f328(f328(f240(x65241),f328(f328(f241(x65241),x65242),x65243)),f328(f328(f241(x65241),x65242),x65244)),f328(f328(f241(x65241),x65242),f328(f328(f240(x65241),x65243),x65244))) % 154.70/154.56 [6555]~P57(x65551)+E(f44(x65551,f328(f328(f81(x65551),x65552),x65553),f328(f328(f81(x65551),x65554),x65553)),f328(f328(f81(x65551),f44(x65551,x65552,x65554)),x65553)) % 154.70/154.56 [6558]~E(f328(f193(f876(x65581)),x65583),f328(f193(f876(x65582)),x65584))+E(f328(f328(f151(f881(x65581,x65582),x65582),f266(x65581,x65582)),f328(f328(f180(x65581,x65582),x65583),x65584)),x65584) % 154.70/154.56 [6559]~E(f328(f193(f876(x65591)),x65593),f328(f193(f876(x65592)),x65594))+E(f328(f328(f151(f881(x65591,x65592),x65591),f262(x65591,x65592)),f328(f328(f180(x65591,x65592),x65593),x65594)),x65593) % 154.70/154.56 [6565]P1(f328(f157(x65651,x65652),x65653))+~P1(f328(f157(x65651,x65652),f328(f328(f148(x65651),x65654),x65653))) % 154.70/154.56 [6566]P1(f328(f157(x65661,x65662),x65663))+~P1(f328(f157(x65661,x65662),f328(f328(f125(x65661),x65664),x65663))) % 154.70/154.56 [6567]P1(f328(f157(x65671,x65672),x65673))+~P1(f328(f157(x65671,x65672),f328(f328(f125(x65671),x65673),x65674))) % 154.70/154.56 [6572]~P58(x65721)+E(f44(x65721,f328(f328(f22(x65721),x65722),f44(x65721,x65723,x65724)),x65724),f44(x65721,f328(f328(f22(x65721),x65722),x65723),x65724)) % 154.70/154.56 [6574]~P57(x65741)+E(f44(x65741,f328(f328(f81(x65741),x65742),f44(x65741,x65743,x65744)),x65744),f44(x65741,f328(f328(f81(x65741),x65742),x65743),x65744)) % 154.70/154.56 [6575]~P57(x65751)+E(f44(x65751,f328(f328(f80(x65751),x65752),f44(x65751,x65753,x65754)),x65754),f44(x65751,f328(f328(f80(x65751),x65752),x65753),x65754)) % 154.70/154.56 [6656]~P105(x66561)+E(f328(f328(f105(f882(x66561,a870)),f299(x66561,x66562,x66563)),f328(f297(x66561),x66564)),f299(x66561,x66562,f328(f328(f240(x66561),x66563),x66564))) % 154.70/154.56 [6657]~P105(x66571)+E(f328(f328(f105(f882(x66571,a870)),f299(x66571,x66572,x66573)),f328(f250(x66571),x66574)),f299(x66571,f328(f328(f241(x66571),x66572),x66574),x66573)) % 154.70/154.56 [6660]~E(f328(f193(f876(x66601)),x66603),f328(f193(f876(x66602)),x66604))+E(f328(f328(f180(x66601,x66602),f328(f166(x66601),x66603)),f328(f166(x66602),x66604)),f328(f166(f881(x66601,x66602)),f328(f328(f180(x66601,x66602),x66603),x66604))) % 154.70/154.56 [6670]E(x66701,f328(f328(f22(a875),f328(f193(f876(x66702)),x66703)),f78(a875)))+E(f118(x66702,f328(f328(f156(x66702,x66703),x66701),x66704)),f328(f328(f156(x66702,f118(x66702,x66703)),x66701),x66704)) % 154.70/154.56 [6685]~P1(f328(f134(x66852),x66854))+P1(f328(f134(f881(x66851,x66852)),f328(f328(f180(x66851,x66852),x66853),x66854))) % 154.70/154.56 [6686]~P1(f328(f134(x66861),x66863))+P1(f328(f134(f881(x66861,x66862)),f328(f328(f180(x66861,x66862),x66863),x66864))) % 154.70/154.56 [6949]E(f328(f328(f38(a875),x69491),x69492),x69493)+~P1(f328(f47(x69491,x69492),f328(f328(f263(a875,a875),x69493),x69494))) % 154.70/154.56 [6973]E(f44(a875,x69731,x69732),x69733)+~P1(f328(f47(x69731,x69732),f328(f328(f263(a875,a875),x69734),x69733))) % 154.70/154.56 [6976]P1(f328(f134(x69761),x69762))+~P1(f328(f134(x69763),f328(f328(f151(x69761,x69763),x69764),x69762))) % 154.70/154.56 [6984]~P26(x69841,x69842,f328(f328(f306(f874(x69841)),x69843),x69844))+P26(x69841,x69842,f328(f328(f306(f874(x69841)),x69843),f192(f882(f874(x69841),a870)))) % 154.70/154.56 [7060]E(f167(x70601,x70602,f328(f328(f125(x70601),x70603),x70604)),f328(f328(f125(x70601),f167(x70601,x70602,x70603)),x70604))+~P1(f328(f328(f330(x70601),x70602),f328(f170(x70601),x70603))) % 154.70/154.56 [7150]~P58(x71501)+E(f44(x71501,f328(f328(f22(x71501),f44(x71501,x71502,x71503)),x71504),x71503),f44(x71501,f328(f328(f22(x71501),x71502),x71504),x71503)) % 154.70/154.56 [7153]~P57(x71531)+E(f44(x71531,f328(f328(f80(x71531),f44(x71531,x71532,x71533)),x71534),x71533),f44(x71531,f328(f328(f80(x71531),x71532),x71534),x71533)) % 154.70/154.56 [7154]~P57(x71541)+E(f44(x71541,f328(f328(f81(x71541),f44(x71541,x71542,x71543)),x71544),x71543),f44(x71541,f328(f328(f81(x71541),x71542),x71544),x71543)) % 154.70/154.56 [7171]P1(f328(f328(f328(a198,x71711),x71712),x71713))+~P1(f328(f328(f328(f328(a200,x71711),x71712),x71714),x71713)) % 154.70/154.56 [7346]~E(x73461,f328(f328(f148(x73462),x73463),x73464))+~P1(f328(f328(f242(a875),f328(f193(f876(x73462)),x73461)),f328(f193(f876(x73462)),x73464))) % 154.70/154.56 [7421]~E(f328(f176(x74211,x74212),x74213),f328(f176(x74211,x74212),x74214))+E(f328(f307(f881(x74211,x74212),x74211,f262(x74211,x74212)),f328(f170(f881(x74211,x74212)),x74213)),f328(f307(f881(x74211,x74212),x74211,f262(x74211,x74212)),f328(f170(f881(x74211,x74212)),x74214))) % 154.70/154.56 [7554]P27(x75541,x75542,x75543,f328(f170(x75541),x75544))+~P1(f328(f134(x75542),f328(f328(f151(x75541,x75542),x75543),x75544))) % 154.70/154.56 [7630]~P1(f328(f328(f242(f882(x76301,a870)),x76302),x76304))+P1(f328(f328(f242(f882(x76301,a870)),x76302),f328(f328(f306(x76301),x76303),x76304))) % 154.70/154.56 [7664]~P58(x76641)+E(f44(x76641,f328(f328(f22(x76641),f44(x76641,x76642,x76643)),f44(x76641,x76644,x76643)),x76643),f44(x76641,f328(f328(f22(x76641),x76642),x76644),x76643)) % 154.70/154.56 [7665]~P57(x76651)+E(f44(x76651,f328(f328(f80(x76651),f44(x76651,x76652,x76653)),f44(x76651,x76654,x76653)),x76653),f44(x76651,f328(f328(f80(x76651),x76652),x76654),x76653)) % 154.70/154.56 [7666]~P57(x76661)+E(f44(x76661,f328(f328(f81(x76661),f44(x76661,x76662,x76663)),f44(x76661,x76664,x76663)),x76663),f44(x76661,f328(f328(f81(x76661),x76662),x76664),x76663)) % 154.70/154.56 [7766]P1(f328(f328(f328(f328(a200,x77661),x77662),f328(a116,x77663)),x77664))+~P1(f328(f328(f328(f328(a200,x77661),x77662),x77663),x77664)) % 154.70/154.56 [7773]~E(f328(x77734,f764(x77734,x77733,x77731,x77732)),f192(f882(x77732,a870)))+E(f328(f328(f41(x77731,f882(x77732,a870)),x77733),x77734),f192(f882(x77732,a870))) % 154.70/154.56 [7774]~E(f328(x77744,f830(x77744,x77743,x77741,x77742)),f251(f882(x77742,a870)))+E(f328(f328(f42(x77741,f882(x77742,a870)),x77743),x77744),f251(f882(x77742,a870))) % 154.70/154.56 [7775]~E(f328(x77754,f765(x77754,x77753,x77752,x77751)),f192(f882(x77752,a870)))+E(f328(f328(f41(x77751,f882(x77752,a870)),x77753),x77754),f192(f882(x77752,a870))) % 154.70/154.56 [7776]~E(f328(x77764,f835(x77764,x77763,x77762,x77761)),f251(f882(x77762,a870)))+E(f328(f328(f42(x77761,f882(x77762,a870)),x77763),x77764),f251(f882(x77762,a870))) % 154.70/154.56 [8172]P1(f328(x81721,x81722))+~P1(f328(f328(f330(x81723),x81722),f328(f328(f105(f882(x81723,a870)),x81724),f328(f248(x81723),x81721)))) % 154.70/154.56 [8216]~P1(f328(f328(f242(f882(x82161,a870)),x82163),x82164))+P1(f328(f328(f242(f882(x82161,a870)),f328(f328(f306(x82161),x82162),x82163)),f328(f328(f306(x82161),x82162),x82164))) % 154.70/154.56 [8391]P1(f328(x83912,x83913))+E(f328(f328(f135(x83911),f328(f193(f876(x83911)),f175(x83911,x83912,f328(f328(f148(x83911),x83913),x83914)))),f328(f328(f148(x83911),x83913),x83914)),f328(f328(f148(x83911),x83913),x83914)) % 154.70/154.56 [8500]P1(f328(f328(f328(a198,x85001),x85002),f446(x85003,x85002,x85004,x85001)))+~P1(f328(f328(f328(a198,f33(x85001,x85004)),x85002),x85003)) % 154.70/154.56 [8501]P1(f328(f328(f328(a198,x85011),x85012),f473(x85013,x85012,x85014,x85011)))+~P1(f328(f328(f328(a198,f33(x85011,x85014)),x85012),x85013)) % 154.70/154.56 [8502]~P1(f328(f328(f243(a875),f328(x85024,x85022)),f328(x85024,x85023)))+P1(f328(f328(f330(f881(x85021,x85021)),f328(f328(f263(x85021,x85021),x85022),x85023)),f328(f328(f284(a875,x85021),a247),x85024))) % 154.70/154.56 [8600]~P1(f328(x86002,f784(x86004,x86002,x86003,x86001)))+E(f175(x86001,x86002,f328(f328(f125(x86001),x86003),x86004)),f328(f328(f125(x86001),x86003),f175(x86001,x86002,x86004))) % 154.70/154.56 [8673]P27(f876(x86731),f876(x86732),f328(f151(x86731,x86732),x86733),x86734)+~P27(x86731,x86732,x86733,f39(f882(x86731,a870),f328(f307(f876(x86731),f882(x86731,a870),f170(x86731)),x86734))) % 154.70/154.56 [8740]~P1(f328(x87402,x87403))+E(f328(f328(f135(x87401),f328(f193(f876(x87401)),f175(x87401,x87402,f328(f328(f148(x87401),x87403),x87404)))),f328(f328(f148(x87401),x87403),x87404)),f328(f328(f135(x87401),f328(f193(f876(x87401)),f175(x87401,x87402,x87404))),x87404)) % 154.70/154.56 [8779]~E(x87792,x87793)+E(f328(f133(x87791,f328(f328(f8(a870,a870,x87791),a323),f328(a325,x87792))),f328(f328(f148(x87791),x87793),x87794)),f328(f133(x87791,f328(f328(f8(a870,a870,x87791),a323),f328(a325,x87792))),x87794)) % 154.70/154.56 [8789]E(f328(f328(f41(x87891,f882(x87892,a870)),x87893),x87894),f192(f882(x87892,a870)))+P1(f328(f328(f330(x87891),f764(x87894,x87893,x87891,x87892)),x87893)) % 154.70/154.56 [8790]E(f328(f328(f42(x87901,f882(x87902,a870)),x87903),x87904),f251(f882(x87902,a870)))+P1(f328(f328(f330(x87901),f830(x87904,x87903,x87901,x87902)),x87903)) % 154.70/154.56 [8791]E(f328(f328(f41(x87911,f882(x87912,a870)),x87913),x87914),f192(f882(x87912,a870)))+P1(f328(f328(f330(x87911),f765(x87914,x87913,x87912,x87911)),x87913)) % 154.70/154.56 [8792]E(f328(f328(f42(x87921,f882(x87922,a870)),x87923),x87924),f251(f882(x87922,a870)))+P1(f328(f328(f330(x87921),f835(x87924,x87923,x87922,x87921)),x87923)) % 154.70/154.56 [8828]P1(f328(f328(f243(a875),f328(x88281,x88282)),f328(x88281,x88283)))+~P1(f328(f328(f330(f881(x88284,x88284)),f328(f328(f263(x88284,x88284),x88282),x88283)),f328(f328(f284(a875,x88284),a247),x88281))) % 154.70/154.56 [8849]E(f175(x88491,x88492,f328(f328(f125(x88491),x88493),x88494)),f328(f328(f125(x88491),x88493),f175(x88491,x88492,x88494)))+P1(f328(f328(f330(x88491),f784(x88494,x88492,x88493,x88491)),f328(f170(x88491),x88493))) % 154.70/154.56 [8966]P1(f328(f328(f328(a198,x89661),f446(x89662,x89663,x89661,x89664)),x89662))+~P1(f328(f328(f328(a198,f33(x89664,x89661)),x89663),x89662)) % 154.70/154.56 [8967]P1(f328(f328(f328(a198,x89671),f473(x89672,x89673,x89671,x89674)),x89672))+~P1(f328(f328(f328(a198,f33(x89674,x89671)),x89673),x89672)) % 154.70/154.56 [9016]P1(f328(f328(f330(x90161),f517(x90162,x90163,x90164,x90161)),x90163))+~P1(f328(f328(f330(f882(x90161,a870)),x90164),f328(f328(f60(x90161),x90163),x90162))) % 154.70/154.56 [9019]E(x90191,x90192)+~P1(f328(f328(f330(f881(x90193,x90193)),f328(f328(f263(x90193,x90193),x90191),x90192)),f328(f328(f187(f881(x90193,x90193),a870),f2(a875)),x90194))) % 154.70/154.56 [9101]E(f328(f282(x91011,x91011,x91012),f328(f328(f306(x91011),f517(x91012,x91013,x91014,x91011)),f192(f882(x91011,a870)))),x91014)+~P1(f328(f328(f330(f882(x91011,a870)),x91014),f328(f328(f60(x91011),x91013),x91012))) % 154.70/154.56 [9106]~P1(f328(f328(f330(f881(x91061,x91061)),f328(f328(f263(x91061,x91061),x91063),x91062)),f304(x91061,x91064)))+P1(f328(f328(f330(f881(x91061,x91061)),f328(f328(f263(x91061,x91061),x91062),x91063)),f304(x91061,f328(f283(x91061,x91061),x91064)))) % 154.70/154.56 [9118]~P57(x91181)+E(f328(f328(f80(x91181),f328(f328(f80(x91181),f328(f328(f81(x91181),x91182),f328(f328(f38(x91181),x91183),x91182))),f44(x91181,x91183,x91182))),x91184),f328(f328(f80(x91181),x91183),x91184)) % 154.70/154.56 [9128]~P1(f328(f328(f330(x91281),x91283),x91284))+P1(f328(f328(f330(f882(x91281,a870)),f328(f282(x91281,x91281,x91282),f328(f328(f306(x91281),x91283),f192(f882(x91281,a870))))),f328(f328(f60(x91281),x91284),x91282))) % 154.70/154.56 [9139]P1(f328(f328(f330(f881(x91391,x91391)),f328(f328(f263(x91391,x91391),x91392),x91393)),f304(x91391,x91394)))+~P1(f328(f328(f330(f881(x91391,x91391)),f328(f328(f263(x91391,x91391),x91393),x91392)),f304(x91391,f328(f283(x91391,x91391),x91394)))) % 154.70/154.56 [9231]E(f328(f328(f156(x92311,f328(f166(x92311),x92312)),f328(f328(f22(a875),f328(f328(f22(a875),f328(f193(f876(x92311)),x92312)),x92313)),f78(a875))),x92314),f328(f166(x92311),f328(f328(f156(x92311,x92312),x92313),x92314)))+~P1(f328(f328(f243(a875),x92313),f328(f193(f876(x92311)),x92312))) % 154.70/154.56 [9234]~P1(f328(x92342,f775(x92344,x92342,x92343,x92341)))+E(f328(f328(f135(x92341),f328(f193(f876(x92341)),f175(x92341,x92342,f328(f328(f125(x92341),x92343),x92344)))),f328(f328(f125(x92341),x92343),x92344)),f328(f328(f135(x92341),f328(f193(f876(x92341)),f175(x92341,x92342,x92344))),x92344)) % 154.70/154.56 [9273]~P27(x92732,x92731,x92733,f251(f882(x92732,a870)))+P1(f328(f328(f242(f882(x92731,a870)),f328(f307(x92732,x92731,x92733),f328(f79(f882(x92732,a870)),x92734))),f328(f79(f882(x92731,a870)),f328(f307(x92732,x92731,x92733),x92734)))) % 154.70/154.56 [9286]~P5(x92861)+E(f328(f139(x92861,x92862,f328(f7(x92862,x92861,x92861),f328(f328(f8(x92861,f882(x92861,x92861),x92862),f114(x92861)),x92863)),f192(x92861)),x92864),f328(f328(f41(x92862,x92861),f328(f170(x92862),x92864)),x92863)) % 154.70/154.56 [9287]~P5(x92871)+E(f328(f139(x92871,x92872,f328(f7(x92872,x92871,x92871),f328(f328(f8(x92871,f882(x92871,x92871),x92872),f105(x92871)),x92873)),f251(x92871)),x92874),f328(f328(f42(x92872,x92871),f328(f170(x92872),x92874)),x92873)) % 154.70/154.56 [9299]E(f328(f328(f135(x92991),f328(f193(f876(x92991)),f175(x92991,x92992,f328(f328(f125(x92991),x92993),x92994)))),f328(f328(f125(x92991),x92993),x92994)),f328(f328(f135(x92991),f328(f193(f876(x92991)),f175(x92991,x92992,x92994))),x92994))+P1(f328(f328(f330(x92991),f775(x92994,x92992,x92993,x92991)),f328(f170(x92991),x92993))) % 154.70/154.56 [9367]~P1(f328(f328(f330(f881(f876(x93674),f876(x93674))),f328(f328(f263(f876(x93674),f876(x93674)),x93673),x93672)),f154(x93674,x93671)))+P1(f328(f328(f243(a875),f688(x93671,x93672,x93673,x93674)),f328(f193(f876(x93674)),x93673))) % 154.70/154.56 [9368]~P57(x93681)+E(f328(f328(f80(x93681),f328(f328(f80(x93681),f328(f328(f81(x93681),f328(f328(f38(x93681),x93682),x93683)),x93683)),f44(x93681,x93682,x93683))),x93684),f328(f328(f80(x93681),x93682),x93684)) % 154.70/154.56 [9395]~P1(f328(f328(f330(f881(f876(x93951),f876(x93951))),f328(f328(f263(f876(x93951),f876(x93951)),x93952),x93953)),f328(f283(f876(x93951),f876(x93951)),f154(x93951,x93954))))+P1(f328(f328(f330(f881(f876(x93951),f876(x93951))),f328(f328(f263(f876(x93951),f876(x93951)),x93952),x93953)),f154(x93951,f328(f283(x93951,x93951),x93954)))) % 154.70/154.56 [9396]P1(f328(f328(f330(f881(f876(x93961),f876(x93961))),f328(f328(f263(f876(x93961),f876(x93961)),x93962),x93963)),f328(f283(f876(x93961),f876(x93961)),f154(x93961,x93964))))+~P1(f328(f328(f330(f881(f876(x93961),f876(x93961))),f328(f328(f263(f876(x93961),f876(x93961)),x93962),x93963)),f154(x93961,f328(f283(x93961,x93961),x93964)))) % 154.70/154.56 [9431]~P1(f328(f328(f330(x94311),x94313),f328(f261(x94311,x94312),x94314)))+P1(f328(f328(f330(f881(x94311,x94312)),f328(f328(f263(x94311,x94312),x94313),f579(x94314,x94312,x94313,x94311))),x94314)) % 154.70/154.56 [9432]~P1(f328(f328(f330(x94321),x94323),f328(f261(x94321,x94322),x94324)))+P1(f328(f328(f330(f881(x94321,x94322)),f328(f328(f263(x94321,x94322),x94323),f583(x94324,x94322,x94323,x94321))),x94324)) % 154.70/154.56 [9542]~P1(f328(f61(f879(x95421)),f328(f307(x95422,f879(x95421),x95423),f251(f882(x95422,a870)))))+P1(f328(f61(f879(x95421)),f328(f307(x95422,f879(x95421),f183(x95422,x95421,x95423,f328(f176(x95422,x95421),x95424))),f251(f882(x95422,a870))))) % 154.70/154.56 [9589]~P1(f328(f328(f330(f881(x95891,x95891)),f328(f328(f263(x95891,x95891),x95892),x95894)),f328(f328(f285(x95891,x95891,x95891),x95893),f304(x95891,x95893))))+P1(f328(f328(f330(f881(x95891,x95891)),f328(f328(f263(x95891,x95891),x95892),f647(x95893,x95894,x95892,x95891))),x95893)) % 154.70/154.56 [9758]~P1(f328(f328(f330(f881(x97582,x97581)),x97584),f328(f283(x97581,x97582),x97583)))+P1(f328(f328(f330(f881(x97581,x97582)),f328(f328(f263(x97581,x97582),f656(x97583,x97584,x97581,x97582)),f655(x97583,x97584,x97581,x97582))),x97583)) % 154.70/154.56 [9786]~P1(f328(f328(f330(f881(f876(x97861),f876(x97861))),f328(f328(f263(f876(x97861),f876(x97861)),x97864),x97863)),f154(x97861,x97862)))+P1(f328(f328(f330(f881(x97861,x97861)),f328(f328(f263(x97861,x97861),f701(x97862,x97863,x97864,x97861)),f702(x97862,x97863,x97864,x97861))),x97862)) % 154.70/154.56 [9882]~P1(f328(f328(f330(f881(f876(x98821),f876(x98821))),f328(f328(f263(f876(x98821),f876(x98821)),x98822),x98824)),f154(x98821,x98823)))+P1(f328(f328(f330(f881(x98821,x98821)),f328(f328(f263(x98821,x98821),f328(f328(f162(x98821),x98822),f688(x98823,x98824,x98822,x98821))),f689(x98823,x98824,x98822,x98821))),x98823)) % 154.70/154.56 [9904]~P1(f328(f61(x99042),x99044))+E(f328(f328(f328(f65(f882(x99041,a870),x99042,f114(f882(x99041,a870))),f328(f328(f7(x99042,f882(x99041,a870),f882(x99041,a870)),f328(f328(f8(x99041,f882(f882(x99041,a870),f882(x99041,a870)),x99042),f306(x99041)),x99043)),f192(f882(x99041,a870)))),f192(f882(x99041,a870))),x99044),f328(f307(x99042,x99041,x99043),x99044)) % 154.70/154.56 [9999]~P27(x99991,x99992,x99993,f251(f882(x99991,a870)))+P1(f328(f328(f242(f882(x99991,a870)),f328(f308(x99991,x99992,x99993),f328(f328(f306(x99992),x99994),f192(f882(x99992,a870))))),f328(f328(f306(x99991),f85(x99991,f328(f328(f7(x99991,x99992,a870),f328(f328(f8(x99992,f882(x99992,a870),x99991),a325),x99993)),x99994))),f192(f882(x99991,a870))))) % 154.70/154.56 [5605]~E(f328(f328(f125(x56051),x56052),x56054),x56053)+E(f328(f328(f173(x56051),f328(f193(f876(x56051)),x56052)),x56053),x56052) % 154.70/154.56 [5606]~E(f328(f328(f125(x56062),x56063),x56061),x56064)+E(x56061,f328(f328(f135(x56062),f328(f193(f876(x56062)),x56063)),x56064)) % 154.70/154.56 [5617]~E(x56174,f2(a875))+E(f328(f328(f162(x56171),f328(f328(f148(x56171),x56172),x56173)),x56174),x56172) % 154.70/154.56 [6139]~P109(x61391)+E(f328(f328(f253(x61391),f328(f328(f253(x61391),x61392),x61393)),x61394),f328(f328(f253(x61391),x61392),f328(f328(f81(a875),x61393),x61394))) % 154.70/154.56 [6140]~P79(x61401)+E(f328(f328(f253(x61401),f328(f328(f253(x61401),x61402),x61403)),x61404),f328(f328(f253(x61401),x61402),f328(f328(f81(a875),x61403),x61404))) % 154.70/154.56 [6157]E(x61571,f2(a875))+E(f328(f328(f162(x61572),f328(f328(f148(x61572),x61573),x61574)),x61571),f328(f328(f162(x61572),x61574),f328(f328(f22(a875),x61571),f78(a875)))) % 154.70/154.56 [6186]~P117(x61861)+E(f328(f328(f286(x61861),f328(f328(f81(x61861),x61862),x61863)),x61864),f328(f328(f81(x61861),x61862),f328(f328(f286(x61861),x61863),x61864))) % 154.70/154.56 [6187]~P2(x61871)+E(f328(f328(f114(x61871),f328(f328(f114(x61871),x61872),x61873)),x61874),f328(f328(f114(x61871),x61872),f328(f328(f114(x61871),x61873),x61874))) % 154.70/154.56 [6189]~P99(x61891)+E(f328(f328(f114(x61891),f328(f328(f114(x61891),x61892),x61893)),x61894),f328(f328(f114(x61891),x61892),f328(f328(f114(x61891),x61893),x61894))) % 154.70/154.56 [6190]~P2(x61901)+E(f328(f328(f105(x61901),f328(f328(f105(x61901),x61902),x61903)),x61904),f328(f328(f105(x61901),x61902),f328(f328(f105(x61901),x61903),x61904))) % 154.70/154.56 [6192]~P100(x61921)+E(f328(f328(f105(x61921),f328(f328(f105(x61921),x61922),x61923)),x61924),f328(f328(f105(x61921),x61922),f328(f328(f105(x61921),x61923),x61924))) % 154.70/154.56 [6193]~P67(x61931)+E(f328(f328(f80(x61931),f328(f328(f80(x61931),x61932),x61933)),x61934),f328(f328(f80(x61931),x61932),f328(f328(f80(x61931),x61933),x61934))) % 154.70/154.56 [6194]~P109(x61941)+E(f328(f328(f80(x61941),f328(f328(f80(x61941),x61942),x61943)),x61944),f328(f328(f80(x61941),x61942),f328(f328(f80(x61941),x61943),x61944))) % 154.70/154.56 [6195]~P109(x61951)+E(f328(f328(f81(x61951),f328(f328(f81(x61951),x61952),x61953)),x61954),f328(f328(f81(x61951),x61952),f328(f328(f81(x61951),x61953),x61954))) % 154.70/154.56 [6196]~P70(x61961)+E(f328(f328(f81(x61961),f328(f328(f81(x61961),x61962),x61963)),x61964),f328(f328(f81(x61961),x61962),f328(f328(f81(x61961),x61963),x61964))) % 154.70/154.56 [6199]~P105(x61991)+E(f328(f328(f240(x61991),f328(f328(f240(x61991),x61992),x61993)),x61994),f328(f328(f240(x61991),x61992),f328(f328(f240(x61991),x61993),x61994))) % 154.70/154.56 [6201]~P105(x62011)+E(f328(f328(f241(x62011),f328(f328(f241(x62011),x62012),x62013)),x62014),f328(f328(f241(x62011),x62012),f328(f328(f241(x62011),x62013),x62014))) % 154.70/154.56 [6212]~P57(x62121)+E(f44(x62121,f328(f328(f80(x62121),x62122),f328(f328(f81(x62121),x62123),x62124)),x62124),f44(x62121,x62122,x62124)) % 154.70/154.56 [6213]~P57(x62131)+E(f44(x62131,f328(f328(f80(x62131),x62132),f328(f328(f81(x62131),x62133),x62134)),x62133),f44(x62131,x62132,x62133)) % 154.70/154.56 [6345]E(f328(f328(f162(x63451),f328(f328(f173(x63451),x63452),x63453)),x63454),f328(f328(f162(x63451),x63453),x63454))+~P1(f328(f328(f243(a875),x63454),x63452)) % 154.70/154.56 [6518]~P109(x65181)+E(f328(f328(f80(x65181),f328(f328(f80(x65181),x65182),x65183)),x65184),f328(f328(f80(x65181),f328(f328(f80(x65181),x65182),x65184)),x65183)) % 154.70/154.56 [6519]~P109(x65191)+E(f328(f328(f81(x65191),f328(f328(f81(x65191),x65192),x65193)),x65194),f328(f328(f81(x65191),f328(f328(f81(x65191),x65192),x65194)),x65193)) % 154.70/154.56 [6578]~P140(x65782)+E(f328(f328(f6(x65781,x65782),f328(f16(x65782,x65781),x65783)),x65784),f328(f328(f81(x65782),f328(f104(x65782),f328(f37(x65781),x65784))),x65783)) % 154.70/154.56 [6748]E(f328(f328(f105(f882(x67481,a870)),f328(f328(f306(x67481),x67482),x67483)),x67484),f328(f328(f105(f882(x67481,a870)),x67483),x67484))+P1(f328(f328(f330(x67481),x67482),x67484)) % 154.70/154.56 [6818]~P96(x68181)+E(f328(f328(f105(x68181),f328(f328(f114(x68181),x68182),x68183)),f328(f328(f114(x68181),x68184),x68183)),f328(f328(f114(x68181),f328(f328(f105(x68181),x68182),x68184)),x68183)) % 154.70/154.56 [6819]~P81(x68191)+E(f328(f328(f240(x68191),f328(f328(f22(x68191),x68192),x68193)),f328(f328(f22(x68191),x68194),x68193)),f328(f328(f22(x68191),f328(f328(f240(x68191),x68192),x68194)),x68193)) % 154.70/154.56 [6820]~P81(x68201)+E(f328(f328(f241(x68201),f328(f328(f22(x68201),x68202),x68203)),f328(f328(f22(x68201),x68204),x68203)),f328(f328(f22(x68201),f328(f328(f241(x68201),x68202),x68204)),x68203)) % 154.70/154.56 [6821]~P96(x68211)+E(f328(f328(f114(x68211),f328(f328(f105(x68211),x68212),x68213)),f328(f328(f105(x68211),x68214),x68213)),f328(f328(f105(x68211),f328(f328(f114(x68211),x68212),x68214)),x68213)) % 154.70/154.56 [6822]~P80(x68221)+E(f328(f328(f240(x68221),f328(f328(f80(x68221),x68222),x68223)),f328(f328(f80(x68221),x68224),x68223)),f328(f328(f80(x68221),f328(f328(f240(x68221),x68222),x68224)),x68223)) % 154.70/154.56 [6823]~P80(x68231)+E(f328(f328(f241(x68231),f328(f328(f80(x68231),x68232),x68233)),f328(f328(f80(x68231),x68234),x68233)),f328(f328(f80(x68231),f328(f328(f241(x68231),x68232),x68234)),x68233)) % 154.70/154.56 [6825]~P110(x68251)+E(f328(f328(f80(x68251),f328(f328(f81(x68251),x68252),x68253)),f328(f328(f81(x68251),x68254),x68253)),f328(f328(f81(x68251),f328(f328(f80(x68251),x68252),x68254)),x68253)) % 154.70/154.56 [6826]~P105(x68261)+E(f328(f328(f241(x68261),f328(f328(f240(x68261),x68262),x68263)),f328(f328(f240(x68261),x68264),x68263)),f328(f328(f240(x68261),f328(f328(f241(x68261),x68262),x68264)),x68263)) % 154.70/154.56 [6827]~P105(x68271)+E(f328(f328(f240(x68271),f328(f328(f241(x68271),x68272),x68273)),f328(f328(f241(x68271),x68274),x68273)),f328(f328(f241(x68271),f328(f328(f240(x68271),x68272),x68274)),x68273)) % 154.70/154.56 [6828]~P109(x68281)+E(f328(f328(f81(x68281),f328(f328(f253(x68281),x68282),x68283)),f328(f328(f253(x68281),x68284),x68283)),f328(f328(f253(x68281),f328(f328(f81(x68281),x68282),x68284)),x68283)) % 154.70/154.56 [6829]~P73(x68291)+E(f328(f328(f81(x68291),f328(f328(f253(x68291),x68292),x68293)),f328(f328(f253(x68291),x68294),x68293)),f328(f328(f253(x68291),f328(f328(f81(x68291),x68292),x68294)),x68293)) % 154.70/154.56 [6830]~P60(x68301)+E(f328(f328(f286(x68301),f328(f328(f253(x68301),x68302),x68303)),f328(f328(f253(x68301),x68304),x68303)),f328(f328(f253(x68301),f328(f328(f286(x68301),x68302),x68304)),x68303)) % 154.70/154.56 [6831]~P117(x68311)+E(f328(f328(f22(x68311),f328(f328(f286(x68311),x68312),x68313)),f328(f328(f286(x68311),x68314),x68313)),f328(f328(f286(x68311),f328(f328(f22(x68311),x68312),x68314)),x68313)) % 154.70/154.56 [6832]~P117(x68321)+E(f328(f328(f80(x68321),f328(f328(f286(x68321),x68322),x68323)),f328(f328(f286(x68321),x68324),x68323)),f328(f328(f286(x68321),f328(f328(f80(x68321),x68322),x68324)),x68323)) % 154.70/154.56 [6833]~P109(x68331)+E(f328(f328(f80(x68331),f328(f328(f81(x68331),x68332),x68333)),f328(f328(f81(x68331),x68334),x68333)),f328(f328(f81(x68331),f328(f328(f80(x68331),x68332),x68334)),x68333)) % 154.70/154.56 [6866]E(f328(f328(f156(x68661,x68662),x68663),x68664),x68662)+~P1(f328(f328(f242(a875),f328(f193(f876(x68661)),x68662)),x68663)) % 154.70/154.56 [6891]~P1(f328(x68913,x68914))+P1(f328(f328(f328(f114(f882(x68911,a870)),x68912),x68913),x68914)) % 154.70/154.56 [6893]~P1(f328(x68932,x68934))+P1(f328(f328(f328(f114(f882(x68931,a870)),x68932),x68933),x68934)) % 154.70/154.56 [6912]E(f328(f328(f162(x69121),f328(f328(f125(x69121),x69122),x69123)),x69124),f328(f328(f162(x69121),x69122),x69124))+~P1(f328(f328(f243(a875),x69124),f328(f193(f876(x69121)),x69122))) % 154.70/154.56 [6922]E(f328(f328(f22(f882(x69221,a870)),f328(f328(f306(x69221),x69222),x69223)),x69224),f328(f328(f22(f882(x69221,a870)),x69223),x69224))+~P1(f328(f328(f330(x69221),x69222),x69224)) % 154.70/154.56 [6963]~E(f136(a875,f328(f298(a875,x69631),x69632)),f328(f328(f148(a875),x69634),x69633))+E(f136(a875,f328(f298(a875,f328(f328(f80(a875),x69631),f78(a875))),x69632)),x69633) % 154.70/154.56 [7034]E(x70341,f2(a875))+E(f328(f328(f148(x70342),x70343),f328(f328(f173(x70342),f328(f328(f22(a875),x70341),f78(a875))),x70344)),f328(f328(f173(x70342),x70341),f328(f328(f148(x70342),x70343),x70344))) % 154.70/154.56 [7134]E(f328(f328(f162(x71341),x71342),f328(f328(f22(a875),x71343),f328(f193(f876(x71341)),x71344))),f328(f328(f162(x71341),f328(f328(f125(x71341),x71344),x71342)),x71343))+P1(f328(f328(f243(a875),x71343),f328(f193(f876(x71341)),x71344))) % 154.70/154.56 [7164]E(f328(f328(f105(f882(x71641,a870)),x71642),f328(f328(f306(x71641),x71643),x71644)),f328(f328(f306(x71641),x71643),f328(f328(f105(f882(x71641,a870)),x71642),x71644)))+~P1(f328(f328(f330(x71641),x71643),x71642)) % 154.70/154.56 [7201]E(f328(f328(f162(x72011),f328(f328(f156(x72011,x72012),x72013),x72014)),x72013),x72014)+~P1(f328(f328(f243(a875),x72013),f328(f193(f876(x72011)),x72012))) % 154.70/154.56 [7222]E(x72221,f192(f882(x72222,a870)))+E(f328(f307(f881(x72223,x72222),x72223,f262(x72223,x72222)),f328(f328(f265(x72223,x72222),x72224),f328(f16(f882(x72222,a870),x72223),x72221))),x72224) % 154.70/154.56 [7223]E(x72231,f192(f882(x72232,a870)))+E(f328(f307(f881(x72232,x72233),x72233,f266(x72232,x72233)),f328(f328(f265(x72232,x72233),x72231),f328(f16(f882(x72233,a870),x72232),x72234))),x72234) % 154.70/154.56 [7290]E(f328(f328(f22(f882(x72901,a870)),f328(f328(f306(x72901),x72902),x72903)),x72904),f328(f328(f306(x72901),x72902),f328(f328(f22(f882(x72901,a870)),x72903),x72904)))+P1(f328(f328(f330(x72901),x72902),x72904)) % 154.70/154.56 [7322]P1(f328(x73221,x73222))+P1(f328(f328(f328(f328(a200,f32(x73221,x73223)),x73222),x73224),x73222)) % 154.70/154.56 [7329]~E(x73294,f192(f882(x73292,a870)))+E(f328(f307(f881(x73291,x73292),x73291,f262(x73291,x73292)),f328(f328(f265(x73291,x73292),x73293),f328(f16(f882(x73292,a870),x73291),x73294))),f192(f882(x73291,a870))) % 154.70/154.56 [7330]~E(x73303,f192(f882(x73301,a870)))+E(f328(f307(f881(x73301,x73302),x73302,f266(x73301,x73302)),f328(f328(f265(x73301,x73302),x73303),f328(f16(f882(x73302,a870),x73301),x73304))),f192(f882(x73302,a870))) % 154.70/154.56 [7386]~P1(f328(f328(f330(x73861),x73862),x73864))+P1(f328(f328(f330(x73861),x73862),f328(f328(f114(f882(x73861,a870)),x73863),x73864))) % 154.70/154.56 [7389]~P1(f328(f328(f330(x73891),x73892),x73893))+P1(f328(f328(f330(x73891),x73892),f328(f328(f114(f882(x73891,a870)),x73893),x73894))) % 154.70/154.56 [7408]E(f328(f328(f105(f882(x74081,a870)),f328(f328(f306(x74081),x74082),x74083)),x74084),f328(f328(f306(x74081),x74082),f328(f328(f105(f882(x74081,a870)),x74083),x74084)))+~P1(f328(f328(f330(x74081),x74082),x74084)) % 154.70/154.56 [7687]P1(f328(x76871,x76872))+~P1(f328(f328(f328(f105(f882(x76873,a870)),x76874),x76871),x76872)) % 154.70/154.56 [7688]P1(f328(x76881,x76882))+~P1(f328(f328(f328(f105(f882(x76883,a870)),x76881),x76884),x76882)) % 154.70/154.56 [7691]E(f328(f328(f6(x76911,a875),x76912),f328(f328(f22(f882(x76911,a870)),x76913),f328(f328(f306(x76911),x76914),f192(f882(x76911,a870))))),f328(f328(f6(x76911,a875),x76912),x76913))+P1(f328(f328(f330(x76911),x76914),x76913)) % 154.70/154.56 [7696]~P66(x76961)+E(f328(f163(x76961),f328(f328(f151(a875,x76961),x76962),f136(a875,f328(f298(a875,x76963),x76964)))),f328(f328(f6(a875,x76961),x76962),f328(f170(a875),f136(a875,f328(f298(a875,x76963),x76964))))) % 154.70/154.56 [7697]~P66(x76971)+E(f328(f328(f6(a875,x76971),x76972),f328(f170(a875),f136(a875,f328(f298(a875,x76973),x76974)))),f328(f163(x76971),f328(f328(f151(a875,x76971),x76972),f136(a875,f328(f298(a875,x76973),x76974))))) % 154.70/154.56 [7812]~E(x78123,x78124)+P1(f328(f62(x78121,x78122,f328(f328(f306(x78121),x78123),f192(f882(x78121,a870)))),x78124)) % 154.70/154.56 [7909]P1(f328(f328(f330(x79091),x79092),f328(f170(x79091),x79093)))+~P1(f328(f328(f330(x79091),x79092),f328(f170(x79091),f328(f328(f173(x79091),x79094),x79093)))) % 154.70/154.56 [7910]P1(f328(f328(f330(x79101),x79102),f328(f170(x79101),x79103)))+~P1(f328(f328(f330(x79101),x79102),f328(f170(x79101),f328(f328(f135(x79101),x79104),x79103)))) % 154.70/154.56 [7980]P1(f328(f328(f330(x79801),x79802),x79803))+~P1(f328(f328(f330(x79801),x79802),f328(f328(f22(f882(x79801,a870)),x79803),x79804))) % 154.70/154.56 [7982]P1(f328(f328(f330(x79821),x79822),x79823))+~P1(f328(f328(f330(x79821),x79822),f328(f328(f105(f882(x79821,a870)),x79824),x79823))) % 154.70/154.56 [7985]P1(f328(f328(f330(x79851),x79852),x79853))+~P1(f328(f328(f330(x79851),x79852),f328(f328(f105(f882(x79851,a870)),x79853),x79854))) % 154.70/154.56 [8000]E(f328(f328(f125(x80001),f328(f328(f173(x80001),x80002),x80003)),f328(f328(f148(x80001),x80004),f328(f328(f135(x80001),f328(a116,x80002)),x80003))),f328(f328(f156(x80001,x80003),x80002),x80004))+~P1(f328(f328(f243(a875),x80002),f328(f193(f876(x80001)),x80003))) % 154.70/154.56 [8023]P1(f328(f328(f330(x80231),x80232),x80233))+~P1(f328(f328(f242(f882(x80231,a870)),f328(f328(f306(x80231),x80232),x80234)),x80233)) % 154.70/154.56 [8056]~P1(f328(f328(f330(x80561),x80562),x80563))+~P1(f328(f328(f330(x80561),x80562),f328(f328(f22(f882(x80561,a870)),x80564),x80563))) % 154.70/154.56 [8090]~P1(f328(f328(f243(a875),x80904),f328(f193(f876(x80901)),x80903)))+P1(f328(f328(f330(x80901),x80902),f328(f170(x80901),f328(f328(f156(x80901,x80903),x80904),x80902)))) % 154.70/154.56 [8146]E(f328(f328(f162(x81461),f328(f328(f135(x81461),x81462),x81463)),x81464),f328(f328(f162(x81461),x81463),f328(f328(f80(a875),x81462),x81464)))+~P1(f328(f328(f242(a875),f328(f328(f80(a875),x81462),x81464)),f328(f193(f876(x81461)),x81463))) % 154.70/154.56 [8156]~P140(x81562)+E(f328(f328(f6(x81561,x81562),f328(f328(f8(a875,x81562,x81561),f104(x81562)),x81563)),x81564),f328(f104(x81562),f328(f328(f6(x81561,a875),x81563),x81564))) % 154.70/154.56 [8157]~P135(x81572)+E(f328(f328(f6(x81571,x81572),f328(f328(f8(a1,x81572,x81571),f106(x81572)),x81573)),x81574),f328(f106(x81572),f328(f328(f6(x81571,a1),x81573),x81574))) % 154.70/154.56 [8218]~P63(x82182)+E(f328(f328(f9(x82181,x82182),f328(f328(f8(x82182,x82182,x82181),f75(x82182)),x82183)),x82184),f328(f75(x82182),f328(f328(f9(x82181,x82182),x82183),x82184))) % 154.70/154.56 [8219]~P65(x82192)+E(f328(f328(f6(x82191,x82192),f328(f328(f8(x82192,x82192,x82191),f79(x82192)),x82193)),x82194),f328(f79(x82192),f328(f328(f6(x82191,x82192),x82193),x82194))) % 154.70/154.56 [8221]E(f328(f328(f6(x82211,a875),x82212),f328(f328(f22(f882(x82211,a870)),x82213),f328(f328(f306(x82211),x82214),f192(f882(x82211,a870))))),f328(f328(f22(a875),f328(f328(f6(x82211,a875),x82212),x82213)),f328(x82212,x82214)))+~P1(f328(f328(f330(x82211),x82214),x82213)) % 154.70/154.56 [8242]P1(f328(f328(f242(f882(x82421,a870)),x82422),x82423))+~P1(f328(f328(f242(f882(x82421,a870)),f328(f328(f306(x82421),x82424),x82422)),x82423)) % 154.70/154.56 [8446]E(f328(a116,f358(x84461,x84462,x84463,x84464)),x84462)+~P1(f328(f328(f328(f328(a200,f328(a26,x84464)),x84463),x84462),x84461)) % 154.70/154.56 [8448]E(f328(f328(f176(x84481,x84482),x84483),x84484),f205(x84482))+P1(f328(f328(f330(x84481),x84484),f328(f307(f881(x84481,x84482),x84481,f262(x84481,x84482)),f328(f170(f881(x84481,x84482)),x84483)))) % 154.70/154.56 [8449]P39(x84491,x84492)+~P39(x84491,f328(f328(f306(f881(x84491,x84491)),f328(f328(f263(x84491,x84491),x84493),x84494)),x84492)) % 154.70/154.56 [8450]P54(x84501,x84502)+~P54(x84501,f328(f328(f306(f881(x84501,x84501)),f328(f328(f263(x84501,x84501),x84503),x84504)),x84502)) % 154.70/154.56 [8456]~P105(x84561)+E(f328(f328(f145(x84561,x84561,f5(x84561)),x84562),f328(f328(f145(x84561,x84561,f5(x84561)),x84563),x84564)),f328(f328(f145(x84561,x84561,f5(x84561)),x84563),f328(f328(f145(x84561,x84561,f5(x84561)),x84562),x84564))) % 154.70/154.56 [8466]E(x84661,x84662)+~P1(f328(f62(x84663,x84664,f328(f328(f306(x84663),x84661),f192(f882(x84663,a870)))),x84662)) % 154.70/154.56 [8477]E(f328(f328(f125(x84771),f328(f328(f173(x84771),x84772),x84773)),f328(f328(f173(x84771),x84774),f328(f328(f135(x84771),x84772),x84773))),f328(f328(f173(x84771),f328(f328(f80(a875),x84772),x84774)),x84773))+~P1(f328(f328(f242(a875),f328(f328(f80(a875),x84772),x84774)),f328(f193(f876(x84771)),x84773))) % 154.70/154.56 [8517]P1(f328(f61(x85171),x85172))+~E(x85172,f328(f307(a875,x85171,x85173),f328(f248(a875),f328(f328(f7(a875,a875,a870),f243(a875)),x85174)))) % 154.70/154.56 [8538]~P88(x85381)+E(f328(f139(x85381,x85381,f80(x85381),f328(f328(f80(x85381),x85382),x85383)),x85384),f328(f328(f80(x85381),x85382),f328(f139(x85381,x85381,f80(x85381),x85383),x85384))) % 154.70/154.56 [8578]P1(f328(f328(f242(f882(x85781,a870)),f328(f261(x85781,x85782),x85783)),f328(f261(x85781,x85782),x85784)))+~P1(f328(f328(f242(f882(f881(x85781,x85782),a870)),x85783),x85784)) % 154.70/154.56 [8591]~P1(f328(f328(f242(a875),x85912),x85914))+P1(f328(f328(f242(f882(x85911,a870)),f328(f170(x85911),f328(f328(f173(x85911),x85912),x85913))),f328(f170(x85911),f328(f328(f173(x85911),x85914),x85913)))) % 154.70/154.56 [8592]~P1(f328(f328(f242(a875),x85924),x85922))+P1(f328(f328(f242(f882(x85921,a870)),f328(f170(x85921),f328(f328(f135(x85921),x85922),x85923))),f328(f170(x85921),f328(f328(f135(x85921),x85924),x85923)))) % 154.70/154.56 [8648]~P1(f328(f61(x86481),f328(f328(f22(f882(x86481,a870)),x86482),x86484)))+P1(f328(f61(x86481),f328(f328(f22(f882(x86481,a870)),x86482),f328(f328(f306(x86481),x86483),x86484)))) % 154.70/154.56 [8684]P1(f328(f328(f330(f881(x86841,x86841)),x86842),f304(x86841,x86843)))+~P1(f328(f328(f330(f881(x86841,x86841)),x86842),f328(f328(f187(f881(x86841,x86841),a870),x86844),x86843))) % 154.70/154.56 [8761]~P1(f328(f61(x87611),f328(f328(f22(f882(x87611,a870)),x87612),f328(f328(f306(x87611),x87614),x87613))))+P1(f328(f61(x87611),f328(f328(f22(f882(x87611,a870)),x87612),x87613))) % 154.70/154.56 [8907]~E(f328(f328(f176(x89071,x89072),x89073),x89074),f205(x89072))+~P1(f328(f328(f330(x89071),x89074),f328(f307(f881(x89071,x89072),x89071,f262(x89071,x89072)),f328(f170(f881(x89071,x89072)),x89073)))) % 154.70/154.56 [8977]~P2(x89771)+P1(f328(f328(f242(x89771),f328(f328(f114(x89771),x89772),f328(f328(f105(x89771),x89773),x89774))),f328(f328(f105(x89771),f328(f328(f114(x89771),x89772),x89773)),f328(f328(f114(x89771),x89772),x89774)))) % 154.70/154.56 [8978]~P105(x89781)+P1(f328(f328(f242(x89781),f328(f328(f241(x89781),x89782),f328(f328(f240(x89781),x89783),x89784))),f328(f328(f240(x89781),f328(f328(f241(x89781),x89782),x89783)),f328(f328(f241(x89781),x89782),x89784)))) % 154.70/154.56 [9124]E(x91241,x91242)+~P1(f328(f328(f330(f881(x91243,x91243)),f328(f328(f263(x91243,x91243),x91241),x91242)),f328(f170(f881(x91243,x91243)),f328(f328(f180(x91243,x91243),x91244),x91244)))) % 154.70/154.56 [9157]~P1(f328(f328(f330(f881(x91571,x91571)),f328(f328(f263(x91571,x91571),x91573),x91572)),f304(x91571,x91574)))+~P39(x91571,f328(f328(f306(f881(x91571,x91571)),f328(f328(f263(x91571,x91571),x91572),x91573)),x91574)) % 154.70/154.56 [9158]~P1(f328(f328(f330(f881(x91581,x91581)),f328(f328(f263(x91581,x91581),x91583),x91582)),f304(x91581,x91584)))+~P54(x91581,f328(f328(f306(f881(x91581,x91581)),f328(f328(f263(x91581,x91581),x91582),x91583)),x91584)) % 154.70/154.56 [9163]E(x91631,x91632)+E(f328(f133(x91633,f328(f328(f8(a870,a870,x91633),a323),f328(a325,x91631))),f328(f328(f148(x91633),x91632),x91634)),f328(f328(f148(x91633),x91632),f328(f133(x91633,f328(f328(f8(a870,a870,x91633),a323),f328(a325,x91631))),x91634))) % 154.70/154.56 [9207]~P2(x92071)+P1(f328(f328(f242(x92071),f328(f328(f114(x92071),f328(f328(f105(x92071),x92072),x92073)),f328(f328(f105(x92071),x92072),x92074))),f328(f328(f105(x92071),x92072),f328(f328(f114(x92071),x92073),x92074)))) % 154.70/154.56 [9208]~P105(x92081)+P1(f328(f328(f242(x92081),f328(f328(f241(x92081),f328(f328(f240(x92081),x92082),x92083)),f328(f328(f240(x92081),x92082),x92084))),f328(f328(f240(x92081),x92082),f328(f328(f241(x92081),x92083),x92084)))) % 154.70/154.56 [9282]~E(f328(f307(x92822,x92821,x92823),f251(f882(x92822,a870))),f251(f882(x92821,a870)))+P1(f328(f328(f242(f882(x92821,a870)),f328(f79(f882(x92821,a870)),f328(f307(x92822,x92821,x92823),x92824))),f328(f307(x92822,x92821,x92823),f328(f79(f882(x92822,a870)),x92824)))) % 154.70/154.56 [9360]P1(f328(f328(f328(f328(a200,f328(f239(a871),f328(a28,x93601))),x93602),f358(x93603,x93604,x93602,x93601)),x93603))+~P1(f328(f328(f328(f328(a200,f328(a26,x93601)),x93602),x93604),x93603)) % 154.70/154.56 [9603]P1(f328(f328(f330(f881(x96031,x96031)),f328(f328(f263(x96031,x96031),x96032),x96033)),f328(f283(x96031,x96031),f328(f328(f285(x96031,x96031,x96031),x96034),f304(x96031,x96034)))))+~P1(f328(f328(f330(f881(x96031,x96031)),f328(f328(f263(x96031,x96031),x96032),x96033)),f328(f328(f285(x96031,x96031,x96031),f328(f283(x96031,x96031),x96034)),f304(x96031,f328(f283(x96031,x96031),x96034))))) % 154.70/154.56 [9604]~P1(f328(f328(f330(f881(x96041,x96041)),f328(f328(f263(x96041,x96041),x96042),x96043)),f328(f283(x96041,x96041),f328(f328(f285(x96041,x96041,x96041),x96044),f304(x96041,x96044)))))+P1(f328(f328(f330(f881(x96041,x96041)),f328(f328(f263(x96041,x96041),x96042),x96043)),f328(f328(f285(x96041,x96041,x96041),f328(f283(x96041,x96041),x96044)),f304(x96041,f328(f283(x96041,x96041),x96044))))) % 154.70/154.56 [9625]~P1(f328(f328(f330(x96252),x96254),f328(f259(x96251,x96252),x96253)))+P1(f328(f328(f330(f881(x96251,x96252)),f328(f328(f263(x96251,x96252),f568(x96253,x96251,x96254,x96252)),x96254)),x96253)) % 154.70/154.56 [9626]~P1(f328(f328(f330(x96262),x96264),f328(f259(x96261,x96262),x96263)))+P1(f328(f328(f330(f881(x96261,x96262)),f328(f328(f263(x96261,x96262),f581(x96263,x96261,x96264,x96262)),x96264)),x96263)) % 154.70/154.56 [9651]~P1(f328(f328(f330(x96511),x96514),f328(f328(f114(f882(x96511,a870)),x96512),x96513)))+P1(f328(f328(f328(f114(f882(x96511,a870)),f328(f328(f7(x96511,f882(x96511,a870),a870),f330(x96511)),x96512)),f328(f328(f7(x96511,f882(x96511,a870),a870),f330(x96511)),x96513)),x96514)) % 154.70/154.56 [9652]~P1(f328(f328(f330(x96521),x96524),f328(f328(f105(f882(x96521,a870)),x96522),x96523)))+P1(f328(f328(f328(f105(f882(x96521,a870)),f328(f328(f7(x96521,f882(x96521,a870),a870),f330(x96521)),x96522)),f328(f328(f7(x96521,f882(x96521,a870),a870),f330(x96521)),x96523)),x96524)) % 154.70/154.56 [9729]~P1(f328(f328(f330(f881(x97291,x97291)),f328(f328(f263(x97291,x97291),x97294),x97293)),f328(f328(f285(x97291,x97291,x97291),x97292),f304(x97291,x97292))))+P1(f328(f328(f330(f881(x97291,x97291)),f328(f328(f263(x97291,x97291),f648(x97292,x97293,x97294,x97291)),x97293)),x97292)) % 154.70/154.56 [9774]P1(f328(f328(f330(x97741),x97742),f328(f328(f114(f882(x97741,a870)),x97743),x97744)))+~P1(f328(f328(f328(f114(f882(x97741,a870)),f328(f328(f7(x97741,f882(x97741,a870),a870),f330(x97741)),x97743)),f328(f328(f7(x97741,f882(x97741,a870),a870),f330(x97741)),x97744)),x97742)) % 154.70/154.56 [9775]P1(f328(f328(f330(x97751),x97752),f328(f328(f105(f882(x97751,a870)),x97753),x97754)))+~P1(f328(f328(f328(f105(f882(x97751,a870)),f328(f328(f7(x97751,f882(x97751,a870),a870),f330(x97751)),x97753)),f328(f328(f7(x97751,f882(x97751,a870),a870),f330(x97751)),x97754)),x97752)) % 154.70/154.56 [10053]P34(x100531,f328(f328(f7(x100531,f882(f881(x100531,x100531),a870),f882(x100531,a870)),f328(f328(f8(f882(x100531,f882(f882(f881(x100531,x100531),a870),a870)),f882(f882(f881(x100531,x100531),a870),f882(x100531,a870)),x100531),f7(x100531,f882(f881(x100531,x100531),a870),a870)),f328(f328(f8(f882(x100531,f881(x100531,x100531)),f882(x100531,f882(f882(f881(x100531,x100531),a870),a870)),x100531),f328(f8(f881(x100531,x100531),f882(f882(f881(x100531,x100531),a870),a870),x100531),f330(f881(x100531,x100531)))),f263(x100531,x100531)))),x100532),x100533,x100534)+~P1(f328(f328(f330(f881(f876(x100531),f876(x100531))),f328(f328(f263(f876(x100531),f876(x100531)),x100533),x100534)),f155(x100531,x100532))) % 154.70/154.56 [10057]P55(x100571,f328(f328(f7(x100571,f882(f881(x100571,x100571),a870),f882(x100571,a870)),f328(f328(f8(f882(x100571,f882(f882(f881(x100571,x100571),a870),a870)),f882(f882(f881(x100571,x100571),a870),f882(x100571,a870)),x100571),f7(x100571,f882(f881(x100571,x100571),a870),a870)),f328(f328(f8(f882(x100571,f881(x100571,x100571)),f882(x100571,f882(f882(f881(x100571,x100571),a870),a870)),x100571),f328(f8(f881(x100571,x100571),f882(f882(f881(x100571,x100571),a870),a870),x100571),f330(f881(x100571,x100571)))),f263(x100571,x100571)))),x100572),x100573,x100574)+~P1(f328(f328(f330(f881(f882(x100571,a870),f882(x100571,a870))),f328(f328(f263(f882(x100571,a870),f882(x100571,a870)),x100573),x100574)),f319(x100571,x100572))) % 154.70/154.56 [10086]E(x100861,x100862)+~E(f328(f328(f7(x100863,f882(f881(x100863,x100864),a870),f882(x100864,a870)),f328(f328(f8(f882(x100864,f882(f882(f881(x100863,x100864),a870),a870)),f882(f882(f881(x100863,x100864),a870),f882(x100864,a870)),x100863),f7(x100864,f882(f881(x100863,x100864),a870),a870)),f328(f328(f8(f882(x100864,f881(x100863,x100864)),f882(x100864,f882(f882(f881(x100863,x100864),a870),a870)),x100863),f328(f8(f881(x100863,x100864),f882(f882(f881(x100863,x100864),a870),a870),x100864),f330(f881(x100863,x100864)))),f263(x100863,x100864)))),x100861),f328(f328(f7(x100863,f882(f881(x100863,x100864),a870),f882(x100864,a870)),f328(f328(f8(f882(x100864,f882(f882(f881(x100863,x100864),a870),a870)),f882(f882(f881(x100863,x100864),a870),f882(x100864,a870)),x100863),f7(x100864,f882(f881(x100863,x100864),a870),a870)),f328(f328(f8(f882(x100864,f881(x100863,x100864)),f882(x100864,f882(f882(f881(x100863,x100864),a870),a870)),x100863),f328(f8(f881(x100863,x100864),f882(f882(f881(x100863,x100864),a870),a870),x100864),f330(f881(x100863,x100864)))),f263(x100863,x100864)))),x100862)) % 154.70/154.56 [10090]~P34(x100901,f328(f328(f7(x100901,f882(f881(x100901,x100901),a870),f882(x100901,a870)),f328(f328(f8(f882(x100901,f882(f882(f881(x100901,x100901),a870),a870)),f882(f882(f881(x100901,x100901),a870),f882(x100901,a870)),x100901),f7(x100901,f882(f881(x100901,x100901),a870),a870)),f328(f328(f8(f882(x100901,f881(x100901,x100901)),f882(x100901,f882(f882(f881(x100901,x100901),a870),a870)),x100901),f328(f8(f881(x100901,x100901),f882(f882(f881(x100901,x100901),a870),a870),x100901),f330(f881(x100901,x100901)))),f263(x100901,x100901)))),x100904),x100902,x100903)+P1(f328(f328(f330(f881(f876(x100901),f876(x100901))),f328(f328(f263(f876(x100901),f876(x100901)),x100902),x100903)),f155(x100901,x100904))) % 154.70/154.56 [10091]~P55(x100911,f328(f328(f7(x100911,f882(f881(x100911,x100911),a870),f882(x100911,a870)),f328(f328(f8(f882(x100911,f882(f882(f881(x100911,x100911),a870),a870)),f882(f882(f881(x100911,x100911),a870),f882(x100911,a870)),x100911),f7(x100911,f882(f881(x100911,x100911),a870),a870)),f328(f328(f8(f882(x100911,f881(x100911,x100911)),f882(x100911,f882(f882(f881(x100911,x100911),a870),a870)),x100911),f328(f8(f881(x100911,x100911),f882(f882(f881(x100911,x100911),a870),a870),x100911),f330(f881(x100911,x100911)))),f263(x100911,x100911)))),x100914),x100912,x100913)+P1(f328(f328(f330(f881(f882(x100911,a870),f882(x100911,a870))),f328(f328(f263(f882(x100911,a870),f882(x100911,a870)),x100912),x100913)),f319(x100911,x100914))) % 154.70/154.56 [7459]~P90(x74591)+E(f328(f328(f80(x74591),f328(f107(x74591),x74592)),f328(f328(f22(x74591),f328(f107(x74591),x74593)),x74594)),f328(f328(f22(x74591),f328(f107(x74591),f328(f328(f80(a1),x74592),x74593))),x74594)) % 154.70/154.56 [7460]~P90(x74601)+E(f328(f328(f80(x74601),f328(f107(x74601),x74602)),f328(f328(f80(x74601),f328(f107(x74601),x74603)),x74604)),f328(f328(f80(x74601),f328(f107(x74601),f328(f328(f80(a1),x74602),x74603))),x74604)) % 154.70/154.56 [7461]~P90(x74611)+E(f328(f328(f81(x74611),f328(f107(x74611),x74612)),f328(f328(f81(x74611),f328(f107(x74611),x74613)),x74614)),f328(f328(f81(x74611),f328(f107(x74611),f328(f328(f81(a1),x74612),x74613))),x74614)) % 154.70/154.56 [7506]~P140(x75061)+E(f328(f163(x75061),f328(f328(f151(x75062,x75061),f328(f16(x75061,x75062),x75063)),x75064)),f328(f328(f81(x75061),f328(f104(x75061),f328(f193(f876(x75062)),x75064))),x75063)) % 154.70/154.56 [7743]E(f328(f274(x77431,f328(f328(f148(f881(a103,x77431)),x77432),x77433)),x77434),f328(f266(a103,x77431),x77432))+~P1(f328(f328(f243(a103),x77434),f328(f262(a103,x77431),x77432))) % 154.70/154.56 [7789]~P90(x77891)+E(f328(f328(f80(x77891),f328(f107(x77891),x77892)),f328(f328(f22(x77891),x77893),f328(f107(x77891),x77894))),f328(f328(f80(x77891),f328(f107(x77891),f328(f328(f80(a1),x77892),f328(f79(a1),x77894)))),x77893)) % 154.70/154.56 [7922]E(f328(f274(x79221,x79222),f328(f328(f22(a103),x79223),f328(f262(a103,x79221),x79224))),f328(f274(x79221,f328(f328(f148(f881(a103,x79221)),x79224),x79222)),x79223))+P1(f328(f328(f243(a103),x79223),f328(f262(a103,x79221),x79224))) % 154.70/154.56 [8368]~P1(f328(f328(f330(x83681),x83682),f328(f170(x83681),f118(x83681,x83684))))+P1(f328(f328(f330(x83681),x83682),f328(f170(x83681),f118(x83681,f328(f328(f125(x83681),x83683),x83684))))) % 154.70/154.56 [8369]~P1(f328(f328(f330(x83691),x83692),f328(f170(x83691),f118(x83691,x83693))))+P1(f328(f328(f330(x83691),x83692),f328(f170(x83691),f118(x83691,f328(f328(f125(x83691),x83693),x83694))))) % 154.70/154.56 [8386]E(f328(f328(f114(f882(x83861,a870)),f328(f328(f105(f882(x83861,a870)),x83862),x83863)),x83864),f328(f328(f105(f882(x83861,a870)),x83862),f328(f328(f114(f882(x83861,a870)),x83863),x83864)))+~P1(f328(f328(f242(f882(x83861,a870)),x83864),x83862)) % 154.70/154.56 [8697]~E(f328(f328(f114(f882(x86971,a870)),f328(f328(f105(f882(x86971,a870)),x86973),x86974)),x86972),f328(f328(f105(f882(x86971,a870)),x86973),f328(f328(f114(f882(x86971,a870)),x86974),x86972)))+P1(f328(f328(f242(f882(x86971,a870)),x86972),x86973)) % 154.70/154.56 [8982]~P1(f328(f328(f242(f882(x89821,a870)),x89822),f328(f328(f114(f882(x89821,a870)),x89823),x89824)))+P1(f328(f328(f242(f882(x89821,a870)),f328(f328(f22(f882(x89821,a870)),x89822),x89823)),x89824)) % 154.70/154.56 [9040]~P1(f328(f328(f328(f328(a200,f328(a26,x90401)),x90402),f328(a116,x90403)),x90404))+P1(f328(f328(f328(f328(a200,f328(f239(a871),f328(a28,x90401))),x90402),x90403),x90404)) % 154.70/154.56 [9103]P1(f328(f328(f242(f882(x91031,a870)),x91032),f328(f328(f114(f882(x91031,a870)),x91033),x91034)))+~P1(f328(f328(f242(f882(x91031,a870)),f328(f328(f22(f882(x91031,a870)),x91032),x91033)),x91034)) % 154.70/154.56 [9156]P1(f328(f328(f328(f328(a200,f328(a26,x91561)),x91562),f328(a116,x91563)),x91564))+~P1(f328(f328(f328(f328(a200,f328(f239(a871),f328(a28,x91561))),x91562),x91563),x91564)) % 154.70/154.56 [9188]~P83(x91881)+E(f328(f75(x91881),f328(f328(f6(x91882,x91881),f328(f328(f8(x91881,x91881,x91882),f75(x91881)),x91883)),x91884)),f328(f328(f6(x91882,x91881),f328(f328(f8(x91881,x91881,x91882),f75(x91881)),x91883)),x91884)) % 154.70/154.56 [9358]~P83(x93581)+P1(f328(f328(f242(x93581),f2(x93581)),f328(f328(f6(x93582,x93581),f328(f328(f8(x93581,x93581,x93582),f75(x93581)),x93583)),x93584))) % 154.70/154.56 [9363]~P65(x93631)+E(f328(f163(x93631),f328(f328(f151(x93632,x93631),f328(f73(x93631,x93631,x93632,f79(x93631)),x93633)),x93634)),f328(f79(x93631),f328(f163(x93631),f328(f328(f151(x93632,x93631),x93633),x93634)))) % 154.70/154.56 [9497]~P83(x94971)+P1(f328(f328(f242(x94971),f328(f75(x94971),f328(f328(f6(x94972,x94971),x94973),x94974))),f328(f328(f6(x94972,x94971),f328(f328(f8(x94971,x94971,x94972),f75(x94971)),x94973)),x94974))) % 154.70/154.56 [9527]~E(f328(f328(f80(a875),x95271),x95274),f328(f328(f80(a875),x95273),x95272))+P1(f328(f328(f330(f881(f881(a875,a875),f881(a875,a875))),f328(f328(f263(f881(a875,a875),f881(a875,a875)),f328(f328(f263(a875,a875),x95271),x95272)),f328(f328(f263(a875,a875),x95273),x95274))),a112)) % 154.70/154.56 [9528]~P1(f328(f328(f243(a875),x95281),x95283))+P1(f328(f328(f330(f881(f881(a875,a875),f881(a875,a875))),f328(f328(f263(f881(a875,a875),f881(a875,a875)),f328(f328(f263(a875,a875),x95281),x95282)),f328(f328(f263(a875,a875),x95283),x95284))),a35)) % 154.70/154.56 [9529]~P1(f328(f328(f243(a875),x95291),x95293))+P1(f328(f328(f330(f881(f881(a875,a875),f881(a875,a875))),f328(f328(f263(f881(a875,a875),f881(a875,a875)),f328(f328(f263(a875,a875),x95291),x95292)),f328(f328(f263(a875,a875),x95293),x95294))),a70)) % 154.70/154.56 [9676]E(f328(f328(f80(a875),x96761),x96762),f328(f328(f80(a875),x96763),x96764))+~P1(f328(f328(f330(f881(f881(a875,a875),f881(a875,a875))),f328(f328(f263(f881(a875,a875),f881(a875,a875)),f328(f328(f263(a875,a875),x96761),x96764)),f328(f328(f263(a875,a875),x96763),x96762))),a112)) % 154.70/154.56 [9703]E(f328(f328(f162(x97031),f328(f328(f135(x97031),f328(f193(f876(x97031)),f175(x97031,x97032,x97033))),x97033)),x97034),f328(f328(f162(x97031),x97033),f328(f328(f80(a875),x97034),f328(f193(f876(x97031)),f175(x97031,x97032,x97033)))))+~P1(f328(f328(f243(a875),x97034),f328(f193(f876(x97031)),f328(f328(f135(x97031),f328(f193(f876(x97031)),f175(x97031,x97032,x97033))),x97033)))) % 154.70/154.56 [9720]~P1(f328(f328(f330(x97202),x97204),f328(f328(f41(x97201,f882(x97202,a870)),f251(f882(x97201,a870))),x97203)))+P1(f328(f328(f328(f41(x97201,f882(x97202,a870)),f251(f882(x97201,a870))),f328(f328(f8(f882(x97202,a870),f882(x97202,a870),x97201),f328(f7(x97202,f882(x97202,a870),a870),f330(x97202))),x97203)),x97204)) % 154.70/154.56 [9721]~P1(f328(f328(f330(x97212),x97214),f328(f328(f42(x97211,f882(x97212,a870)),f251(f882(x97211,a870))),x97213)))+P1(f328(f328(f328(f42(x97211,f882(x97212,a870)),f251(f882(x97211,a870))),f328(f328(f8(f882(x97212,a870),f882(x97212,a870),x97211),f328(f7(x97212,f882(x97212,a870),a870),f330(x97212))),x97213)),x97214)) % 154.70/154.56 [9802]~P1(f328(f48(x98021,x98022),f328(f328(f263(a1,a1),x98024),x98023)))+P1(f328(f48(f328(f79(a1),x98021),x98022),f328(f328(f263(a1,a1),f328(f328(f328(f100(a1),f328(f328(a325,x98023),f2(a1))),f328(f79(a1),x98024)),f328(f328(f22(a1),f328(f79(a1),x98024)),f78(a1)))),f328(f328(f328(f100(a1),f328(f328(a325,x98023),f2(a1))),f2(a1)),f328(f328(f22(a1),x98022),x98023))))) % 154.70/154.56 [9811]P1(f328(f328(f330(x98111),x98112),f328(f328(f41(x98113,f882(x98111,a870)),f251(f882(x98113,a870))),x98114)))+~P1(f328(f328(f328(f41(x98113,f882(x98111,a870)),f251(f882(x98113,a870))),f328(f328(f8(f882(x98111,a870),f882(x98111,a870),x98113),f328(f7(x98111,f882(x98111,a870),a870),f330(x98111))),x98114)),x98112)) % 154.70/154.56 [9812]P1(f328(f328(f330(x98121),x98122),f328(f328(f42(x98123,f882(x98121,a870)),f251(f882(x98123,a870))),x98124)))+~P1(f328(f328(f328(f42(x98123,f882(x98121,a870)),f251(f882(x98123,a870))),f328(f328(f8(f882(x98121,a870),f882(x98121,a870),x98123),f328(f7(x98121,f882(x98121,a870),a870),f330(x98121))),x98124)),x98122)) % 154.70/154.56 [9824]E(f328(f328(f41(a875,f882(x98241,a870)),f251(f882(a875,a870))),x98242),f328(f328(f41(a875,f882(x98241,a870)),f251(f882(a875,a870))),x98243))+~E(f328(f328(f41(a875,f882(x98241,a870)),f328(f298(a875,f2(a875)),f380(x98242,x98244,x98243,x98241))),x98243),f328(f328(f41(a875,f882(x98241,a870)),f328(f298(a875,f2(a875)),f328(f328(f80(a875),f380(x98242,x98244,x98243,x98241)),x98244))),x98242)) % 154.70/154.56 [10146]~P1(f328(f328(f242(f882(f881(x101461,x101462),a870)),x101463),x101464))+P1(f328(f328(f242(f882(x101461,f882(x101462,a870))),f328(f328(f7(x101461,f882(f881(x101461,x101462),a870),f882(x101462,a870)),f328(f328(f8(f882(x101462,f882(f882(f881(x101461,x101462),a870),a870)),f882(f882(f881(x101461,x101462),a870),f882(x101462,a870)),x101461),f7(x101462,f882(f881(x101461,x101462),a870),a870)),f328(f328(f8(f882(x101462,f881(x101461,x101462)),f882(x101462,f882(f882(f881(x101461,x101462),a870),a870)),x101461),f328(f8(f881(x101461,x101462),f882(f882(f881(x101461,x101462),a870),a870),x101462),f330(f881(x101461,x101462)))),f263(x101461,x101462)))),x101463)),f328(f328(f7(x101461,f882(f881(x101461,x101462),a870),f882(x101462,a870)),f328(f328(f8(f882(x101462,f882(f882(f881(x101461,x101462),a870),a870)),f882(f882(f881(x101461,x101462),a870),f882(x101462,a870)),x101461),f7(x101462,f882(f881(x101461,x101462),a870),a870)),f328(f328(f8(f882(x101462,f881(x101461,x101462)),f882(x101462,f882(f882(f881(x101461,x101462),a870),a870)),x101461),f328(f8(f881(x101461,x101462),f882(f882(f881(x101461,x101462),a870),a870),x101462),f330(f881(x101461,x101462)))),f263(x101461,x101462)))),x101464))) % 154.70/154.56 [10163]P1(f328(f328(f242(f882(f881(x101631,x101632),a870)),x101633),x101634))+~P1(f328(f328(f242(f882(x101631,f882(x101632,a870))),f328(f328(f7(x101631,f882(f881(x101631,x101632),a870),f882(x101632,a870)),f328(f328(f8(f882(x101632,f882(f882(f881(x101631,x101632),a870),a870)),f882(f882(f881(x101631,x101632),a870),f882(x101632,a870)),x101631),f7(x101632,f882(f881(x101631,x101632),a870),a870)),f328(f328(f8(f882(x101632,f881(x101631,x101632)),f882(x101632,f882(f882(f881(x101631,x101632),a870),a870)),x101631),f328(f8(f881(x101631,x101632),f882(f882(f881(x101631,x101632),a870),a870),x101632),f330(f881(x101631,x101632)))),f263(x101631,x101632)))),x101633)),f328(f328(f7(x101631,f882(f881(x101631,x101632),a870),f882(x101632,a870)),f328(f328(f8(f882(x101632,f882(f882(f881(x101631,x101632),a870),a870)),f882(f882(f881(x101631,x101632),a870),f882(x101632,a870)),x101631),f7(x101632,f882(f881(x101631,x101632),a870),a870)),f328(f328(f8(f882(x101632,f881(x101631,x101632)),f882(x101632,f882(f882(f881(x101631,x101632),a870),a870)),x101631),f328(f8(f881(x101631,x101632),f882(f882(f881(x101631,x101632),a870),a870),x101632),f330(f881(x101631,x101632)))),f263(x101631,x101632)))),x101634))) % 154.70/154.56 [9237]~P1(f328(f328(f330(f881(x92371,x92371)),x92372),f304(x92371,x92374)))+P1(f328(f328(f330(f881(x92371,x92371)),x92372),f304(x92371,f328(f328(f114(f882(f881(x92371,x92371),a870)),x92373),x92374)))) % 154.70/154.56 [9238]~P1(f328(f328(f330(f881(x92381,x92381)),x92382),f304(x92381,x92383)))+P1(f328(f328(f330(f881(x92381,x92381)),x92382),f304(x92381,f328(f328(f114(f882(f881(x92381,x92381),a870)),x92383),x92384)))) % 154.70/154.56 [9595]~E(f328(f170(x95951),x95954),f182(x95951,x95952,x95953))+E(f328(f176(x95951,x95952),f328(f328(f151(x95951,f881(x95951,x95952)),f328(f328(f18(x95951,x95952,f881(x95951,x95952)),f263(x95951,x95952)),f328(f328(f8(f879(x95952),x95952,x95951),f239(x95952)),x95953))),x95954)),x95953) % 154.70/154.56 [9918]~P1(f328(f328(f243(a875),f328(f328(f80(a875),x99181),x99184)),f328(f328(f80(a875),x99183),x99182)))+P1(f328(f328(f243(a1),f328(a89,f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),f328(f328(f263(a875,a875),x99181),x99182)),f192(f882(f881(a875,a875),a870)))))),f328(a89,f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),f328(f328(f263(a875,a875),x99183),x99184)),f192(f882(f881(a875,a875),a870))))))) % 154.70/154.56 [9919]~P1(f328(f328(f242(a875),f328(f328(f80(a875),x99191),x99194)),f328(f328(f80(a875),x99193),x99192)))+P1(f328(f328(f242(a1),f328(a89,f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),f328(f328(f263(a875,a875),x99191),x99192)),f192(f882(f881(a875,a875),a870)))))),f328(a89,f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),f328(f328(f263(a875,a875),x99193),x99194)),f192(f882(f881(a875,a875),a870))))))) % 154.70/154.56 [9996]P1(f328(f328(f243(a875),f328(f328(f80(a875),x99961),x99962)),f328(f328(f80(a875),x99963),x99964)))+~P1(f328(f328(f243(a1),f328(a89,f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),f328(f328(f263(a875,a875),x99961),x99964)),f192(f882(f881(a875,a875),a870)))))),f328(a89,f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),f328(f328(f263(a875,a875),x99963),x99962)),f192(f882(f881(a875,a875),a870))))))) % 154.70/154.56 [9997]P1(f328(f328(f242(a875),f328(f328(f80(a875),x99971),x99972)),f328(f328(f80(a875),x99973),x99974)))+~P1(f328(f328(f242(a1),f328(a89,f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),f328(f328(f263(a875,a875),x99971),x99974)),f192(f882(f881(a875,a875),a870)))))),f328(a89,f328(f282(f881(a875,a875),f881(a875,a875),a112),f328(f328(f306(f881(a875,a875)),f328(f328(f263(a875,a875),x99973),x99972)),f192(f882(f881(a875,a875),a870))))))) % 154.70/154.56 [10038]P1(f328(f328(f242(f882(x100381,a870)),f328(f328(f41(a875,f882(x100381,a870)),f251(f882(a875,a870))),x100382)),f328(f328(f41(a875,f882(x100381,a870)),f251(f882(a875,a870))),x100383)))+~P1(f328(f328(f242(f882(x100381,a870)),f328(f328(f41(a875,f882(x100381,a870)),f328(f298(a875,f2(a875)),f381(x100383,x100384,x100382,x100381))),x100382)),f328(f328(f41(a875,f882(x100381,a870)),f328(f298(a875,f2(a875)),f328(f328(f80(a875),f381(x100383,x100384,x100382,x100381)),x100384))),x100383))) % 154.70/154.56 [10136]~P1(f328(f328(f330(x101362),x101364),f328(f259(x101361,x101362),x101363)))+P1(f328(f258(x101361,x101362,f328(f328(f7(x101361,f882(f881(x101361,x101362),a870),f882(x101362,a870)),f328(f328(f8(f882(x101362,f882(f882(f881(x101361,x101362),a870),a870)),f882(f882(f881(x101361,x101362),a870),f882(x101362,a870)),x101361),f7(x101362,f882(f881(x101361,x101362),a870),a870)),f328(f328(f8(f882(x101362,f881(x101361,x101362)),f882(x101362,f882(f882(f881(x101361,x101362),a870),a870)),x101361),f328(f8(f881(x101361,x101362),f882(f882(f881(x101361,x101362),a870),a870),x101362),f330(f881(x101361,x101362)))),f263(x101361,x101362)))),x101363)),x101364)) % 154.70/154.56 [10137]~P1(f328(f328(f330(x101371),x101374),f328(f261(x101371,x101372),x101373)))+P1(f328(f257(x101371,x101372,f328(f328(f7(x101371,f882(f881(x101371,x101372),a870),f882(x101372,a870)),f328(f328(f8(f882(x101372,f882(f882(f881(x101371,x101372),a870),a870)),f882(f882(f881(x101371,x101372),a870),f882(x101372,a870)),x101371),f7(x101372,f882(f881(x101371,x101372),a870),a870)),f328(f328(f8(f882(x101372,f881(x101371,x101372)),f882(x101372,f882(f882(f881(x101371,x101372),a870),a870)),x101371),f328(f8(f881(x101371,x101372),f882(f882(f881(x101371,x101372),a870),a870),x101372),f330(f881(x101371,x101372)))),f263(x101371,x101372)))),x101373)),x101374)) % 154.70/154.56 [10149]P1(f328(f328(f330(x101491),x101492),f328(f259(x101493,x101491),x101494)))+~P1(f328(f258(x101493,x101491,f328(f328(f7(x101493,f882(f881(x101493,x101491),a870),f882(x101491,a870)),f328(f328(f8(f882(x101491,f882(f882(f881(x101493,x101491),a870),a870)),f882(f882(f881(x101493,x101491),a870),f882(x101491,a870)),x101493),f7(x101491,f882(f881(x101493,x101491),a870),a870)),f328(f328(f8(f882(x101491,f881(x101493,x101491)),f882(x101491,f882(f882(f881(x101493,x101491),a870),a870)),x101493),f328(f8(f881(x101493,x101491),f882(f882(f881(x101493,x101491),a870),a870),x101491),f330(f881(x101493,x101491)))),f263(x101493,x101491)))),x101494)),x101492)) % 154.70/154.56 [10150]P1(f328(f328(f330(x101501),x101502),f328(f261(x101501,x101503),x101504)))+~P1(f328(f257(x101501,x101503,f328(f328(f7(x101501,f882(f881(x101501,x101503),a870),f882(x101503,a870)),f328(f328(f8(f882(x101503,f882(f882(f881(x101501,x101503),a870),a870)),f882(f882(f881(x101501,x101503),a870),f882(x101503,a870)),x101501),f7(x101503,f882(f881(x101501,x101503),a870),a870)),f328(f328(f8(f882(x101503,f881(x101501,x101503)),f882(x101503,f882(f882(f881(x101501,x101503),a870),a870)),x101501),f328(f8(f881(x101501,x101503),f882(f882(f881(x101501,x101503),a870),a870),x101503),f330(f881(x101501,x101503)))),f263(x101501,x101503)))),x101504)),x101502)) % 154.70/154.56 [9834]P1(f328(f157(x98341,x98342),x98343))+~P1(f328(f157(x98341,f328(f328(f18(x98341,a870,a870),f328(f328(f8(a870,f882(a870,a870),x98341),a326),x98344)),x98342)),x98343)) % 154.70/154.56 [9835]P1(f328(f157(x98351,x98352),x98353))+~P1(f328(f157(x98351,f328(f328(f18(x98351,a870,a870),f328(f328(f8(a870,f882(a870,a870),x98351),a326),x98352)),x98354)),x98353)) % 154.70/154.56 [9920]~P109(x99201)+E(f328(f328(f81(x99201),f328(f328(f80(x99201),f78(x99201)),f78(x99201))),f328(f328(f6(a875,x99201),f328(f328(f8(x99201,x99201,a875),f328(f80(x99201),x99202)),f328(f328(f7(a875,x99201,x99201),f328(f328(f8(x99201,f882(x99201,x99201),a875),f81(x99201)),f104(x99201))),x99203))),f328(f249(a875),x99204))),f328(f328(f81(x99201),f328(f104(x99201),x99204)),f328(f328(f80(x99201),x99202),f328(f328(f80(x99201),x99202),f328(f328(f81(x99201),f328(f104(x99201),f328(f328(f22(a875),x99204),f78(a875)))),x99203))))) % 154.70/154.56 [10060]P1(f328(x100601,f567(x100602,x100603,x100604,x100601)))+P39(x100602,f328(f248(f881(x100602,x100602)),f328(f267(x100602,x100602,a870),f328(f328(f8(f882(x100602,a870),f882(x100602,a870),x100602),f328(f18(x100602,a870,a870),f328(f328(f8(a870,f882(a870,a870),x100602),a326),x100601))),f328(f328(f7(x100602,f882(x100602,x100602),f882(x100602,a870)),f328(f328(f8(f882(x100602,a870),f882(f882(x100602,x100602),f882(x100602,a870)),x100602),f8(x100602,a870,x100602)),a325)),x100603))))) % 154.70/154.56 [10074]~P1(f328(f328(f243(a875),f328(x100744,f328(x100743,f567(x100741,x100743,x100744,x100742)))),f328(x100744,f567(x100741,x100743,x100744,x100742))))+P39(x100741,f328(f248(f881(x100741,x100741)),f328(f267(x100741,x100741,a870),f328(f328(f8(f882(x100741,a870),f882(x100741,a870),x100741),f328(f18(x100741,a870,a870),f328(f328(f8(a870,f882(a870,a870),x100741),a326),x100742))),f328(f328(f7(x100741,f882(x100741,x100741),f882(x100741,a870)),f328(f328(f8(f882(x100741,a870),f882(f882(x100741,x100741),f882(x100741,a870)),x100741),f8(x100741,a870,x100741)),a325)),x100743))))) % 154.70/154.56 [10176]~P1(f328(f328(f330(f881(x101761,x101761)),f328(f328(f263(x101761,x101761),x101763),x101764)),f328(f328(f114(f882(f881(x101761,x101761),a870)),x101762),f304(x101761,f192(f882(f881(x101761,x101761),a870))))))+P1(f328(f328(f328(f328(f114(f882(x101761,f882(x101761,a870))),f328(f328(f7(x101761,f882(f881(x101761,x101761),a870),f882(x101761,a870)),f328(f328(f8(f882(x101761,f882(f882(f881(x101761,x101761),a870),a870)),f882(f882(f881(x101761,x101761),a870),f882(x101761,a870)),x101761),f7(x101761,f882(f881(x101761,x101761),a870),a870)),f328(f328(f8(f882(x101761,f881(x101761,x101761)),f882(x101761,f882(f882(f881(x101761,x101761),a870),a870)),x101761),f328(f8(f881(x101761,x101761),f882(f882(f881(x101761,x101761),a870),a870),x101761),f330(f881(x101761,x101761)))),f263(x101761,x101761)))),x101762)),a325),x101763),x101764)) % 154.70/154.56 [10186]P1(f328(f328(f330(f881(x101861,x101861)),f328(f328(f263(x101861,x101861),x101862),x101863)),f328(f328(f114(f882(f881(x101861,x101861),a870)),x101864),f304(x101861,f192(f882(f881(x101861,x101861),a870))))))+~P1(f328(f328(f328(f328(f114(f882(x101861,f882(x101861,a870))),f328(f328(f7(x101861,f882(f881(x101861,x101861),a870),f882(x101861,a870)),f328(f328(f8(f882(x101861,f882(f882(f881(x101861,x101861),a870),a870)),f882(f882(f881(x101861,x101861),a870),f882(x101861,a870)),x101861),f7(x101861,f882(f881(x101861,x101861),a870),a870)),f328(f328(f8(f882(x101861,f881(x101861,x101861)),f882(x101861,f882(f882(f881(x101861,x101861),a870),a870)),x101861),f328(f8(f881(x101861,x101861),f882(f882(f881(x101861,x101861),a870),a870),x101861),f330(f881(x101861,x101861)))),f263(x101861,x101861)))),x101864)),a325),x101862),x101863)) % 154.70/154.56 [10046]~P108(x100463)+E(f90(x100461,f328(f328(f18(x100461,a870,a870),f328(f328(f8(a870,f882(a870,a870),x100461),a326),x100462)),f328(f328(f8(f882(x100461,a870),a870,x100461),f88(x100461)),f328(f328(f8(f882(x100461,a870),f882(x100461,a870),x100461),f328(f18(x100461,a870,a870),f328(f328(f8(a870,f882(a870,a870),x100461),a331),x100462))),f328(f328(f8(x100463,f882(x100461,a870),x100461),f328(f7(x100461,x100463,a870),f328(f328(f8(x100463,f882(x100463,a870),x100461),f242(x100463)),x100464))),x100464))))),f328(f93(x100461,x100463,x100464),x100462)) % 154.70/154.56 [10089]~P108(x100893)+E(f90(x100891,f328(f328(f18(x100891,a870,a870),f328(f328(f8(a870,f882(a870,a870),x100891),a326),x100892)),f328(f328(f8(f882(x100891,a870),a870,x100891),f88(x100891)),f328(f328(f8(f882(x100891,a870),f882(x100891,a870),x100891),f328(f18(x100891,a870,a870),f328(f328(f8(a870,f882(a870,a870),x100891),a331),x100892))),f328(f328(f7(x100891,f882(x100891,x100893),f882(x100891,a870)),f328(f328(f8(f882(x100893,a870),f882(f882(x100891,x100893),f882(x100891,a870)),x100891),f8(x100893,a870,x100891)),f328(f328(f8(x100893,f882(x100893,a870),x100891),f242(x100893)),x100894))),x100894))))),f96(x100891,x100893,x100894,x100892)) % 154.70/154.56 [10134]E(f328(f328(f148(f876(x101341)),f328(f328(f148(x101341),x101342),f328(f139(f876(x101341),f876(x101341),f125(x101341),f117(x101341)),f328(f328(f151(f876(x101341),f876(x101341)),f153(f876(x101341),x101341,f117(x101341),f328(f328(f8(f876(x101341),f882(f876(x101341),f876(x101341)),x101341),f16(f876(x101341),f876(x101341))),f328(f328(f7(x101341,f876(x101341),f876(x101341)),f148(x101341)),f117(x101341))))),x101343)))),f178(x101341,f328(f328(f148(f876(x101341)),x101344),f328(f139(f876(f876(x101341)),f876(f876(x101341)),f125(f876(x101341)),f117(f876(x101341))),f328(f328(f151(f876(x101341),f876(f876(x101341))),f153(f876(f876(x101341)),x101341,f117(f876(x101341)),f328(f16(f882(f876(x101341),f876(f876(x101341))),x101341),f328(f328(f7(f876(x101341),f876(f876(x101341)),f876(f876(x101341))),f148(f876(x101341))),f117(f876(x101341)))))),x101343))))),f178(x101341,f328(f328(f148(f876(x101341)),f328(f328(f148(x101341),x101342),x101344)),x101343)))+~P1(f328(f316(f876(f876(x101341)),f179(x101341)),f328(f328(f148(f876(x101341)),f328(f328(f148(x101341),x101342),x101344)),x101343))) % 154.70/154.56 [10175]~P1(f328(f61(x101752),f328(f248(x101752),x101754)))+P1(f328(f61(x101751),f328(f248(x101751),f328(f328(f8(f882(x101752,a870),a870,x101751),f87(x101752)),f328(f328(f7(x101751,f882(x101752,a870),f882(x101752,a870)),f328(f328(f8(f882(x101752,f882(a870,a870)),f882(f882(x101752,a870),f882(x101752,a870)),x101751),f18(x101752,a870,a870)),f328(f328(f8(f882(x101752,a870),f882(x101752,f882(a870,a870)),x101751),f328(f8(a870,f882(a870,a870),x101752),a326)),f328(f328(f7(x101751,f882(x101752,x101751),f882(x101752,a870)),f328(f328(f8(f882(x101751,a870),f882(f882(x101752,x101751),f882(x101752,a870)),x101751),f8(x101751,a870,x101752)),a325)),x101753)))),x101754))))) % 154.70/154.56 [5253]E(x52531,x52532)+~E(f127(x52533,x52534,x52531),f127(x52533,x52535,x52532)) % 154.70/154.56 [5254]E(x52541,x52542)+~E(f127(x52543,x52541,x52544),f127(x52543,x52542,x52545)) % 154.70/154.56 [5255]E(x52551,x52552)+~E(f168(x52553,x52551,x52554),f168(x52553,x52552,x52555)) % 154.70/154.56 [5630]E(f328(f328(f306(x56301),x56302),f182(x56301,x56303,x56304)),f182(x56301,x56303,x56304))+~E(f328(x56304,x56302),f328(f235(x56303),x56305)) % 154.70/154.56 [6035]P1(f328(f258(x60351,x60352,x60353),x60354))+~P1(f328(f328(x60353,x60355),x60354)) % 154.70/154.56 [6037]P1(f328(f257(x60371,x60372,x60373),x60374))+~P1(f328(f328(x60373,x60374),x60375)) % 154.70/154.56 [6040]~E(f328(x60404,x60402),f328(f235(x60403),x60405))+P1(f328(f328(f330(x60401),x60402),f182(x60401,x60403,x60404))) % 154.70/154.56 [6041]~E(f328(x60414,x60415),f328(f235(x60411),x60412))+P1(f328(f328(f330(x60411),x60412),f184(x60413,x60411,x60414))) % 154.70/154.56 [6508]~E(x65085,f2(a103))+E(f328(f204(x65081,x65082,x65083,x65084),x65085),f119(x65082)) % 154.70/154.56 [6509]~E(x65095,f2(a103))+E(f328(f202(x65091,x65092,x65093,x65094),x65095),f128(x65092)) % 154.70/154.56 [6645]~E(x66453,f2(a103))+E(f328(f277(x66451,x66452,x66453,x66454),x66455),f328(f263(x66451,x66452),x66455)) % 154.70/154.56 [6717]~E(f328(x67174,x67175),f205(x67172))+E(f328(f237(f879(x67171),x67172,f205(x67171),x67173),f328(x67174,x67175)),f205(x67171)) % 154.70/154.56 [7341]E(f328(x73411,x73412),f205(x73413))+~E(f328(f183(x73414,x73413,x73415,x73411),x73412),f205(x73413)) % 154.70/154.56 [7342]E(f328(x73421,x73422),f205(x73423))+~E(f328(f183(x73424,x73423,x73421,x73425),x73422),f205(x73423)) % 154.70/154.56 [7378]E(f328(f183(x73781,x73782,x73783,x73784),x73785),f328(x73783,x73785))+P1(f328(f328(f330(x73781),x73785),f182(x73781,x73782,x73784))) % 154.70/154.56 [7379]E(f328(f183(x73791,x73792,x73793,x73794),x73795),f328(x73794,x73795))+P1(f328(f328(f330(x73791),x73795),f182(x73791,x73792,x73793))) % 154.70/154.56 [7701]~P22(x77014,x77011,x77012,x77015)+E(f328(f73(x77011,x77011,x77011,f328(x77012,x77013)),f328(x77012,x77013)),f328(x77012,x77013)) % 154.70/154.56 [7745]E(f328(f183(x77451,x77452,x77453,x77454),x77455),f328(x77454,x77455))+~P1(f328(f328(f330(x77451),x77455),f182(x77451,x77452,x77454))) % 154.70/154.56 [8091]~P18(x80915,x80911,x80912)+E(f328(f73(x80911,x80911,x80911,f328(x80912,x80913)),f328(x80912,x80914)),f328(f73(x80911,x80911,x80911,f328(x80912,x80914)),f328(x80912,x80913))) % 154.70/154.56 [8430]P1(f328(f328(f330(f881(x84301,x84301)),f328(f328(f263(x84301,x84301),x84302),x84303)),f322(x84301,x84304,x84305)))+~P1(f328(f328(f243(a875),f328(x84304,x84302)),f328(x84304,x84303))) % 154.70/154.56 [8523]~P1(f328(f328(f330(x85234),x85233),f295(x85234,x85231,x85232,x85235)))+P1(f328(f328(x85231,x85232),x85233)) % 154.70/154.56 [8524]~P1(f328(f328(f330(x85244),x85243),f292(x85244,x85241,x85242,x85245)))+P1(f328(f328(x85241,x85242),x85243)) % 154.70/154.56 [8525]~P1(f328(f328(f330(x85254),x85252),f295(x85254,x85251,x85255,x85253)))+P1(f328(f328(x85251,x85252),x85253)) % 154.70/154.56 [8526]~P1(f328(f328(f330(x85264),x85262),f292(x85264,x85261,x85265,x85263)))+P1(f328(f328(x85261,x85262),x85263)) % 154.70/154.56 [8674]~P53(x86742,x86741,x86745,x86743,x86744)+E(f328(f307(x86741,x86742,x86743),x86744),f251(f882(x86742,a870))) % 154.70/154.56 [9114]~P36(x91141,x91142,x91143,x91144,x91145)+P36(x91141,x91142,x91143,f328(f166(x91141),x91144),f328(f166(x91142),x91145)) % 154.70/154.56 [9116]~P36(x91161,x91162,x91163,f328(f166(x91161),x91164),x91165)+P36(x91161,x91162,x91163,x91164,f328(f166(x91162),x91165)) % 154.70/154.56 [9117]~P36(x91171,x91172,x91173,x91174,f328(f166(x91172),x91175))+P36(x91171,x91172,x91173,f328(f166(x91171),x91174),x91175) % 154.70/154.56 [9123]P36(x91231,x91232,x91233,x91234,x91235)+~P36(x91231,x91232,x91233,f328(f166(x91231),x91234),f328(f166(x91232),x91235)) % 154.70/154.56 [9518]P1(f328(f328(f330(f881(f876(x95181),f876(x95181))),f328(f328(f263(f876(x95181),f876(x95181)),f328(f328(f148(x95181),x95182),x95183)),f328(f328(f148(x95181),x95182),x95184))),f154(x95181,x95185)))+~P1(f328(f328(f330(f881(f876(x95181),f876(x95181))),f328(f328(f263(f876(x95181),f876(x95181)),x95183),x95184)),f154(x95181,x95185))) % 154.70/154.56 [9519]P1(f328(f328(f330(f881(f876(x95191),f876(x95191))),f328(f328(f263(f876(x95191),f876(x95191)),f328(f328(f125(x95191),x95192),x95193)),f328(f328(f125(x95191),x95192),x95194))),f144(x95191,x95195)))+~P1(f328(f328(f330(f881(f876(x95191),f876(x95191))),f328(f328(f263(f876(x95191),f876(x95191)),x95193),x95194)),f144(x95191,x95195))) % 154.70/154.56 [9710]E(f328(f328(f148(x97101),f670(x97102,x97103,x97104,x97105,x97101)),f671(x97102,x97103,x97104,x97105,x97101)),x97105)+~P1(f328(f328(f330(f881(f876(x97101),f876(x97101))),f328(f328(f263(f876(x97101),f876(x97101)),x97105),f328(f328(f148(x97101),x97104),x97103))),f155(x97101,x97102))) % 154.70/154.56 [9732]E(f328(f328(f148(x97321),f672(x97322,x97323,x97324,x97325,x97321)),f673(x97322,x97323,x97324,x97325,x97321)),x97323)+~P1(f328(f328(f330(f881(f876(x97321),f876(x97321))),f328(f328(f263(f876(x97321),f876(x97321)),f328(f328(f148(x97321),x97325),x97324)),x97323)),f155(x97321,x97322))) % 154.70/154.56 [9894]~P1(f328(f328(f330(f881(f876(x98941),f876(x98941))),f328(f328(f263(f876(x98941),f876(x98941)),f328(f328(f148(x98941),x98945),x98942)),x98944)),f155(x98941,x98943)))+P1(f328(f328(f330(f881(f876(x98941),f876(x98941))),f328(f328(f263(f876(x98941),f876(x98941)),x98942),f673(x98943,x98944,x98942,x98945,x98941))),f155(x98941,x98943))) % 154.70/154.56 [9964]~P1(f328(f328(f330(f881(f876(x99641),f876(x99641))),f328(f328(f263(f876(x99641),f876(x99641)),x99645),f328(f328(f148(x99641),x99644),x99643))),f155(x99641,x99642)))+P1(f328(f328(f330(f881(f876(x99641),f876(x99641))),f328(f328(f263(f876(x99641),f876(x99641)),f671(x99642,x99643,x99644,x99645,x99641)),x99643)),f155(x99641,x99642))) % 154.70/154.56 [10129]P1(f328(f328(f330(f881(x101291,x101291)),f328(f328(f263(x101291,x101291),f328(x101292,f328(f328(f80(a875),x101293),x101294))),f328(x101292,x101293))),f304(x101291,x101295)))+~P1(f328(f328(f330(f881(x101291,x101291)),f328(f328(f263(x101291,x101291),f328(x101292,f328(a116,f627(x101294,x101293,x101295,x101292,x101291)))),f328(x101292,f627(x101294,x101293,x101295,x101292,x101291)))),f304(x101291,x101295))) % 154.70/154.56 [5219]E(x52191,x52192)+~E(f328(f328(f148(x52193),x52194),x52191),f328(f328(f148(x52193),x52195),x52192)) % 154.70/154.56 [5220]E(x52201,x52202)+~E(f328(f328(f148(x52203),x52201),x52204),f328(f328(f148(x52203),x52202),x52205)) % 154.70/154.56 [5271]P1(f328(x52711,x52712))+~E(f328(f133(x52713,x52711),x52714),f328(f328(f148(x52713),x52712),x52715)) % 154.70/154.56 [5272]P1(f328(x52721,x52722))+~E(f328(f328(f148(x52723),x52722),x52724),f328(f133(x52723,x52721),x52725)) % 154.70/154.56 [5428]~E(f328(f328(f135(x54281),x54283),x54282),f328(f328(f148(x54281),x54284),x54285))+E(f328(f328(f162(x54281),x54282),x54283),x54284) % 154.70/154.56 [5560]~P17(x55604,x55605,x55601)+E(f328(f328(x55601,x55602),f328(f328(x55601,x55602),x55603)),f328(f328(x55601,x55602),x55603)) % 154.70/154.56 [6093]~E(x60934,f2(a103))+E(f328(f328(f121(x60931,x60932,x60933),x60934),x60935),f328(f328(f263(f876(x60932),x60931),f117(x60932)),x60935)) % 154.70/154.56 [6167]~P105(x61672)+~E(f328(f328(f145(x61671,x61672,x61673),x61674),x61675),f117(x61671)) % 154.70/154.56 [6545]E(x65451,x65452)+~E(f328(f328(f125(x65453),x65454),f328(f328(f148(x65453),x65451),f117(x65453))),f328(f328(f125(x65453),x65455),f328(f328(f148(x65453),x65452),f117(x65453)))) % 154.70/154.56 [6546]E(x65461,x65462)+~E(f328(f328(f125(x65463),x65461),f328(f328(f148(x65463),x65464),f117(x65463))),f328(f328(f125(x65463),x65462),f328(f328(f148(x65463),x65465),f117(x65463)))) % 154.70/154.56 [6801]E(f328(f186(x68011,x68012,x68013,x68014),x68015),f205(x68012))+P1(f328(f328(f330(x68011),x68015),x68014)) % 154.70/154.56 [6864]E(f328(f328(f306(x68641),f328(x68642,x68643)),f328(f307(x68644,x68641,x68642),x68645)),f328(f307(x68644,x68641,x68642),x68645))+~P1(f328(f328(f330(x68644),x68643),x68645)) % 154.70/154.56 [6871]~P1(f328(x68714,f328(x68713,x68715)))+P1(f328(f328(f308(x68711,x68712,x68713),x68714),x68715)) % 154.70/154.56 [6874]~P1(f328(f328(x68743,x68745),x68744))+P1(f328(f328(f252(x68741,x68742,x68743),x68744),x68745)) % 154.70/154.56 [6967]~E(f328(f307(x69671,x69672,x69673),x69674),x69675)+E(f328(f307(f882(x69671,a870),f882(x69672,a870),f307(x69671,x69672,x69673)),f328(f305(x69671),x69674)),f328(f305(x69672),x69675)) % 154.70/154.56 [6997]E(f328(f186(x69971,x69972,x69973,x69974),x69975),f328(x69973,x69975))+~P1(f328(f328(f330(x69971),x69975),x69974)) % 154.70/154.56 [7298]P27(x72981,x72982,x72983,x72984)+~P27(x72981,x72982,x72983,f328(f328(f306(x72981),x72985),x72984)) % 154.70/154.56 [7368]P1(f328(x73681,x73682))+~P1(f328(f328(f95(x73683,x73684,x73681),x73685),x73682)) % 154.70/154.56 [7412]~P1(f328(f328(f330(x74124),x74123),x74125))+P1(f328(f328(f330(x74121),f328(x74122,x74123)),f328(f307(x74124,x74121,x74122),x74125))) % 154.70/154.56 [7435]~P105(x74352)+E(f147(x74351,x74352,x74353,f328(f133(x74351,x74354),x74355)),f328(f133(x74351,x74354),f147(x74351,x74352,x74353,x74355))) % 154.70/154.56 [7468]P1(f328(x74681,f328(x74682,x74683)))+~P1(f328(f328(f308(x74684,x74685,x74682),x74681),x74683)) % 154.70/154.56 [7471]P1(f328(f328(x74711,x74712),x74713))+~P1(f328(f328(f252(x74714,x74715,x74711),x74713),x74712)) % 154.70/154.56 [7472]P1(f328(f328(x74721,x74722),x74723))+~P1(f328(f328(f95(x74724,x74721,x74725),x74722),x74723)) % 154.70/154.56 [7535]~P1(f328(f328(f330(x75353),f328(x75354,x75352)),x75355))+P1(f328(f328(f330(x75351),x75352),f328(f308(x75351,x75353,x75354),x75355))) % 154.70/154.56 [7936]~P1(f328(f328(f330(x79365),x79363),f328(f308(x79365,x79361,x79362),x79364)))+P1(f328(f328(f330(x79361),f328(x79362,x79363)),x79364)) % 154.70/154.56 [8158]~E(x81583,f328(f328(f328(f72(x81581,f879(x81582)),f328(f16(f879(x81582),x81581),f205(x81582))),x81584),f328(f235(x81582),x81585)))+E(f182(x81581,x81582,x81583),f328(f328(f306(x81581),x81584),f192(f882(x81581,a870)))) % 154.70/154.56 [8247]~P18(x82472,x82471,x82473)+E(f328(f139(x82471,x82472,f328(f7(x82472,x82471,x82471),x82473),x82474),f149(x82472,x82475)),f328(f328(f64(x82472,x82471,x82473),x82474),f328(f170(x82472),x82475))) % 154.70/154.56 [8266]E(f328(x82661,f776(x82662,x82661,x82663,x82664)),x82664)+~P1(f328(f328(f330(x82665),x82664),f328(f307(x82663,x82665,x82661),x82662))) % 154.70/154.56 [8267]E(f328(x82671,f462(x82672,x82671,x82673,x82674)),x82674)+~P1(f328(f328(f330(x82675),x82674),f328(f307(x82673,x82675,x82671),x82672))) % 154.70/154.56 [8576]~E(x85762,f328(f328(f148(x85761),x85764),x85765))+P1(f328(f328(f330(f881(f876(x85761),f876(x85761))),f328(f328(f263(f876(x85761),f876(x85761)),f117(x85761)),x85762)),f144(x85761,x85763))) % 154.70/154.56 [8629]~P36(x86291,x86293,x86295,x86292,x86294)+E(f328(f193(f876(x86291)),x86292),f328(f193(f876(x86293)),x86294)) % 154.70/154.56 [8642]P1(f328(f328(f242(f882(x86421,a870)),f328(f328(f42(x86422,f882(x86421,a870)),x86423),x86424)),f328(x86424,x86425)))+~P1(f328(f328(f330(x86422),x86425),x86423)) % 154.70/154.56 [8690]~P53(x86901,x86902,x86903,x86905,x86904)+E(f328(f307(x86901,x86902,x86903),f251(f882(x86901,a870))),x86904) % 154.70/154.56 [8893]E(f328(f328(f328(f72(x88931,f879(x88932)),f186(x88931,x88932,x88933,x88934)),x88935),f205(x88932)),f186(x88931,x88932,x88933,x88934))+P1(f328(f328(f330(x88931),x88935),x88934)) % 154.70/154.56 [8898]E(f328(f133(x88981,x88982),f785(x88983,x88984,x88985,x88982,x88981)),x88983)+~E(f328(f133(x88981,x88982),x88985),f328(f328(f148(x88981),x88984),x88983)) % 154.70/154.56 [8899]E(f328(f133(x88991,x88992),f788(x88993,x88992,x88994,x88995,x88991)),x88994)+~E(f328(f328(f148(x88991),x88995),x88994),f328(f133(x88991,x88992),x88993)) % 154.70/154.56 [8900]E(f328(x89001,f712(x89002,x89003,x89001,x89004,x89005)),x89002)+~E(f328(f328(f206(x89005,x89004),x89001),x89003),f328(f235(x89004),x89002)) % 154.70/154.56 [8904]E(f328(f235(x89041),f712(x89042,x89043,x89044,x89045,x89041)),x89043)+~E(f328(f328(f206(x89041,x89045),x89044),x89043),f328(f235(x89045),x89042)) % 154.70/154.56 [9003]E(f328(f193(f876(x90031)),x90032),x90033)+~P1(f328(f328(f330(f881(f876(x90031),f876(x90031))),f328(f328(f263(f876(x90031),f876(x90031)),x90034),x90032)),f328(f140(x90031,x90035),x90033))) % 154.70/154.56 [9004]E(f328(f193(f876(x90041)),x90042),x90043)+~P1(f328(f328(f330(f881(f876(x90041),f876(x90041))),f328(f328(f263(f876(x90041),f876(x90041)),x90042),x90044)),f328(f140(x90041,x90045),x90043))) % 154.70/154.56 [9072]P1(f328(f328(f330(x90721),f776(x90722,x90723,x90721,x90724)),x90722))+~P1(f328(f328(f330(x90725),x90724),f328(f307(x90721,x90725,x90723),x90722))) % 154.70/154.56 [9073]P1(f328(f328(f330(x90731),f462(x90732,x90733,x90731,x90734)),x90732))+~P1(f328(f328(f330(x90735),x90734),f328(f307(x90731,x90735,x90733),x90732))) % 154.70/154.56 [9235]E(f328(f307(x92351,x92352,x92353),f867(x92354,x92353,x92351,x92355,x92352)),x92355)+~P1(f328(f328(f242(f882(x92352,a870)),x92355),f328(f307(x92351,x92352,x92353),x92354))) % 154.70/154.56 [9488]E(f328(x94881,f773(x94882,x94881,x94883,x94884,x94885)),f328(f235(x94885),x94884))+~P1(f328(f328(f330(x94885),x94884),f184(x94883,x94885,f186(x94883,x94885,x94881,x94882)))) % 154.70/154.56 [9535]P1(f328(f328(f330(f881(f876(x95351),f876(x95351))),f328(f328(f263(f876(x95351),f876(x95351)),f328(f328(f148(x95351),x95352),x95353)),f328(f328(f148(x95351),x95352),x95354))),f304(f876(x95351),f154(x95351,x95355))))+~P1(f328(f328(f330(f881(f876(x95351),f876(x95351))),f328(f328(f263(f876(x95351),f876(x95351)),x95353),x95354)),f304(f876(x95351),f154(x95351,x95355)))) % 154.70/154.56 [9566]~E(f328(x95663,f714(x95665,x95664,x95663,x95662,x95661)),f328(x95665,f714(x95665,x95664,x95663,x95662,x95661)))+E(f328(f328(f151(x95661,x95662),x95663),x95664),f328(f328(f151(x95661,x95662),x95665),x95664)) % 154.70/154.56 [9642]~E(f328(f133(x96421,x96425),x96424),f328(f328(f148(x96421),x96423),x96422))+E(f328(f328(f125(x96421),f786(x96422,x96423,x96424,x96425,x96421)),f328(f328(f148(x96421),x96423),f785(x96422,x96423,x96424,x96425,x96421))),x96424) % 154.70/154.56 [9643]~E(f328(f328(f148(x96431),x96435),x96434),f328(f133(x96431,x96433),x96432))+E(f328(f328(f125(x96431),f789(x96432,x96433,x96434,x96435,x96431)),f328(f328(f148(x96431),x96435),f788(x96432,x96433,x96434,x96435,x96431))),x96432) % 154.70/154.56 [9647]E(f328(f328(f151(x96471,x96472),x96473),x96474),f328(f328(f151(x96471,x96472),x96475),x96474))+P1(f328(f328(f330(x96471),f714(x96473,x96474,x96475,x96472,x96471)),f328(f170(x96471),x96474))) % 154.70/154.56 [9677]~P1(f328(f328(f330(x96775),x96774),f328(f282(x96771,x96775,x96773),x96772)))+P1(f328(f328(f330(x96771),f529(x96772,x96773,x96771,x96774,x96775)),x96772)) % 154.70/154.56 [9678]~P1(f328(f328(f330(x96785),x96784),f328(f282(x96781,x96785,x96783),x96782)))+P1(f328(f328(f330(x96781),f551(x96782,x96783,x96781,x96784,x96785)),x96782)) % 154.70/154.56 [9704]~P1(f328(f328(f242(f882(x97045,a870)),x97044),f328(f307(x97041,x97045,x97043),x97042)))+P1(f328(f328(f242(f882(x97041,a870)),f867(x97042,x97043,x97041,x97044,x97045)),x97042)) % 154.70/154.56 [9755]~P1(f328(f328(f330(x97555),x97554),f184(x97551,x97555,f186(x97551,x97555,x97553,x97552))))+P1(f328(f328(f330(x97551),f773(x97552,x97553,x97551,x97554,x97555)),x97552)) % 154.70/154.56 [10152]E(x101521,f2(a103))+E(f328(f237(f881(f876(x101522),x101523),f881(x101522,x101523),f328(f328(f263(f876(x101522),x101523),f117(x101522)),x101524),f328(f267(x101522,x101523,f881(f876(x101522),x101523)),f328(f328(f7(x101522,f882(x101523,f881(f876(x101522),x101523)),f882(x101523,f881(f876(x101522),x101523))),f328(f328(f8(f882(f881(f876(x101522),x101523),f881(f876(x101522),x101523)),f882(f882(x101523,f881(f876(x101522),x101523)),f882(x101523,f881(f876(x101522),x101523))),x101522),f8(f881(f876(x101522),x101523),f881(f876(x101522),x101523),x101523)),f328(f328(f8(f882(f876(x101522),f882(x101523,f881(f876(x101522),x101523))),f882(f881(f876(x101522),x101523),f881(f876(x101522),x101523)),x101522),f267(f876(x101522),x101523,f881(f876(x101522),x101523))),f328(f328(f8(f882(f876(x101522),f876(x101522)),f882(f876(x101522),f882(x101523,f881(f876(x101522),x101523))),x101522),f328(f8(f876(x101522),f882(x101523,f881(f876(x101522),x101523)),f876(x101522)),f263(f876(x101522),x101523))),f148(x101522))))),f328(f121(x101523,x101522,x101525),f328(f328(f22(a103),x101521),f78(a103)))))),f328(x101525,x101524)),f328(f328(f121(x101523,x101522,x101525),x101521),x101524)) % 154.70/154.56 [5441]~E(f328(x54413,x54414),x54415)+E(f328(f328(f328(f72(x54411,x54412),x54413),x54414),x54415),x54413) % 154.70/154.56 [5883]E(f328(x58831,x58832),x58833)+~E(f328(f328(f328(f72(x58834,x58835),x58831),x58832),x58833),x58831) % 154.70/154.56 [5975]E(x59751,x59752)+~E(f328(f266(x59753,x59754),f328(f328(f263(x59753,x59754),x59755),x59751)),x59752) % 154.70/154.56 [5976]E(x59761,x59762)+~E(f328(f262(x59763,x59764),f328(f328(f263(x59763,x59764),x59761),x59765)),x59762) % 154.70/154.56 [6243]~E(x62433,f328(f328(f125(x62431),x62434),f328(f328(f148(x62431),x62432),x62435)))+P1(f328(f328(f330(x62431),x62432),f328(f170(x62431),x62433))) % 154.70/154.56 [6631]E(f328(f307(x66311,x66312,f328(f16(x66312,x66311),x66313)),x66314),f328(f328(f306(x66312),x66313),f192(f882(x66312,a870))))+~P1(f328(f328(f330(x66311),x66315),x66314)) % 154.70/154.56 [6702]E(f328(f328(f114(f882(x67021,a870)),f328(f170(x67021),x67022)),f328(f170(x67021),x67023)),f328(f170(x67021),x67024))+~E(f164(x67021,x67025,x67024),f328(f328(f263(f876(x67021),f876(x67021)),x67022),x67023)) % 154.70/154.56 [6805]~P105(x68052)+E(f328(f193(f876(x68051)),f328(f328(f145(x68051,x68052,x68053),x68054),x68055)),f328(a116,f328(f193(f876(x68051)),x68055))) % 154.70/154.56 [6817]~P105(x68172)+E(f328(f170(x68171),f328(f328(f145(x68171,x68172,x68173),x68174),x68175)),f328(f328(f306(x68171),x68174),f328(f170(x68171),x68175))) % 154.70/154.56 [7088]~P109(x70881)+E(f328(f328(f80(x70881),f328(f328(f80(x70881),x70882),x70883)),f328(f328(f80(x70881),x70884),x70885)),f328(f328(f80(x70881),f328(f328(f80(x70881),x70882),x70884)),f328(f328(f80(x70881),x70883),x70885))) % 154.70/154.56 [7089]~P109(x70891)+E(f328(f328(f81(x70891),f328(f328(f81(x70891),x70892),x70893)),f328(f328(f81(x70891),x70894),x70895)),f328(f328(f81(x70891),f328(f328(f81(x70891),x70892),x70894)),f328(f328(f81(x70891),x70893),x70895))) % 154.70/154.56 [7090]~P60(x70901)+E(f328(f328(f286(x70901),f328(f328(f81(x70901),x70902),x70903)),f328(f328(f81(x70901),x70904),x70905)),f328(f328(f81(x70901),f328(f328(f286(x70901),x70902),x70904)),f328(f328(f286(x70901),x70903),x70905))) % 154.70/154.56 [7104]~P105(x71041)+E(f302(x71041,f328(f328(f241(x71041),x71042),x71043),f328(f328(f240(x71041),x71044),x71045)),f328(f328(f105(f882(x71041,a870)),f302(x71041,x71042,x71044)),f302(x71041,x71043,x71045))) % 154.70/154.56 [7105]~P105(x71051)+E(f301(x71051,f328(f328(f241(x71051),x71052),x71053),f328(f328(f240(x71051),x71054),x71055)),f328(f328(f105(f882(x71051,a870)),f301(x71051,x71052,x71054)),f301(x71051,x71053,x71055))) % 154.70/154.56 [7106]~P105(x71061)+E(f299(x71061,f328(f328(f241(x71061),x71062),x71063),f328(f328(f240(x71061),x71064),x71065)),f328(f328(f105(f882(x71061,a870)),f299(x71061,x71062,x71064)),f299(x71061,x71063,x71065))) % 154.70/154.56 [7107]~P105(x71071)+E(f328(f328(f105(f882(x71071,a870)),f328(f298(x71071,x71072),x71073)),f328(f298(x71071,x71074),x71075)),f328(f298(x71071,f328(f328(f241(x71071),x71072),x71074)),f328(f328(f240(x71071),x71073),x71075))) % 154.70/154.56 [7224]~P1(f328(x72241,f526(x72243,x72242,x72241)))+P1(f328(x72241,f328(f328(f263(x72242,x72243),x72244),x72245))) % 154.70/154.56 [7311]~E(f328(x73113,x73114),f205(x73112))+E(f184(x73111,x73112,f328(f328(f328(f72(x73111,f879(x73112)),x73113),x73114),f328(f235(x73112),x73115))),f328(f328(f306(x73112),x73115),f184(x73111,x73112,x73113))) % 154.70/154.56 [7332]~E(x73322,f328(x73324,x73325))+P1(f328(f328(f330(x73321),x73322),f328(f307(x73323,x73321,x73324),f251(f882(x73323,a870))))) % 154.70/154.56 [7390]~E(f328(x73903,x73904),f205(x73902))+E(f328(f328(f22(f882(x73901,a870)),f182(x73901,x73902,x73903)),f328(f328(f306(x73901),x73904),x73905)),f328(f328(f22(f882(x73901,a870)),f182(x73901,x73902,x73903)),x73905)) % 154.70/154.56 [7409]~P17(x74093,x74092,x74094)+P17(x74091,x74092,f328(f328(f8(x74093,f882(x74092,x74092),x74091),x74094),x74095)) % 154.70/154.56 [7410]~P18(x74103,x74102,x74104)+P18(x74101,x74102,f328(f328(f8(x74103,f882(x74102,x74102),x74101),x74104),x74105)) % 154.70/154.56 [7551]~P27(x75511,x75512,x75513,x75514)+P27(x75511,x75512,x75513,f328(f328(f22(f882(x75511,a870)),x75514),x75515)) % 154.70/154.56 [7710]~P1(f328(f328(x77103,x77104),x77105))+P1(f328(f328(f267(x77101,x77102,a870),x77103),f328(f328(f263(x77101,x77102),x77104),x77105))) % 154.70/154.56 [7825]~P1(f328(x78252,x78254))+~E(f328(f328(f135(x78251),f328(f193(f876(x78251)),f175(x78251,x78252,x78253))),x78253),f328(f328(f148(x78251),x78254),x78255)) % 154.70/154.56 [7845]P27(x78451,x78452,x78453,x78454)+~P27(x78451,x78452,x78453,f328(f328(f114(f882(x78451,a870)),x78455),x78454)) % 154.70/154.56 [7846]P27(x78461,x78462,x78463,x78464)+~P27(x78461,x78462,x78463,f328(f328(f114(f882(x78461,a870)),x78464),x78465)) % 154.70/154.56 [7893]~P105(x78932)+E(f328(f328(f145(x78931,x78932,x78933),x78934),f147(x78931,x78932,x78933,x78935)),f147(x78931,x78932,x78933,f328(f328(f148(x78931),x78934),x78935))) % 154.70/154.56 [8049]~P29(x80491,f328(a116,x80492),f328(f328(f328(f92(x80491),x80493),f328(a26,x80494)),x80495))+P29(x80491,x80492,f328(f328(f328(f92(x80491),x80493),f328(f239(a871),f328(a28,x80494))),x80495)) % 154.70/154.56 [8188]P29(x81881,f328(a116,x81882),f328(f328(f328(f92(x81881),x81883),f328(a26,x81884)),x81885))+~P29(x81881,x81882,f328(f328(f328(f92(x81881),x81883),f328(f239(a871),f328(a28,x81884))),x81885)) % 154.70/154.56 [8222]~P17(x82222,x82221,x82223)+E(f328(f139(x82221,x82222,f328(f7(x82222,x82221,x82221),x82223),x82224),x82225),f328(f328(f64(x82222,x82221,x82223),x82224),f328(f170(x82222),x82225))) % 154.70/154.56 [8252]~E(f328(f328(f135(x82521),f328(f193(f876(x82521)),f175(x82521,x82522,x82523))),x82523),f328(f328(f148(x82521),x82524),x82525))+E(f328(f328(f125(x82521),f175(x82521,x82522,x82523)),f328(f328(f148(x82521),x82524),x82525)),x82523) % 154.70/154.56 [8277]P1(f328(f328(x82771,x82772),x82773))+~P1(f328(f328(f267(x82774,x82775,a870),x82771),f328(f328(f263(x82774,x82775),x82772),x82773))) % 154.70/154.56 [8339]~E(f328(f328(f176(x83391,x83392),x83395),x83393),f328(f235(x83392),x83394))+P1(f328(f328(f330(f881(x83391,x83392)),f328(f328(f263(x83391,x83392),x83393),x83394)),f328(f170(f881(x83391,x83392)),x83395))) % 154.70/154.56 [8745]P1(f328(f328(f242(f882(x87451,a870)),f328(f307(x87452,x87451,x87453),x87454)),f328(f307(x87452,x87451,x87453),x87455)))+~P1(f328(f328(f242(f882(x87452,a870)),x87454),x87455)) % 154.70/154.56 [8746]P1(f328(f328(f242(f882(x87461,a870)),f328(f308(x87461,x87462,x87463),x87464)),f328(f308(x87461,x87462,x87463),x87465)))+~P1(f328(f328(f242(f882(x87462,a870)),x87464),x87465)) % 154.70/154.56 [8821]E(x88211,f2(a103))+E(f328(f328(f269(x88212,x88213,x88212,f881(x88213,x88212)),f328(x88214,x88215)),f277(x88213,x88212,f328(f328(f22(a103),x88211),f78(a103)),x88214)),f328(f277(x88213,x88212,x88211,x88214),x88215)) % 154.70/154.56 [9144]P29(x91441,x91442,f328(f328(f328(f92(x91441),x91443),x91444),x91445))+P1(f328(f328(x91443,f349(x91445,x91444,x91443,x91442)),f354(x91445,x91444,x91443,x91442))) % 154.70/154.56 [9344]E(f328(f235(x93441),f716(x93442,x93443,x93444,x93441,x93445)),f328(f328(f176(x93445,x93441),x93442),x93444))+~P1(f328(f328(f330(f881(x93445,x93441)),f328(f328(f263(x93445,x93441),x93444),x93443)),f328(f170(f881(x93445,x93441)),x93442))) % 154.70/154.56 [9388]P29(x93881,x93882,f328(f328(f328(f92(x93881),x93883),x93884),x93885))+~P1(f328(f328(x93885,f349(x93885,x93884,x93883,x93882)),f355(x93885,x93884,x93883,x93882))) % 154.70/154.56 [9448]P29(x94481,x94482,f328(f328(f328(f92(x94481),x94483),x94484),x94485))+P1(f328(f328(f328(f328(a200,x94484),f354(x94485,x94484,x94483,x94482)),x94482),f355(x94485,x94484,x94483,x94482))) % 154.70/154.56 [9451]~P26(x94511,x94512,f328(f328(f306(f874(x94511)),f328(f328(f328(f92(x94511),x94513),f328(f239(a871),f328(a28,x94514))),x94515)),f192(f882(f874(x94511),a870))))+P26(x94511,x94512,f328(f328(f306(f874(x94511)),f328(f328(f328(f92(x94511),x94513),f328(a26,x94514)),x94515)),f192(f882(f874(x94511),a870)))) % 154.70/154.56 [9479]~P1(f328(f61(x94793),f328(f307(x94792,x94793,x94795),f251(f882(x94792,a870)))))+P1(f328(f61(x94791),f328(f307(x94792,x94791,f328(f328(f8(x94793,x94791,x94792),x94794),x94795)),f251(f882(x94792,a870))))) % 154.70/154.56 [9501]P1(f328(f328(f242(f882(f882(x95011,a870),a870)),f328(f307(f882(x95012,a870),f882(x95011,a870),f307(x95012,x95011,x95013)),f328(f305(x95012),x95014))),f328(f305(x95011),x95015)))+~P1(f328(f328(f242(f882(x95011,a870)),f328(f307(x95012,x95011,x95013),x95014)),x95015)) % 154.70/154.56 [9514]~P1(f328(f61(f879(x95141)),f328(f307(x95142,f879(x95141),x95143),f251(f882(x95142,a870)))))+P1(f328(f61(f879(x95141)),f328(f307(x95142,f879(x95141),f328(f328(f328(f72(x95142,f879(x95141)),x95143),x95144),f328(f235(x95141),x95145))),f251(f882(x95142,a870))))) % 154.70/154.56 [9575]E(x95751,x95752)+~P1(f328(f66(x95753,x95754,x95755,x95751,f192(f882(x95753,a870))),x95752)) % 154.70/154.56 [9590]E(f328(f328(f263(x95901,x95902),f580(x95903,x95904,x95905,x95902,x95901)),f582(x95903,x95904,x95905,x95902,x95901)),x95905)+~P1(f328(f328(f330(f881(x95901,x95902)),x95905),f328(f328(f265(x95901,x95902),x95904),x95903))) % 154.70/154.56 [9683]P1(f328(f328(f330(x96831),f580(x96832,x96833,x96834,x96835,x96831)),x96833))+~P1(f328(f328(f330(f881(x96831,x96835)),x96834),f328(f328(f265(x96831,x96835),x96833),x96832))) % 154.70/154.56 [9791]P26(x97915,x97914,f328(f328(f306(f874(x97915)),f328(f328(f328(f92(x97915),x97911),x97913),x97912)),f192(f882(f874(x97915),a870))))+P1(f328(f328(x97911,f363(x97912,x97913,x97914,x97915,x97911)),f372(x97912,x97913,x97914,x97915,x97911))) % 154.70/154.56 [9842]P1(f328(f328(f330(x98421),f582(x98422,x98423,x98424,x98421,x98425)),f328(x98422,f580(x98422,x98423,x98424,x98421,x98425))))+~P1(f328(f328(f330(f881(x98425,x98421)),x98424),f328(f328(f265(x98425,x98421),x98423),x98422))) % 154.70/154.56 [9870]P1(f328(f328(f330(f881(x98701,x98701)),f328(f328(f263(x98701,x98701),x98702),f650(x98703,x98704,x98705,x98702,x98701))),x98703))+~P1(f328(f328(f330(f881(x98701,x98701)),f328(f328(f263(x98701,x98701),x98702),x98705)),f328(f328(f187(f881(x98701,x98701),a870),f328(a116,x98704)),x98703))) % 154.70/154.56 [9871]P1(f328(f328(f330(f881(x98711,x98711)),f328(f328(f263(x98711,x98711),x98712),f652(x98713,x98714,x98715,x98712,x98711))),x98713))+~P1(f328(f328(f330(f881(x98711,x98711)),f328(f328(f263(x98711,x98711),x98712),x98715)),f328(f328(f187(f881(x98711,x98711),a870),f328(a116,x98714)),x98713))) % 154.70/154.56 [9889]~P1(f328(f328(f330(f881(f876(x98891),f876(x98891))),f328(f328(f263(f876(x98891),f876(x98891)),f328(f328(f148(x98891),x98892),x98895)),x98894)),f155(x98891,x98893)))+P1(f328(f328(f330(f881(x98891,x98891)),f328(f328(f263(x98891,x98891),x98892),f672(x98893,x98894,x98895,x98892,x98891))),x98893)) % 154.70/154.56 [9891]~P26(x98911,x98912,f328(f328(f306(f874(x98911)),f328(f328(f328(f92(x98911),f95(x98911,x98913,x98914)),x98915),x98913)),f192(f882(f874(x98911),a870))))+P26(x98911,x98912,f328(f328(f306(f874(x98911)),f328(f328(f328(f92(x98911),x98913),f32(x98914,x98915)),f95(x98911,x98913,f328(f73(a870,a870,a872,a323),x98914)))),f192(f882(f874(x98911),a870)))) % 154.70/154.56 [9892]~P30(x98921,x98922,f328(f328(f306(f874(x98921)),f328(f328(f328(f92(x98921),f95(x98921,x98923,x98924)),x98925),x98923)),f192(f882(f874(x98921),a870))))+P30(x98921,x98922,f328(f328(f306(f874(x98921)),f328(f328(f328(f92(x98921),x98923),f32(x98924,x98925)),f95(x98921,x98923,f328(f73(a870,a870,a872,a323),x98924)))),f192(f882(f874(x98921),a870)))) % 154.70/154.56 [10153]P26(x101531,x101532,f328(f328(f306(f874(x101531)),f328(f328(f328(f92(x101531),x101533),x101534),x101535)),f192(f882(f874(x101531),a870))))+~P26(x101531,x101532,f328(f328(f306(f874(x101531)),f328(f328(f328(f92(x101531),f328(f16(f882(a872,a870),x101531),f328(f328(f7(a872,a872,a870),a325),f372(x101535,x101534,x101532,x101531,x101533)))),x101534),f328(f16(f882(a872,a870),x101531),f328(x101535,f363(x101535,x101534,x101532,x101531,x101533))))),f192(f882(f874(x101531),a870)))) % 154.70/154.56 [6317]P1(f328(x63172,x63174))+E(f175(x63171,x63172,f328(f328(f125(x63171),x63173),f328(f328(f148(x63171),x63174),x63175))),f175(x63171,x63172,x63173)) % 154.70/154.56 [6364]~P2(x63642)+E(f328(f328(f328(f114(f882(x63641,x63642)),x63643),x63644),x63645),f328(f328(f114(x63642),f328(x63643,x63645)),f328(x63644,x63645))) % 154.70/154.56 [6366]~P64(x63662)+E(f328(f328(f328(f22(f882(x63661,x63662)),x63663),x63664),x63665),f328(f328(f22(x63662),f328(x63663,x63665)),f328(x63664,x63665))) % 154.70/154.56 [6368]~P2(x63682)+E(f328(f328(f328(f105(f882(x63681,x63682)),x63683),x63684),x63685),f328(f328(f105(x63682),f328(x63683,x63685)),f328(x63684,x63685))) % 154.70/154.56 [6386]E(x63861,x63862)+E(f328(f328(f162(x63863),f328(f328(f156(x63863,x63864),x63861),x63865)),x63862),f328(f328(f162(x63863),x63864),x63862)) % 154.70/154.56 [6650]~E(x66504,f192(f882(x66503,a870)))+E(f328(f328(f114(f882(x66501,a870)),x66502),f328(f328(f41(x66503,f882(x66501,a870)),x66504),x66505)),x66502) % 154.70/154.56 [6651]~E(x66514,f192(f882(x66513,a870)))+E(f328(f328(f22(f882(x66511,a870)),x66512),f328(f328(f41(x66513,f882(x66511,a870)),x66514),x66515)),x66512) % 154.70/154.56 [6652]~E(x66524,f192(f882(x66523,a870)))+E(f328(f328(f105(f882(x66521,a870)),x66522),f328(f328(f42(x66523,f882(x66521,a870)),x66524),x66525)),x66522) % 154.70/154.56 [6666]~E(x66664,f192(f882(x66663,a870)))+E(f328(f328(f306(x66661),x66662),f328(f328(f41(x66663,f882(x66661,a870)),x66664),x66665)),f328(f328(f306(x66661),x66662),f192(f882(x66661,a870)))) % 154.70/154.56 [7457]E(f328(f328(f162(x74571),f328(f328(f151(x74572,x74571),x74573),x74574)),x74575),f328(x74573,f328(f328(f162(x74572),x74574),x74575)))+~P1(f328(f328(f243(a875),x74575),f328(f193(f876(x74572)),x74574))) % 154.70/154.56 [7523]E(f328(f328(f114(f882(x75231,a870)),f328(x75232,x75233)),f328(f328(f41(x75234,f882(x75231,a870)),x75235),x75232)),f328(f328(f41(x75234,f882(x75231,a870)),x75235),x75232))+~P1(f328(f328(f330(x75234),x75233),x75235)) % 154.70/154.56 [7524]E(f328(f328(f105(f882(x75241,a870)),f328(x75242,x75243)),f328(f328(f42(x75244,f882(x75241,a870)),x75245),x75242)),f328(f328(f42(x75244,f882(x75241,a870)),x75245),x75242))+~P1(f328(f328(f330(x75244),x75243),x75245)) % 154.70/154.56 [8129]~E(x81293,f192(f882(x81291,a870)))+E(f328(f328(f41(x81291,f882(x81292,a870)),x81293),f328(f328(f8(f882(x81292,a870),f882(x81292,a870),x81291),f328(f306(x81292),x81294)),x81295)),f192(f882(x81292,a870))) % 154.70/154.56 [8134]~P1(f328(f328(f330(x81344),x81343),x81345))+P1(f328(f328(f242(f882(x81341,a870)),f328(x81342,x81343)),f328(f328(f41(x81344,f882(x81341,a870)),x81345),x81342))) % 154.70/154.56 [8276]~E(f328(x82764,x82762),x82765)+P1(f328(f328(f330(x82761),x82762),f328(f308(x82761,x82763,x82764),f328(f328(f306(x82763),x82765),f192(f882(x82763,a870)))))) % 154.70/154.56 [8321]~P51(x83211,x83212,f328(f283(x83212,x83211),x83213))+E(f328(f328(f105(f882(x83211,a870)),f328(f282(x83212,x83211,x83213),x83214)),f328(f282(x83212,x83211,x83213),x83215)),f328(f282(x83212,x83211,x83213),f328(f328(f105(f882(x83212,a870)),x83214),x83215))) % 154.70/154.56 [8397]E(x83971,f2(a103))+E(f328(f120(x83972,x83973,f328(x83974,f328(f328(f22(a103),x83971),f78(a103)))),f328(f328(f7(x83972,a103,f877(x83973)),x83975),x83971)),f328(f204(x83972,x83973,x83974,x83975),x83971)) % 154.70/154.56 [8437]E(x84371,f192(f882(x84372,a870)))+E(f328(f328(f41(x84372,f882(x84373,a870)),x84371),f328(f328(f8(f882(x84373,a870),f882(x84373,a870),x84372),f328(f306(x84373),x84374)),x84375)),f328(f328(f306(x84373),x84374),f328(f328(f41(x84372,f882(x84373,a870)),x84371),x84375))) % 154.70/154.56 [8487]~P27(x84872,x84871,x84873,f251(f882(x84872,a870)))+E(f328(f328(f22(f882(x84871,a870)),f328(f307(x84872,x84871,x84873),x84874)),f328(f307(x84872,x84871,x84873),x84875)),f328(f307(x84872,x84871,x84873),f328(f328(f22(f882(x84872,a870)),x84874),x84875))) % 154.70/154.56 [8488]~P27(x84882,x84881,x84883,f251(f882(x84882,a870)))+E(f328(f328(f105(f882(x84881,a870)),f328(f307(x84882,x84881,x84883),x84884)),f328(f307(x84882,x84881,x84883),x84885)),f328(f307(x84882,x84881,x84883),f328(f328(f105(f882(x84882,a870)),x84884),x84885))) % 154.70/154.56 [8562]~P1(f328(f328(f67(x85621,x85622,x85625),x85623),x85624))+P1(f328(f328(f330(f881(x85621,x85622)),f328(f328(f263(x85621,x85622),x85623),x85624)),x85625)) % 154.70/154.56 [8594]P1(f328(f328(f330(x85941),x85942),f328(f259(x85943,x85941),x85944)))+~P1(f328(f328(f330(f881(x85943,x85941)),f328(f328(f263(x85943,x85941),x85945),x85942)),x85944)) % 154.70/154.56 [8596]P1(f328(f328(f330(x85961),x85962),f328(f261(x85961,x85963),x85964)))+~P1(f328(f328(f330(f881(x85961,x85963)),f328(f328(f263(x85961,x85963),x85962),x85965)),x85964)) % 154.70/154.56 [8732]P1(f328(f328(f67(x87321,x87322,x87323),x87324),x87325))+~P1(f328(f328(f330(f881(x87321,x87322)),f328(f328(f263(x87321,x87322),x87324),x87325)),x87323)) % 154.70/154.56 [8767]E(f328(x87671,x87672),x87673)+~P1(f328(f328(f330(x87674),x87672),f328(f308(x87674,x87675,x87671),f328(f328(f306(x87675),x87673),f192(f882(x87675,a870)))))) % 154.70/154.56 [9000]P1(f328(f328(f330(f881(x90001,x90002)),f328(f328(f263(x90001,x90002),x90003),x90004)),f328(f283(x90002,x90001),x90005)))+~P1(f328(f328(f330(f881(x90002,x90001)),f328(f328(f263(x90002,x90001),x90004),x90003)),x90005)) % 154.70/154.56 [9018]~P1(f328(f328(x90181,x90185),x90184))+P1(f328(f328(x90181,f328(f266(x90182,x90183),f328(f328(f263(x90182,x90183),x90184),x90185))),f328(f262(x90182,x90183),f328(f328(f263(x90182,x90183),x90184),x90185)))) % 154.70/154.56 [9048]~P1(f328(f328(f330(f881(x90482,x90481)),f328(f328(f263(x90482,x90481),x90484),x90483)),f328(f283(x90481,x90482),x90485)))+P1(f328(f328(f330(f881(x90481,x90482)),f328(f328(f263(x90481,x90482),x90483),x90484)),x90485)) % 154.70/154.56 [9081]~P1(f328(f328(f330(f881(x90813,x90811)),f328(f328(f263(x90813,x90811),x90815),x90812)),x90814))+P1(f328(f328(f330(x90811),x90812),f328(f282(x90813,x90811,x90814),f328(f328(f306(x90813),x90815),f192(f882(x90813,a870)))))) % 154.70/154.56 [9126]P1(f328(f328(f330(f881(x91261,x91262)),f328(f328(f263(x91261,x91262),x91263),x91264)),x91265))+~P1(f328(f328(f330(x91262),x91264),f328(f282(x91261,x91262,x91265),f328(f328(f306(x91261),x91263),f192(f882(x91261,a870)))))) % 154.70/154.56 [9147]E(f328(f328(f328(f72(x91471,f879(x91472)),f186(x91471,x91472,x91473,x91474)),x91475),f205(x91472)),f186(x91471,x91472,x91473,f328(f328(f22(f882(x91471,a870)),x91474),f328(f328(f306(x91471),x91475),f192(f882(x91471,a870))))))+~P1(f328(f328(f330(x91471),x91475),x91474)) % 154.70/154.56 [9215]~P66(x92151)+E(f328(f328(f6(a875,x92151),x92152),f299(a875,f328(f328(f80(a875),x92153),x92154),f328(f328(f80(a875),x92155),x92154))),f328(f328(f6(a875,x92151),f328(f328(f8(a875,x92151,a875),x92152),f328(f328(f7(a875,a875,a875),f80(a875)),x92154))),f299(a875,x92153,x92155))) % 154.70/154.56 [9239]~P66(x92391)+E(f328(f328(f6(a875,x92391),x92392),f328(f298(a875,f328(f328(f80(a875),x92393),x92394)),f328(f328(f80(a875),x92395),x92394))),f328(f328(f6(a875,x92391),f328(f328(f8(a875,x92391,a875),x92392),f328(f328(f7(a875,a875,a875),f80(a875)),x92394))),f328(f298(a875,x92393),x92395))) % 154.70/154.56 [9292]~P27(x92921,x92922,x92923,f251(f882(x92921,a870)))+E(f328(f328(f151(x92921,x92922),x92923),f328(f133(x92921,f328(f328(f8(a870,a870,x92921),a323),f328(a325,x92924))),x92925)),f328(f133(x92922,f328(f328(f8(a870,a870,x92922),a323),f328(a325,f328(x92923,x92924)))),f328(f328(f151(x92921,x92922),x92923),x92925))) % 154.70/154.56 [9310]~P27(x93101,x93102,x93103,f328(f328(f306(x93101),x93104),f328(f170(x93101),x93105)))+E(f328(f328(f151(x93101,x93102),x93103),f328(f133(x93101,f328(f328(f8(a870,a870,x93101),a323),f328(a325,x93104))),x93105)),f328(f133(x93102,f328(f328(f8(a870,a870,x93102),a323),f328(a325,f328(x93103,x93104)))),f328(f328(f151(x93101,x93102),x93103),x93105))) % 154.70/154.56 [9466]P1(f328(f328(f330(f881(f876(x94661),f876(x94661))),f328(f328(f263(f876(x94661),f876(x94661)),f328(f328(f148(x94661),x94662),x94663)),f328(f328(f148(x94661),x94664),x94663))),f154(x94661,x94665)))+~P1(f328(f328(f330(f881(x94661,x94661)),f328(f328(f263(x94661,x94661),x94662),x94664)),x94665)) % 154.70/154.56 [9502]P1(f328(f328(f328(f328(a200,x95021),x95022),x95023),f347(x95024,x95023,x95022,x95025,x95021)))+~P1(f328(f328(f328(f328(a200,f33(x95021,x95025)),x95022),x95023),x95024)) % 154.70/154.56 [9573]P26(x95731,x95732,f328(f328(f306(f874(x95731)),f328(f328(f328(f92(x95731),x95733),f328(a26,x95734)),x95735)),f192(f882(f874(x95731),a870))))+~P26(x95731,f328(f328(f306(f874(x95731)),f328(f328(f328(f92(x95731),x95733),f328(a26,x95734)),x95735)),x95732),f328(f328(f306(f874(x95731)),f328(f328(f328(f92(x95731),x95733),f328(f239(a871),f328(a28,x95734))),x95735)),f192(f882(f874(x95731),a870)))) % 154.70/154.56 [9585]E(f328(f328(f306(x95851),f844(x95852,x95853,x95854,x95855,x95851)),f847(x95852,x95853,x95854,x95855,x95851)),f328(f328(f306(x95851),x95854),x95853))+~P1(f328(f62(x95851,x95855,f328(f328(f306(x95851),x95854),x95853)),x95852)) % 154.70/154.56 [9586]E(f328(f328(f306(x95861),f848(x95862,x95863,x95864,x95865,x95861)),f849(x95862,x95863,x95864,x95865,x95861)),f328(f328(f306(x95861),x95864),x95863))+~P1(f328(f62(x95861,x95865,f328(f328(f306(x95861),x95864),x95863)),x95862)) % 154.70/154.56 [9668]P1(f328(f328(f330(x96681),f833(x96682,x96683,x96684,x96685,x96681)),x96684))+P1(f328(f328(f328(f42(x96681,f882(x96685,a870)),x96684),x96683),x96682)) % 154.70/154.56 [9673]P1(f328(f328(f330(x96731),f829(x96732,x96733,x96731,x96734,x96735)),x96733))+P1(f328(f328(f330(x96735),x96734),f328(f328(f42(x96731,f882(x96735,a870)),x96733),x96732))) % 154.70/154.56 [9681]P1(f328(f328(f330(x96811),f353(x96812,x96813,x96811,x96814,x96815)),x96813))+P1(f328(f328(f242(f882(x96815,a870)),x96814),f328(f328(f42(x96811,f882(x96815,a870)),x96813),x96812))) % 154.70/154.56 [9684]P1(f328(f328(x96841,f699(x96842,x96841,x96843,x96844,x96845)),x96842))+~P1(f328(f328(f328(f41(x96845,f882(x96844,a870)),x96843),x96841),x96842)) % 154.70/154.56 [9687]P1(f328(f328(f330(x96871),f699(x96872,x96873,x96874,x96875,x96871)),x96874))+~P1(f328(f328(f328(f41(x96871,f882(x96875,a870)),x96874),x96873),x96872)) % 154.70/154.56 [9697]P1(f328(f328(f330(x96971),f754(x96972,x96973,x96971,x96974,x96975)),x96973))+~P1(f328(f328(f330(x96975),x96974),f328(f328(f41(x96971,f882(x96975,a870)),x96973),x96972))) % 154.70/154.56 [9702]P1(f328(f328(f330(x97021),x97022),f328(x97023,f754(x97023,x97024,x97025,x97022,x97021))))+~P1(f328(f328(f330(x97021),x97022),f328(f328(f41(x97025,f882(x97021,a870)),x97024),x97023))) % 154.70/154.56 [9796]~P1(f328(f328(x97964,f833(x97965,x97964,x97963,x97962,x97961)),x97965))+P1(f328(f328(f328(f42(x97961,f882(x97962,a870)),x97963),x97964),x97965)) % 154.70/154.56 [9799]~P1(f328(f328(f330(x97991),x97992),f328(x97995,f829(x97995,x97994,x97993,x97992,x97991))))+P1(f328(f328(f330(x97991),x97992),f328(f328(f42(x97993,f882(x97991,a870)),x97994),x97995))) % 154.70/154.56 [9803]~P1(f328(f328(f242(f882(x98031,a870)),x98032),f328(x98035,f353(x98035,x98034,x98033,x98032,x98031))))+P1(f328(f328(f242(f882(x98031,a870)),x98032),f328(f328(f42(x98033,f882(x98031,a870)),x98034),x98035))) % 154.70/154.56 [9848]P1(f328(f328(f328(f328(a200,x98481),f347(x98482,x98483,x98484,x98481,x98485)),x98483),x98482))+~P1(f328(f328(f328(f328(a200,f33(x98485,x98481)),x98484),x98483),x98482)) % 154.70/154.56 [9874]~P1(f328(f328(f330(x98741),f844(x98745,x98744,x98743,x98742,x98741)),f847(x98745,x98744,x98743,x98742,x98741)))+~P1(f328(f62(x98741,x98742,f328(f328(f306(x98741),x98743),x98744)),x98745)) % 154.70/154.56 [9875]~P1(f328(f328(f330(x98751),f848(x98755,x98754,x98753,x98752,x98751)),f849(x98755,x98754,x98753,x98752,x98751)))+~P1(f328(f62(x98751,x98752,f328(f328(f306(x98751),x98753),x98754)),x98755)) % 154.70/154.56 [9876]~P1(f328(f328(f330(f881(x98761,x98761)),f328(f328(f263(x98761,x98761),x98762),x98765)),f328(f328(f187(f881(x98761,x98761),a870),f328(a116,x98764)),x98763)))+P1(f328(f328(f330(f881(x98761,x98761)),f328(f328(f263(x98761,x98761),x98762),f651(x98763,x98764,x98765,x98762,x98761))),f328(f328(f187(f881(x98761,x98761),a870),x98764),x98763))) % 154.70/154.56 [9883]P1(f328(f66(x98831,x98831,x98832,f844(x98833,x98834,x98835,x98832,x98831),f847(x98833,x98834,x98835,x98832,x98831)),x98833))+~P1(f328(f62(x98831,x98832,f328(f328(f306(x98831),x98835),x98834)),x98833)) % 154.70/154.56 [9884]P1(f328(f66(x98841,x98841,x98842,f848(x98843,x98844,x98845,x98842,x98841),f849(x98843,x98844,x98845,x98842,x98841)),x98843))+~P1(f328(f62(x98841,x98842,f328(f328(f306(x98841),x98845),x98844)),x98843)) % 154.70/154.56 [9896]~P105(x98961)+P16(x98961,f328(f328(f151(x98962,x98961),x98963),f328(f133(x98962,f328(f328(f7(x98962,x98961,a870),f328(f328(f8(x98961,f882(x98961,a870),x98962),a325),x98963)),f328(x98964,x98965))),x98965))) % 154.70/154.56 [9936]~P1(f328(f328(f330(x99362),x99365),f328(f282(x99361,x99362,x99364),x99363)))+P1(f328(f328(f330(f881(x99361,x99362)),f328(f328(f263(x99361,x99362),f529(x99363,x99364,x99361,x99365,x99362)),x99365)),x99364)) % 154.70/154.56 [9937]~P1(f328(f328(f330(x99372),x99375),f328(f282(x99371,x99372,x99374),x99373)))+P1(f328(f328(f330(f881(x99371,x99372)),f328(f328(f263(x99371,x99372),f551(x99373,x99374,x99371,x99375,x99372)),x99375)),x99374)) % 154.70/154.56 [9957]~P1(f328(f328(f330(f881(x99571,x99571)),f328(f328(f263(x99571,x99571),x99575),x99574)),f328(f328(f187(f881(x99571,x99571),a870),f328(a116,x99573)),x99572)))+P1(f328(f328(f330(f881(x99571,x99571)),f328(f328(f263(x99571,x99571),f651(x99572,x99573,x99574,x99575,x99571)),x99574)),x99572)) % 154.70/154.56 [9960]~P1(f328(f328(f330(f881(x99601,x99601)),f328(f328(f263(x99601,x99601),x99605),x99604)),f328(f328(f187(f881(x99601,x99601),a870),f328(a116,x99603)),x99602)))+P1(f328(f328(f330(f881(x99601,x99601)),f328(f328(f263(x99601,x99601),f650(x99602,x99603,x99604,x99605,x99601)),x99604)),f328(f328(f187(f881(x99601,x99601),a870),x99603),x99602))) % 154.70/154.56 [9961]~P1(f328(f328(f330(f881(x99611,x99611)),f328(f328(f263(x99611,x99611),x99615),x99614)),f328(f328(f187(f881(x99611,x99611),a870),f328(a116,x99613)),x99612)))+P1(f328(f328(f330(f881(x99611,x99611)),f328(f328(f263(x99611,x99611),f652(x99612,x99613,x99614,x99615,x99611)),x99614)),f328(f328(f187(f881(x99611,x99611),a870),x99613),x99612))) % 154.70/154.56 [9962]~P1(f328(f328(f330(f881(f876(x99621),f876(x99621))),f328(f328(f263(f876(x99621),f876(x99621)),x99625),f328(f328(f148(x99621),x99624),x99623))),f155(x99621,x99622)))+P1(f328(f328(f330(f881(x99621,x99621)),f328(f328(f263(x99621,x99621),f670(x99622,x99623,x99624,x99625,x99621)),x99624)),x99622)) % 154.70/154.56 [7050]E(x70501,f205(x70502))+E(f182(x70503,x70502,f328(f328(f328(f72(x70503,f879(x70502)),x70504),x70505),x70501)),f328(f328(f306(x70503),x70505),f182(x70503,x70502,x70504))) % 154.70/154.56 [7544]~E(x75443,f192(f882(x75442,a870)))+E(f328(f328(f114(f882(x75441,a870)),f328(f328(f41(x75442,f882(x75441,a870)),x75443),x75444)),x75445),x75445) % 154.70/154.56 [7545]~E(x75453,f192(f882(x75452,a870)))+E(f328(f328(f105(f882(x75451,a870)),f328(f328(f42(x75452,f882(x75451,a870)),x75453),x75454)),x75455),x75455) % 154.70/154.56 [7908]~E(x79085,f205(x79082))+E(f182(x79081,x79082,f328(f328(f328(f72(x79081,f879(x79082)),x79083),x79084),x79085)),f328(f328(f22(f882(x79081,a870)),f182(x79081,x79082,x79083)),f328(f328(f306(x79081),x79084),f192(f882(x79081,a870))))) % 154.70/154.56 [7974]~E(x79743,f192(f882(x79742,a870)))+E(f328(f328(f22(f882(x79741,a870)),f328(f328(f42(x79742,f882(x79741,a870)),x79743),x79744)),x79745),f328(f328(f22(f882(x79741,a870)),f251(f882(x79741,a870))),x79745)) % 154.70/154.56 [8101]E(f328(f328(f156(x81011,f328(f328(f125(x81011),x81012),x81013)),x81014),x81015),f328(f328(f125(x81011),f328(f328(f156(x81011,x81012),x81014),x81015)),x81013))+~P1(f328(f328(f243(a875),x81014),f328(f193(f876(x81011)),x81012))) % 154.70/154.56 [8226]P1(f328(f328(f330(x82261),x82265),f328(f170(x82261),x82263)))+E(f328(f328(f176(x82261,x82262),f328(f328(f180(x82261,x82262),x82263),f328(f328(f151(x82261,x82262),x82264),x82263))),x82265),f205(x82262)) % 154.70/154.56 [8348]~P1(f328(f328(f330(x83481),x83485),f328(f170(x83481),x83483)))+E(f328(f328(f176(x83481,x83482),f328(f328(f180(x83481,x83482),x83483),f328(f328(f151(x83481,x83482),x83484),x83483))),x83485),f328(f235(x83482),f328(x83484,x83485))) % 154.70/154.56 [8385]E(f328(f328(f162(x83851),f328(f328(f151(a875,x83851),x83852),f136(a875,f328(f298(a875,x83853),x83854)))),x83855),f328(x83852,f328(f328(f80(a875),x83853),x83855)))+~P1(f328(f328(f243(a875),x83855),f328(f328(f22(a875),x83854),x83853))) % 154.70/154.56 [8402]E(x84021,f2(a103))+E(f123(x84022,x84023,f328(x84024,f328(f328(f22(a103),x84021),f78(a103))),f328(f328(f7(x84022,a103,f877(f879(x84023))),x84025),x84021)),f328(f202(x84022,x84023,x84024,x84025),x84021)) % 154.70/154.56 [8427]~E(x84273,f192(f882(x84271,a870)))+E(f328(f328(f41(x84271,f882(x84272,a870)),x84273),f328(f328(f8(f882(x84272,a870),f882(x84272,a870),x84271),f328(f114(f882(x84272,a870)),x84274)),x84275)),f192(f882(x84272,a870))) % 154.70/154.56 [8428]~E(x84283,f192(f882(x84281,a870)))+E(f328(f328(f42(x84281,f882(x84282,a870)),x84283),f328(f328(f8(f882(x84282,a870),f882(x84282,a870),x84281),f328(f22(f882(x84282,a870)),x84284)),x84285)),f251(f882(x84282,a870))) % 154.70/154.56 [8429]~E(x84293,f192(f882(x84291,a870)))+E(f328(f328(f42(x84291,f882(x84292,a870)),x84293),f328(f328(f8(f882(x84292,a870),f882(x84292,a870),x84291),f328(f105(f882(x84292,a870)),x84294)),x84295)),f251(f882(x84292,a870))) % 154.70/154.56 [8431]~P139(x84312)+E(f328(f328(f6(x84311,x84312),f328(f328(f8(x84312,x84312,x84311),f328(f81(x84312),x84313)),x84314)),x84315),f328(f328(f81(x84312),x84313),f328(f328(f6(x84311,x84312),x84314),x84315))) % 154.70/154.56 [8717]E(x87171,f192(f882(x87172,a870)))+E(f328(f328(f41(x87172,f882(x87173,a870)),x87171),f328(f328(f8(f882(x87173,a870),f882(x87173,a870),x87172),f328(f114(f882(x87173,a870)),x87174)),x87175)),f328(f328(f114(f882(x87173,a870)),x87174),f328(f328(f41(x87172,f882(x87173,a870)),x87171),x87175))) % 154.70/154.56 [8718]E(x87181,f192(f882(x87182,a870)))+E(f328(f328(f42(x87182,f882(x87183,a870)),x87181),f328(f328(f8(f882(x87183,a870),f882(x87183,a870),x87182),f328(f22(f882(x87183,a870)),x87184)),x87185)),f328(f328(f22(f882(x87183,a870)),x87184),f328(f328(f41(x87182,f882(x87183,a870)),x87181),x87185))) % 154.70/154.56 [8719]E(x87191,f192(f882(x87192,a870)))+E(f328(f328(f42(x87192,f882(x87193,a870)),x87191),f328(f328(f8(f882(x87193,a870),f882(x87193,a870),x87192),f328(f105(f882(x87193,a870)),x87194)),x87195)),f328(f328(f105(f882(x87193,a870)),x87194),f328(f328(f42(x87192,f882(x87193,a870)),x87191),x87195))) % 154.70/154.56 [8913]~P1(f328(f328(f243(a875),f328(x89134,x89132)),f328(x89134,x89133)))+P1(f328(f328(f330(f881(x89131,x89131)),f328(f328(f263(x89131,x89131),x89132),x89133)),f150(x89131,f328(f328(f148(f882(x89131,a875)),x89134),x89135)))) % 154.70/154.56 [9182]~P27(x91822,x91821,x91823,f328(f328(f114(f882(x91822,a870)),x91824),x91825))+E(f328(f328(f105(f882(x91821,a870)),f328(f307(x91822,x91821,x91823),f328(f328(f22(f882(x91822,a870)),x91824),x91825))),f328(f307(x91822,x91821,x91823),f328(f328(f22(f882(x91822,a870)),x91825),x91824))),f192(f882(x91821,a870))) % 154.70/154.56 [9462]~P1(f328(f328(f242(f882(x94623,a870)),f328(f282(x94621,x94623,x94624),x94622)),x94625))+P1(f328(f328(f242(f882(x94621,a870)),x94622),f328(f79(f882(x94621,a870)),f328(f282(x94623,x94621,f328(f283(x94621,x94623),x94624)),f328(f79(f882(x94623,a870)),x94625))))) % 154.70/154.56 [9487]~P27(x94871,x94872,x94873,f328(f328(f306(x94871),x94874),x94875))+~P1(f328(f328(f330(x94872),f328(x94873,x94874)),f328(f307(x94871,x94872,x94873),f328(f328(f22(f882(x94871,a870)),x94875),f328(f328(f306(x94871),x94874),f192(f882(x94871,a870))))))) % 154.70/154.56 [9539]P1(f328(f328(f242(f882(x95391,a870)),f328(f282(x95392,x95391,x95393),x95394)),x95395))+~P1(f328(f328(f242(f882(x95392,a870)),x95394),f328(f79(f882(x95392,a870)),f328(f282(x95391,x95392,f328(f283(x95392,x95391),x95393)),f328(f79(f882(x95391,a870)),x95395))))) % 154.70/154.56 [9613]~P83(x96131)+P1(f328(f328(f242(x96131),f328(f75(x96131),f328(f328(f22(x96131),f328(f328(f80(x96131),x96132),x96133)),f328(f328(f80(x96131),x96134),x96135)))),f328(f328(f80(x96131),f328(f75(x96131),f328(f328(f22(x96131),x96132),x96134))),f328(f75(x96131),f328(f328(f22(x96131),x96133),x96135))))) % 154.70/154.56 [9717]P1(f328(f328(f330(x97171),f352(x97172,x97173,x97174,x97171,x97175)),x97174))+P1(f328(f328(f242(f882(x97175,a870)),f328(f328(f41(x97171,f882(x97175,a870)),x97174),x97173)),x97172)) % 154.70/154.56 [9914]~P1(f328(f328(f242(f882(x99141,a870)),f328(x99144,f352(x99145,x99144,x99143,x99142,x99141))),x99145))+P1(f328(f328(f242(f882(x99141,a870)),f328(f328(f41(x99142,f882(x99141,a870)),x99143),x99144)),x99145)) % 154.70/154.56 [8537]E(f328(f328(f125(x85371),x85372),f328(f328(f156(x85371,x85373),f328(f328(f22(a875),x85374),f328(f193(f876(x85371)),x85372))),x85375)),f328(f328(f156(x85371,f328(f328(f125(x85371),x85372),x85373)),x85374),x85375))+P1(f328(f328(f243(a875),x85374),f328(f193(f876(x85371)),x85372))) % 154.70/154.56 [8570]~P138(x85701)+E(f328(f328(f80(x85701),f328(f328(f81(x85701),x85702),x85703)),f328(f328(f80(x85701),f328(f328(f81(x85701),x85704),x85703)),x85705)),f328(f328(f80(x85701),f328(f328(f81(x85701),f328(f328(f80(x85701),x85702),x85704)),x85703)),x85705)) % 154.70/154.56 [9136]~P139(x91361)+E(f328(f163(x91361),f328(f328(f151(x91362,x91361),f328(f328(f8(x91361,x91361,x91362),f328(f81(x91361),x91363)),x91364)),x91365)),f328(f328(f81(x91361),x91363),f328(f163(x91361),f328(f328(f151(x91362,x91361),x91364),x91365)))) % 154.70/154.56 [9309]E(f328(f193(f876(x93091)),f328(f328(f173(x93091),f328(f328(f240(a875),f328(f193(f876(x93091)),x93092)),f328(f193(f876(x93093)),x93094))),x93092)),f328(f193(f876(x93093)),f328(f328(f173(x93093),f328(f328(f240(a875),f328(f193(f876(x93091)),x93092)),f328(f193(f876(x93093)),x93094))),x93094)))+P1(f328(x93095,f328(f328(f180(x93091,x93093),x93092),x93094))) % 154.70/154.56 [9550]~P139(x95502)+E(f328(f328(f6(x95501,x95502),f328(f328(f7(x95501,x95502,x95502),f328(f328(f8(x95502,f882(x95502,x95502),x95501),f81(x95502)),x95503)),x95504)),x95505),f328(f328(f81(x95502),f328(f328(f6(x95501,x95502),x95503),x95505)),x95504)) % 154.70/154.56 [9551]~P61(x95512)+E(f328(f328(f6(x95511,x95512),f328(f328(f7(x95511,x95512,x95512),f328(f328(f8(x95512,f882(x95512,x95512),x95511),f286(x95512)),x95513)),x95514)),x95515),f328(f328(f286(x95512),f328(f328(f6(x95511,x95512),x95513),x95515)),x95514)) % 154.70/154.56 [9558]~P65(x95582)+E(f328(f328(f6(x95581,x95582),f328(f328(f18(x95581,x95582,x95582),f328(f328(f8(x95582,f882(x95582,x95582),x95581),f22(x95582)),x95583)),x95584)),x95585),f328(f328(f22(x95582),f328(f328(f6(x95581,x95582),x95583),x95585)),f328(f328(f6(x95581,x95582),x95584),x95585))) % 154.70/154.56 [9559]~P66(x95592)+E(f328(f328(f6(x95591,x95592),f328(f328(f18(x95591,x95592,x95592),f328(f328(f8(x95592,f882(x95592,x95592),x95591),f80(x95592)),x95593)),x95594)),x95595),f328(f328(f80(x95592),f328(f328(f6(x95591,x95592),x95593),x95595)),f328(f328(f6(x95591,x95592),x95594),x95595))) % 154.70/154.56 [9560]~P73(x95602)+E(f328(f328(f9(x95601,x95602),f328(f328(f18(x95601,x95602,x95602),f328(f328(f8(x95602,f882(x95602,x95602),x95601),f81(x95602)),x95603)),x95604)),x95605),f328(f328(f81(x95602),f328(f328(f9(x95601,x95602),x95603),x95605)),f328(f328(f9(x95601,x95602),x95604),x95605))) % 154.70/154.56 [9598]~E(x95983,f192(f882(x95981,a870)))+E(f328(f328(f41(x95981,f882(x95982,a870)),x95983),f328(f328(f7(x95981,f882(x95982,a870),f882(x95982,a870)),f328(f328(f8(f882(x95982,a870),f882(f882(x95982,a870),f882(x95982,a870)),x95981),f114(f882(x95982,a870))),x95984)),x95985)),f192(f882(x95982,a870))) % 154.70/154.56 [9599]~E(x95993,f192(f882(x95991,a870)))+E(f328(f328(f42(x95991,f882(x95992,a870)),x95993),f328(f328(f7(x95991,f882(x95992,a870),f882(x95992,a870)),f328(f328(f8(f882(x95992,a870),f882(f882(x95992,a870),f882(x95992,a870)),x95991),f22(f882(x95992,a870))),x95994)),x95995)),f251(f882(x95992,a870))) % 154.70/154.56 [9600]~E(x96003,f192(f882(x96001,a870)))+E(f328(f328(f42(x96001,f882(x96002,a870)),x96003),f328(f328(f7(x96001,f882(x96002,a870),f882(x96002,a870)),f328(f328(f8(f882(x96002,a870),f882(f882(x96002,a870),f882(x96002,a870)),x96001),f105(f882(x96002,a870))),x96004)),x96005)),f251(f882(x96002,a870))) % 154.70/154.56 [9621]E(x96211,f192(f882(x96212,a870)))+E(f328(f328(f41(x96212,f882(x96213,a870)),x96211),f328(f328(f7(x96212,f882(x96213,a870),f882(x96213,a870)),f328(f328(f8(f882(x96213,a870),f882(f882(x96213,a870),f882(x96213,a870)),x96212),f114(f882(x96213,a870))),x96214)),x96215)),f328(f328(f114(f882(x96213,a870)),f328(f328(f41(x96212,f882(x96213,a870)),x96211),x96214)),x96215)) % 154.70/154.56 [9622]E(x96221,f192(f882(x96222,a870)))+E(f328(f328(f42(x96222,f882(x96223,a870)),x96221),f328(f328(f7(x96222,f882(x96223,a870),f882(x96223,a870)),f328(f328(f8(f882(x96223,a870),f882(f882(x96223,a870),f882(x96223,a870)),x96222),f22(f882(x96223,a870))),x96224)),x96225)),f328(f328(f22(f882(x96223,a870)),f328(f328(f42(x96222,f882(x96223,a870)),x96221),x96224)),x96225)) % 154.70/154.56 [9623]E(x96231,f192(f882(x96232,a870)))+E(f328(f328(f42(x96232,f882(x96233,a870)),x96231),f328(f328(f7(x96232,f882(x96233,a870),f882(x96233,a870)),f328(f328(f8(f882(x96233,a870),f882(f882(x96233,a870),f882(x96233,a870)),x96232),f105(f882(x96233,a870))),x96234)),x96235)),f328(f328(f105(f882(x96233,a870)),f328(f328(f42(x96232,f882(x96233,a870)),x96231),x96234)),x96235)) % 154.70/154.56 [9189]~P1(f328(f328(f242(a875),x91891),x91894))+E(f328(f328(f22(a875),f328(f328(f80(a875),f328(f328(f81(a875),x91891),x91892)),x91893)),f328(f328(f80(a875),f328(f328(f81(a875),x91894),x91892)),x91895)),f328(f328(f22(a875),x91893),f328(f328(f80(a875),f328(f328(f81(a875),f328(f328(f22(a875),x91894),x91891)),x91892)),x91895))) % 154.70/154.56 [9777]~P139(x97771)+E(f328(f163(x97771),f328(f328(f151(x97772,x97771),f328(f328(f7(x97772,x97771,x97771),f328(f328(f8(x97771,f882(x97771,x97771),x97772),f81(x97771)),x97773)),x97774)),x97775)),f328(f328(f81(x97771),f328(f163(x97771),f328(f328(f151(x97772,x97771),x97773),x97775))),x97774)) % 154.70/154.56 [9783]~P65(x97831)+E(f328(f163(x97831),f328(f328(f151(x97832,x97831),f328(f328(f18(x97832,x97831,x97831),f328(f328(f8(x97831,f882(x97831,x97831),x97832),f22(x97831)),x97833)),x97834)),x97835)),f328(f328(f22(x97831),f328(f163(x97831),f328(f328(f151(x97832,x97831),x97833),x97835))),f328(f163(x97831),f328(f328(f151(x97832,x97831),x97834),x97835)))) % 154.70/154.56 [9784]~P66(x97841)+E(f328(f163(x97841),f328(f328(f151(x97842,x97841),f328(f328(f18(x97842,x97841,x97841),f328(f328(f8(x97841,f882(x97841,x97841),x97842),f80(x97841)),x97843)),x97844)),x97845)),f328(f328(f80(x97841),f328(f163(x97841),f328(f328(f151(x97842,x97841),x97843),x97845))),f328(f163(x97841),f328(f328(f151(x97842,x97841),x97844),x97845)))) % 154.70/154.56 [9927]P1(f328(x99271,f328(f328(f180(x99272,x99273),x99274),x99275)))+~P1(f328(x99271,f328(f328(f180(x99272,x99273),f328(f328(f173(x99272),f328(f328(f240(a875),f328(f193(f876(x99272)),x99274)),f328(f193(f876(x99273)),x99275))),x99274)),f328(f328(f173(x99273),f328(f328(f240(a875),f328(f193(f876(x99272)),x99274)),f328(f193(f876(x99273)),x99275))),x99275)))) % 154.70/154.56 [10162]~P1(f328(f328(f330(f881(x101622,x101621)),f328(f328(f263(x101622,x101621),x101624),x101625)),f328(f283(x101621,x101622),x101623)))+P1(f328(f328(f252(x101621,x101622,f328(f328(f7(x101621,f882(f881(x101621,x101622),a870),f882(x101622,a870)),f328(f328(f8(f882(x101622,f882(f882(f881(x101621,x101622),a870),a870)),f882(f882(f881(x101621,x101622),a870),f882(x101622,a870)),x101621),f7(x101622,f882(f881(x101621,x101622),a870),a870)),f328(f328(f8(f882(x101622,f881(x101621,x101622)),f882(x101622,f882(f882(f881(x101621,x101622),a870),a870)),x101621),f328(f8(f881(x101621,x101622),f882(f882(f881(x101621,x101622),a870),a870),x101622),f330(f881(x101621,x101622)))),f263(x101621,x101622)))),x101623)),x101624),x101625)) % 154.70/154.56 [10171]P1(f328(f328(f330(f881(x101711,x101712)),f328(f328(f263(x101711,x101712),x101713),x101714)),f328(f283(x101712,x101711),x101715)))+~P1(f328(f328(f252(x101712,x101711,f328(f328(f7(x101712,f882(f881(x101712,x101711),a870),f882(x101711,a870)),f328(f328(f8(f882(x101711,f882(f882(f881(x101712,x101711),a870),a870)),f882(f882(f881(x101712,x101711),a870),f882(x101711,a870)),x101712),f7(x101711,f882(f881(x101712,x101711),a870),a870)),f328(f328(f8(f882(x101711,f881(x101712,x101711)),f882(x101711,f882(f882(f881(x101712,x101711),a870),a870)),x101712),f328(f8(f881(x101712,x101711),f882(f882(f881(x101712,x101711),a870),a870),x101711),f330(f881(x101712,x101711)))),f263(x101712,x101711)))),x101715)),x101713),x101714)) % 154.70/154.56 [9430]~P1(f328(f328(f242(a875),x94304),x94301))+E(f328(f328(f22(a875),f328(f328(f80(a875),f328(f328(f81(a875),x94301),x94302)),x94303)),f328(f328(f80(a875),f328(f328(f81(a875),x94304),x94302)),x94305)),f328(f328(f22(a875),f328(f328(f80(a875),f328(f328(f81(a875),f328(f328(f22(a875),x94301),x94304)),x94302)),x94303)),x94305)) % 154.70/154.56 [10180]P26(x101801,x101802,f328(f307(a873,f874(x101801),f328(f328(f18(a873,f882(x101801,f882(a872,a870)),f874(x101801)),f328(f328(f18(a873,a871,f882(f882(x101801,f882(a872,a870)),f874(x101801))),f328(f328(f8(f882(x101801,f882(a872,a870)),f882(a871,f882(f882(x101801,f882(a872,a870)),f874(x101801))),a873),f92(x101801)),x101803)),a26)),x101804)),x101805))+~P26(x101801,f328(f328(f114(f882(f874(x101801),a870)),x101802),f328(f307(a873,f874(x101801),f328(f328(f18(a873,f882(x101801,f882(a872,a870)),f874(x101801)),f328(f328(f18(a873,a871,f882(f882(x101801,f882(a872,a870)),f874(x101801))),f328(f328(f8(f882(x101801,f882(a872,a870)),f882(a871,f882(f882(x101801,f882(a872,a870)),f874(x101801))),a873),f92(x101801)),x101803)),a26)),x101804)),x101805)),f328(f307(a873,f874(x101801),f328(f328(f18(a873,f882(x101801,f882(a872,a870)),f874(x101801)),f328(f328(f18(a873,a871,f882(f882(x101801,f882(a872,a870)),f874(x101801))),f328(f328(f8(f882(x101801,f882(a872,a870)),f882(a871,f882(f882(x101801,f882(a872,a870)),f874(x101801))),a873),f92(x101801)),x101803)),f328(f328(f8(f879(a871),a871,a873),f239(a871)),a28))),x101804)),x101805)) % 154.70/154.56 [10181]P30(x101811,x101812,f328(f307(a873,f874(x101811),f328(f328(f18(a873,f882(x101811,f882(a872,a870)),f874(x101811)),f328(f328(f18(a873,a871,f882(f882(x101811,f882(a872,a870)),f874(x101811))),f328(f328(f8(f882(x101811,f882(a872,a870)),f882(a871,f882(f882(x101811,f882(a872,a870)),f874(x101811))),a873),f92(x101811)),x101813)),a26)),x101814)),x101815))+~P30(x101811,f328(f328(f114(f882(f874(x101811),a870)),x101812),f328(f307(a873,f874(x101811),f328(f328(f18(a873,f882(x101811,f882(a872,a870)),f874(x101811)),f328(f328(f18(a873,a871,f882(f882(x101811,f882(a872,a870)),f874(x101811))),f328(f328(f8(f882(x101811,f882(a872,a870)),f882(a871,f882(f882(x101811,f882(a872,a870)),f874(x101811))),a873),f92(x101811)),x101813)),a26)),x101814)),x101815)),f328(f307(a873,f874(x101811),f328(f328(f18(a873,f882(x101811,f882(a872,a870)),f874(x101811)),f328(f328(f18(a873,a871,f882(f882(x101811,f882(a872,a870)),f874(x101811))),f328(f328(f8(f882(x101811,f882(a872,a870)),f882(a871,f882(f882(x101811,f882(a872,a870)),f874(x101811))),a873),f92(x101811)),x101813)),f328(f328(f8(f879(a871),a871,a873),f239(a871)),a28))),x101814)),x101815)) % 154.70/154.56 [5247]E(x52471,x52472)+~E(f30(x52473,x52474,x52471),f30(x52475,x52476,x52472)) % 154.70/154.56 [5248]E(x52481,x52482)+~E(f30(x52483,x52481,x52484),f30(x52485,x52482,x52486)) % 154.70/154.56 [5249]E(x52491,x52492)+~E(f30(x52491,x52493,x52494),f30(x52492,x52495,x52496)) % 154.70/154.56 [5250]E(x52501,x52502)+~E(f29(x52503,x52504,x52501),f29(x52505,x52506,x52502)) % 154.70/154.56 [5251]E(x52511,x52512)+~E(f29(x52513,x52511,x52514),f29(x52515,x52512,x52516)) % 154.70/154.56 [5252]E(x52521,x52522)+~E(f29(x52521,x52523,x52524),f29(x52522,x52525,x52526)) % 154.70/154.56 [6693]E(f328(f183(x66931,x66932,x66933,x66934),x66935),f328(f235(x66932),x66936))+~E(f328(x66934,x66935),f328(f235(x66932),x66936)) % 154.70/154.56 [6837]E(f328(f237(f879(x68371),x68372,f205(x68371),x68373),f328(x68374,x68375)),f328(x68373,x68376))+~E(f328(x68374,x68375),f328(f235(x68372),x68376)) % 154.70/154.56 [8371]~P21(x83715,x83711,x83712,x83716)+E(f328(f73(x83711,x83711,x83711,f328(x83712,x83713)),f328(x83712,x83714)),f328(f73(x83711,x83711,x83711,f328(x83712,x83714)),f328(x83712,x83713))) % 154.70/154.56 [8611]~P53(x86114,x86115,x86112,x86111,x86116)+E(f328(x86111,f328(x86112,x86113)),x86113) % 154.70/154.56 [8765]P27(x87651,x87652,x87653,x87654)+~P27(x87651,x87655,f328(f73(x87652,x87655,x87651,x87656),x87653),x87654) % 154.70/154.56 [8848]~P27(x88484,x88482,f328(f73(x88481,x88482,x88484,x88483),x88485),x88486)+P27(x88481,x88482,x88483,f328(f307(x88484,x88481,x88485),x88486)) % 154.70/154.56 [9561]P1(f328(f61(x95611),x95612))+~P1(f328(f66(x95611,x95613,x95614,x95615,x95612),x95616)) % 154.70/154.56 [9569]~P1(f328(f328(f330(x95694),x95693),f296(x95694,x95695,x95691,x95692,x95696)))+P1(f328(f328(x95691,x95692),x95693)) % 154.70/154.56 [9570]~P1(f328(f328(f330(x95704),x95703),f293(x95704,x95701,x95705,x95702,x95706)))+P1(f328(f328(x95701,x95702),x95703)) % 154.70/154.56 [9571]~P1(f328(f328(f330(x95714),x95712),f296(x95714,x95711,x95715,x95716,x95713)))+P1(f328(f328(x95711,x95712),x95713)) % 154.70/154.56 [9572]~P1(f328(f328(f330(x95724),x95722),f293(x95724,x95725,x95721,x95726,x95723)))+P1(f328(f328(x95721,x95722),x95723)) % 154.70/154.56 [5751]E(x57511,x57512)+~E(f328(f328(f263(x57513,x57514),x57515),x57511),f328(f328(f263(x57513,x57514),x57516),x57512)) % 154.70/154.56 [5753]E(x57531,x57532)+~E(f328(f328(f263(x57533,x57534),x57531),x57535),f328(f328(f263(x57533,x57534),x57532),x57536)) % 154.70/154.56 [5877]~P18(x58775,x58776,x58771)+E(f328(f328(x58771,x58772),f328(f328(x58771,x58773),x58774)),f328(f328(x58771,x58773),f328(f328(x58771,x58772),x58774))) % 154.70/154.56 [7292]~P34(x72924,x72921,f328(f328(f148(x72924),x72922),x72925),f328(f328(f148(x72924),x72923),x72926))+P1(f328(f328(x72921,x72922),x72923)) % 154.70/154.56 [7660]P34(x76601,x76602,x76603,x76604)+~P34(x76601,x76602,f328(f328(f148(x76601),x76605),x76603),f328(f328(f148(x76601),x76606),x76604)) % 154.70/154.56 [8708]~P53(x87085,x87081,x87082,x87086,x87084)+P1(f328(f328(f330(x87081),f328(x87082,x87083)),x87084)) % 154.70/154.56 [8876]E(f328(f76(x88761,x88762,x88763,x88764,x88765),x88766),f328(x88763,x88766))+P1(f328(f328(f330(x88761),x88766),x88765)) % 154.70/154.56 [8896]~E(x88963,f328(f328(f148(x88961),x88965),x88966))+P1(f328(f328(f330(f881(f876(x88961),f876(x88961))),f328(f328(f263(f876(x88961),f876(x88961)),x88962),f328(f328(f125(x88961),x88962),x88963))),f144(x88961,x88964))) % 154.70/154.56 [8903]E(f328(f76(x89031,x89032,x89033,x89034,x89035),x89036),f328(x89034,x89036))+~P1(f328(f328(f330(x89031),x89036),x89035)) % 154.70/154.56 [8908]E(f328(f185(x89081,x89082,x89083,x89084,x89085),x89086),f328(x89083,x89086))+P1(f328(f328(f330(x89081),x89086),f328(f170(x89081),x89084))) % 154.70/154.56 [9140]~P36(x91401,x91402,x91403,x91405,x91406)+P36(x91401,x91402,x91403,f328(f328(f173(x91401),x91404),x91405),f328(f328(f173(x91402),x91404),x91406)) % 154.70/154.56 [9141]~P36(x91411,x91412,x91413,x91415,x91416)+P36(x91411,x91412,x91413,f328(f328(f135(x91411),x91414),x91415),f328(f328(f135(x91412),x91414),x91416)) % 154.70/154.56 [9633]~P25(x96334,x96332,x96335,x96333,x96336,x96331)+E(f328(x96331,f192(f882(x96332,a870))),x96333) % 154.70/154.56 [9877]~E(f328(x98774,f328(f262(x98771,x98773),x98775)),f328(x98776,f328(f262(x98771,x98773),x98775)))+E(f328(f268(x98771,x98772,x98773,x98773,x98774,f34(x98773)),x98775),f328(f268(x98771,x98772,x98773,x98773,x98776,f34(x98773)),x98775)) % 154.70/154.56 [9878]~E(f328(x98784,f328(f266(x98781,x98782),x98785)),f328(x98786,f328(f266(x98781,x98782),x98785)))+E(f328(f268(x98781,x98781,x98782,x98783,f34(x98781),x98784),x98785),f328(f268(x98781,x98781,x98782,x98783,f34(x98781),x98786),x98785)) % 154.70/154.56 [9923]~E(f328(f268(x99232,x99236,x99233,x99233,x99231,f34(x99233)),x99234),f328(f268(x99232,x99236,x99233,x99233,x99235,f34(x99233)),x99234))+E(f328(x99231,f328(f262(x99232,x99233),x99234)),f328(x99235,f328(f262(x99232,x99233),x99234))) % 154.70/154.56 [9924]~E(f328(f268(x99242,x99242,x99243,x99246,f34(x99242),x99241),x99244),f328(f268(x99242,x99242,x99243,x99246,f34(x99242),x99245),x99244))+E(f328(x99241,f328(f266(x99242,x99243),x99244)),f328(x99245,f328(f266(x99242,x99243),x99244))) % 154.70/154.56 [8804]P1(f328(f328(f330(x88041),x88042),x88043))+~P1(f328(f328(f330(f881(x88041,x88044)),f328(f328(f263(x88041,x88044),x88042),x88045)),f328(f328(f265(x88041,x88044),x88043),x88046))) % 154.70/154.56 [8818]P1(f328(f328(f330(x88181),x88182),f328(x88183,x88184)))+~P1(f328(f328(f330(f881(x88185,x88181)),f328(f328(f263(x88185,x88181),x88184),x88182)),f328(f328(f265(x88185,x88181),x88186),x88183))) % 154.70/154.56 [8905]~E(f328(f193(f876(x89051)),x89054),f328(f193(f876(x89052)),x89055))+E(f185(x89051,x89052,x89053,x89054,f328(f328(f125(x89052),x89055),x89056)),f185(x89051,x89052,x89053,x89054,x89055)) % 154.70/154.56 [8906]~E(f328(f193(f876(x89061)),x89064),f328(f193(f876(x89062)),x89066))+E(f185(x89061,x89062,x89063,f328(f328(f125(x89061),x89064),x89065),x89066),f185(x89061,x89062,x89063,x89064,x89066)) % 154.70/154.56 [9161]P1(f328(f328(f330(x91611),x91614),f182(x91611,x91612,x91616)))+E(f183(x91611,x91612,f328(f328(f328(f72(x91611,f879(x91612)),x91613),x91614),f328(f235(x91612),x91615)),x91616),f328(f328(f328(f72(x91611,f879(x91612)),f183(x91611,x91612,x91613,x91616)),x91614),f328(f235(x91612),x91615))) % 154.70/154.56 [9260]P1(f328(f328(f330(f881(x92601,x92601)),f328(f328(f263(x92601,x92601),f328(x92602,x92603)),f328(x92602,x92604))),x92605))+~P1(f328(f328(f330(f881(x92606,x92606)),f328(f328(f263(x92606,x92606),x92603),x92604)),f328(f328(f284(x92601,x92606),x92605),x92602))) % 154.70/154.56 [9280]~P1(f328(f328(f330(f881(x92804,x92804)),f328(f328(f263(x92804,x92804),f328(x92806,x92802)),f328(x92806,x92803))),x92805))+P1(f328(f328(f330(f881(x92801,x92801)),f328(f328(f263(x92801,x92801),x92802),x92803)),f328(f328(f284(x92804,x92801),x92805),x92806))) % 154.70/154.56 [9926]E(f328(f328(f263(x99261,x99262),f659(x99263,x99264,x99265,x99266,x99262,x99261)),f660(x99263,x99264,x99265,x99266,x99262,x99261)),x99266)+~P1(f328(f328(f330(f881(x99261,x99262)),x99266),f328(f328(f285(x99261,x99265,x99262),x99264),x99263))) % 154.70/154.56 [10127]~P1(f328(f328(f330(f881(x101271,x101276)),x101275),f328(f328(f285(x101271,x101272,x101276),x101274),x101273)))+P1(f328(f328(f330(f881(x101271,x101272)),f328(f328(f263(x101271,x101272),f659(x101273,x101274,x101272,x101275,x101276,x101271)),f661(x101273,x101274,x101272,x101275,x101276,x101271))),x101274)) % 154.70/154.56 [10128]~P1(f328(f328(f330(f881(x101286,x101282)),x101285),f328(f328(f285(x101286,x101281,x101282),x101284),x101283)))+P1(f328(f328(f330(f881(x101281,x101282)),f328(f328(f263(x101281,x101282),f661(x101283,x101284,x101281,x101285,x101282,x101286)),f660(x101283,x101284,x101281,x101285,x101282,x101286))),x101283)) % 154.70/154.56 [6154]~E(x61546,x61544)+E(f328(f328(f328(f328(f72(x61541,x61542),x61543),x61544),x61545),x61546),x61545) % 154.70/154.56 [6206]E(x62061,x62062)+E(f328(f328(f328(f328(f72(x62063,x62064),x62065),x62062),x62066),x62061),f328(x62065,x62061)) % 154.70/154.56 [7731]~P5(x77312)+E(f328(f328(f41(x77311,x77312),x77313),f328(f328(f7(x77311,x77314,x77312),x77315),x77316)),f328(f328(f328(f41(x77311,f882(x77314,x77312)),x77313),x77315),x77316)) % 154.70/154.56 [7732]~P5(x77322)+E(f328(f328(f42(x77321,x77322),x77323),f328(f328(f7(x77321,x77324,x77322),x77325),x77326)),f328(f328(f328(f42(x77321,f882(x77324,x77322)),x77323),x77325),x77326)) % 154.70/154.56 [8518]E(f328(f328(f41(x85181,f882(x85182,a870)),x85183),f328(f328(f8(f882(x85182,a870),f882(x85182,a870),x85181),f328(f306(x85182),x85184)),x85185)),f328(f328(f306(x85182),x85184),f328(f328(f41(x85181,f882(x85182,a870)),x85183),x85185)))+~P1(f328(f328(f330(x85181),x85186),x85183)) % 154.70/154.56 [8960]~P5(x89602)+E(f328(f328(f41(x89601,x89602),x89603),f328(f328(f8(f882(x89604,x89602),x89602,x89601),f328(f41(x89604,x89602),x89605)),f328(f7(x89604,x89601,x89602),x89606))),f328(f328(f41(x89604,x89602),x89605),f328(f328(f8(f882(x89601,x89602),x89602,x89604),f328(f41(x89601,x89602),x89603)),x89606))) % 154.70/154.56 [8961]~P5(x89612)+E(f328(f328(f42(x89611,x89612),x89613),f328(f328(f8(f882(x89614,x89612),x89612,x89611),f328(f42(x89614,x89612),x89615)),f328(f7(x89614,x89611,x89612),x89616))),f328(f328(f42(x89614,x89612),x89615),f328(f328(f8(f882(x89611,x89612),x89612,x89614),f328(f42(x89611,x89612),x89613)),x89616))) % 154.70/154.56 [9170]P1(f328(f328(f330(x91701),x91702),f328(f170(x91701),x91703)))+~P1(f328(f328(f330(f881(x91704,x91701)),f328(f328(f263(x91704,x91701),x91705),x91702)),f328(f170(f881(x91704,x91701)),f328(f328(f180(x91704,x91701),x91706),x91703)))) % 154.70/154.56 [9171]P1(f328(f328(f330(x91711),x91712),f328(f170(x91711),x91713)))+~P1(f328(f328(f330(f881(x91711,x91714)),f328(f328(f263(x91711,x91714),x91712),x91715)),f328(f170(f881(x91711,x91714)),f328(f328(f180(x91711,x91714),x91713),x91716)))) % 154.70/154.56 [9274]P1(f328(f328(f242(f882(x92741,a870)),f328(f282(x92742,x92741,x92743),x92744)),x92745))+~P1(f328(f328(f242(f882(f881(x92742,x92741),a870)),x92743),f328(f328(f265(x92742,x92741),x92746),f328(f16(f882(x92741,a870),x92742),x92745)))) % 154.70/154.56 [9465]P1(f328(f328(f330(f881(f876(x94651),f876(x94651))),f328(f328(f263(f876(x94651),f876(x94651)),f328(f328(f148(x94651),x94652),x94653)),f328(f328(f148(x94651),x94654),x94655))),f144(x94651,x94656)))+~P1(f328(f328(f330(f881(x94651,x94651)),f328(f328(f263(x94651,x94651),x94652),x94654)),x94656)) % 154.70/154.56 [9922]E(f328(f328(f263(x99221,x99222),f607(x99223,x99224,x99225,x99222,x99221,x99226)),f608(x99223,x99224,x99225,x99222,x99221,x99226)),x99226)+P1(f328(f328(f330(x99225),x99224),f328(f328(f267(x99221,x99222,f882(x99225,a870)),x99223),x99226))) % 154.70/154.56 [9928]E(f328(f328(f263(x99281,x99282),f609(x99283,x99284,x99282,x99281,x99285,x99286)),f610(x99283,x99284,x99282,x99281,x99285,x99286)),x99283)+~P1(f328(f328(f330(x99286),x99285),f328(f328(f267(x99281,x99282,f882(x99286,a870)),x99284),x99283))) % 154.70/154.56 [10085]P1(f328(f328(f330(x100851),x100852),f328(f328(x100853,f609(x100854,x100853,x100855,x100856,x100852,x100851)),f610(x100854,x100853,x100855,x100856,x100852,x100851))))+~P1(f328(f328(f330(x100851),x100852),f328(f328(f267(x100856,x100855,f882(x100851,a870)),x100853),x100854))) % 154.70/154.56 [10104]~P1(f328(f328(f330(x101041),x101042),f328(f328(x101045,f607(x101045,x101042,x101041,x101044,x101043,x101046)),f608(x101045,x101042,x101041,x101044,x101043,x101046))))+P1(f328(f328(f330(x101041),x101042),f328(f328(f267(x101043,x101044,f882(x101041,a870)),x101045),x101046))) % 154.70/154.56 [7854]P1(f328(f328(f330(x78541),x78544),x78546))+E(f186(x78541,x78542,f328(f328(f328(f72(x78541,f879(x78542)),x78543),x78544),x78545),x78546),f186(x78541,x78542,x78543,x78546)) % 154.70/154.56 [7931]P1(f328(f328(f330(x79311),x79314),x79316))+E(f328(f307(x79311,x79312,f328(f328(f328(f72(x79311,x79312),x79313),x79314),x79315)),x79316),f328(f307(x79311,x79312,x79313),x79316)) % 154.70/154.56 [7958]P1(f328(f328(f330(x79581),x79584),f328(f170(x79581),x79586)))+E(f328(f328(f151(x79581,x79582),f328(f328(f328(f72(x79581,x79582),x79583),x79584),x79585)),x79586),f328(f328(f151(x79581,x79582),x79583),x79586)) % 154.70/154.56 [8419]E(x84191,x84192)+E(f328(f328(f156(x84193,f328(f328(f156(x84193,x84194),x84191),x84195)),x84192),x84196),f328(f328(f156(x84193,f328(f328(f156(x84193,x84194),x84192),x84196)),x84191),x84195)) % 154.70/154.56 [8968]~P1(f328(f328(f330(x89683),x89686),x89685))+E(f328(f328(f306(x89681),x89682),f328(f307(x89683,x89681,x89684),f328(f328(f22(f882(x89683,a870)),x89685),f328(f328(f306(x89683),x89686),f192(f882(x89683,a870)))))),f328(f307(x89683,x89681,f328(f328(f328(f72(x89683,x89681),x89684),x89686),x89682)),x89685)) % 154.70/154.56 [9739]E(f185(x97391,x97392,x97393,f328(f328(f125(x97391),x97394),f328(f328(f148(x97391),x97395),f117(x97391))),x97396),f328(f328(f328(f72(x97391,f879(x97392)),f185(x97391,x97392,x97393,x97394,x97396)),x97395),f328(f235(x97392),f328(f328(f162(x97392),x97396),f328(f193(f876(x97391)),x97394)))))+~P1(f328(f328(f243(a875),f328(f193(f876(x97391)),x97394)),f328(f193(f876(x97392)),x97396))) % 154.70/154.56 [8747]~E(x87473,x87476)+E(f328(f328(f176(x87471,x87472),f328(f328(f148(f881(x87471,x87472)),f328(f328(f263(x87471,x87472),x87473),x87474)),x87475)),x87476),f328(f235(x87472),x87474)) % 154.70/154.56 [8774]E(x87741,x87742)+E(f328(f328(f176(x87743,x87744),f328(f328(f148(f881(x87743,x87744)),f328(f328(f263(x87743,x87744),x87741),x87745)),x87746)),x87742),f328(f328(f176(x87743,x87744),x87746),x87742)) % 154.70/154.56 [9042]~P1(f328(f328(x90424,x90425),x90426))+P1(f328(f328(f328(f328(f114(f882(x90421,f882(x90422,a870))),x90423),x90424),x90425),x90426)) % 154.70/154.56 [9044]~P1(f328(f328(x90443,x90445),x90446))+P1(f328(f328(f328(f328(f114(f882(x90441,f882(x90442,a870))),x90443),x90444),x90445),x90446)) % 154.70/154.56 [9331]P1(f328(f328(x93311,x93312),x93313))+~P1(f328(f328(f328(f328(f105(f882(x93314,f882(x93315,a870))),x93316),x93311),x93312),x93313)) % 154.70/154.56 [9332]P1(f328(f328(x93321,x93322),x93323))+~P1(f328(f328(f328(f328(f105(f882(x93324,f882(x93325,a870))),x93321),x93326),x93322),x93323)) % 154.70/154.56 [9761]~P66(x97612)+E(f328(f328(f6(x97611,x97612),f328(f328(f7(x97611,f882(x97613,a870),x97612),f328(f328(f8(f882(x97613,x97612),f882(f882(x97613,a870),x97612),x97611),f6(x97613,x97612)),x97614)),x97615)),x97616),f328(f328(f6(f881(x97611,x97613),x97612),f328(f267(x97611,x97613,x97612),x97614)),f328(f328(f265(x97611,x97613),x97616),f328(f16(f882(x97613,a870),x97611),x97615)))) % 154.70/154.56 [9762]~P73(x97622)+E(f328(f328(f9(x97621,x97622),f328(f328(f7(x97621,f882(x97623,a870),x97622),f328(f328(f8(f882(x97623,x97622),f882(f882(x97623,a870),x97622),x97621),f9(x97623,x97622)),x97624)),x97625)),x97626),f328(f328(f9(f881(x97621,x97623),x97622),f328(f267(x97621,x97623,x97622),x97624)),f328(f328(f265(x97621,x97623),x97626),f328(f16(f882(x97623,a870),x97621),x97625)))) % 154.70/154.56 [9905]~P66(x99052)+E(f328(f328(f6(x99051,x99052),f328(f328(f7(x99051,f882(x99053,a870),x99052),f328(f328(f8(f882(x99053,x99052),f882(f882(x99053,a870),x99052),x99051),f6(x99053,x99052)),f328(f7(x99053,x99051,x99052),x99054))),x99055)),x99056),f328(f328(f6(x99053,x99052),f328(f328(f7(x99053,f882(x99051,a870),x99052),f328(f328(f8(f882(x99051,x99052),f882(f882(x99051,a870),x99052),x99053),f6(x99051,x99052)),x99054)),x99056)),x99055)) % 154.70/154.56 [9602]~P1(f328(f328(f330(x96021),x96025),x96024))+E(f328(f328(f328(f72(x96021,f879(x96022)),f186(x96021,x96022,x96023,f328(f328(f22(f882(x96021,a870)),x96024),f328(f328(f306(x96021),x96025),f192(f882(x96021,a870)))))),x96025),x96026),f186(x96021,x96022,f328(f328(f328(f72(x96021,f879(x96022)),x96023),x96025),x96026),x96024)) % 154.70/154.56 [10184]~P1(f328(f328(f330(f881(x101841,x101842)),f328(f328(f263(x101841,x101842),x101845),x101846)),f328(f328(f114(f882(f881(x101841,x101842),a870)),x101843),x101844)))+P1(f328(f328(f328(f328(f114(f882(x101841,f882(x101842,a870))),f328(f328(f7(x101841,f882(f881(x101841,x101842),a870),f882(x101842,a870)),f328(f328(f8(f882(x101842,f882(f882(f881(x101841,x101842),a870),a870)),f882(f882(f881(x101841,x101842),a870),f882(x101842,a870)),x101841),f7(x101842,f882(f881(x101841,x101842),a870),a870)),f328(f328(f8(f882(x101842,f881(x101841,x101842)),f882(x101842,f882(f882(f881(x101841,x101842),a870),a870)),x101841),f328(f8(f881(x101841,x101842),f882(f882(f881(x101841,x101842),a870),a870),x101842),f330(f881(x101841,x101842)))),f263(x101841,x101842)))),x101843)),f328(f328(f7(x101841,f882(f881(x101841,x101842),a870),f882(x101842,a870)),f328(f328(f8(f882(x101842,f882(f882(f881(x101841,x101842),a870),a870)),f882(f882(f881(x101841,x101842),a870),f882(x101842,a870)),x101841),f7(x101842,f882(f881(x101841,x101842),a870),a870)),f328(f328(f8(f882(x101842,f881(x101841,x101842)),f882(x101842,f882(f882(f881(x101841,x101842),a870),a870)),x101841),f328(f8(f881(x101841,x101842),f882(f882(f881(x101841,x101842),a870),a870),x101842),f330(f881(x101841,x101842)))),f263(x101841,x101842)))),x101844)),x101845),x101846)) % 154.70/154.56 [10185]~P1(f328(f328(f330(f881(x101851,x101852)),f328(f328(f263(x101851,x101852),x101855),x101856)),f328(f328(f105(f882(f881(x101851,x101852),a870)),x101853),x101854)))+P1(f328(f328(f328(f328(f105(f882(x101851,f882(x101852,a870))),f328(f328(f7(x101851,f882(f881(x101851,x101852),a870),f882(x101852,a870)),f328(f328(f8(f882(x101852,f882(f882(f881(x101851,x101852),a870),a870)),f882(f882(f881(x101851,x101852),a870),f882(x101852,a870)),x101851),f7(x101852,f882(f881(x101851,x101852),a870),a870)),f328(f328(f8(f882(x101852,f881(x101851,x101852)),f882(x101852,f882(f882(f881(x101851,x101852),a870),a870)),x101851),f328(f8(f881(x101851,x101852),f882(f882(f881(x101851,x101852),a870),a870),x101852),f330(f881(x101851,x101852)))),f263(x101851,x101852)))),x101853)),f328(f328(f7(x101851,f882(f881(x101851,x101852),a870),f882(x101852,a870)),f328(f328(f8(f882(x101852,f882(f882(f881(x101851,x101852),a870),a870)),f882(f882(f881(x101851,x101852),a870),f882(x101852,a870)),x101851),f7(x101852,f882(f881(x101851,x101852),a870),a870)),f328(f328(f8(f882(x101852,f881(x101851,x101852)),f882(x101852,f882(f882(f881(x101851,x101852),a870),a870)),x101851),f328(f8(f881(x101851,x101852),f882(f882(f881(x101851,x101852),a870),a870),x101852),f330(f881(x101851,x101852)))),f263(x101851,x101852)))),x101854)),x101855),x101856)) % 154.70/154.56 [10191]P1(f328(f328(f330(f881(x101911,x101912)),f328(f328(f263(x101911,x101912),x101913),x101914)),f328(f328(f114(f882(f881(x101911,x101912),a870)),x101915),x101916)))+~P1(f328(f328(f328(f328(f114(f882(x101911,f882(x101912,a870))),f328(f328(f7(x101911,f882(f881(x101911,x101912),a870),f882(x101912,a870)),f328(f328(f8(f882(x101912,f882(f882(f881(x101911,x101912),a870),a870)),f882(f882(f881(x101911,x101912),a870),f882(x101912,a870)),x101911),f7(x101912,f882(f881(x101911,x101912),a870),a870)),f328(f328(f8(f882(x101912,f881(x101911,x101912)),f882(x101912,f882(f882(f881(x101911,x101912),a870),a870)),x101911),f328(f8(f881(x101911,x101912),f882(f882(f881(x101911,x101912),a870),a870),x101912),f330(f881(x101911,x101912)))),f263(x101911,x101912)))),x101915)),f328(f328(f7(x101911,f882(f881(x101911,x101912),a870),f882(x101912,a870)),f328(f328(f8(f882(x101912,f882(f882(f881(x101911,x101912),a870),a870)),f882(f882(f881(x101911,x101912),a870),f882(x101912,a870)),x101911),f7(x101912,f882(f881(x101911,x101912),a870),a870)),f328(f328(f8(f882(x101912,f881(x101911,x101912)),f882(x101912,f882(f882(f881(x101911,x101912),a870),a870)),x101911),f328(f8(f881(x101911,x101912),f882(f882(f881(x101911,x101912),a870),a870),x101912),f330(f881(x101911,x101912)))),f263(x101911,x101912)))),x101916)),x101913),x101914)) % 154.70/154.56 [10192]P1(f328(f328(f330(f881(x101921,x101922)),f328(f328(f263(x101921,x101922),x101923),x101924)),f328(f328(f105(f882(f881(x101921,x101922),a870)),x101925),x101926)))+~P1(f328(f328(f328(f328(f105(f882(x101921,f882(x101922,a870))),f328(f328(f7(x101921,f882(f881(x101921,x101922),a870),f882(x101922,a870)),f328(f328(f8(f882(x101922,f882(f882(f881(x101921,x101922),a870),a870)),f882(f882(f881(x101921,x101922),a870),f882(x101922,a870)),x101921),f7(x101922,f882(f881(x101921,x101922),a870),a870)),f328(f328(f8(f882(x101922,f881(x101921,x101922)),f882(x101922,f882(f882(f881(x101921,x101922),a870),a870)),x101921),f328(f8(f881(x101921,x101922),f882(f882(f881(x101921,x101922),a870),a870),x101922),f330(f881(x101921,x101922)))),f263(x101921,x101922)))),x101925)),f328(f328(f7(x101921,f882(f881(x101921,x101922),a870),f882(x101922,a870)),f328(f328(f8(f882(x101922,f882(f882(f881(x101921,x101922),a870),a870)),f882(f882(f881(x101921,x101922),a870),f882(x101922,a870)),x101921),f7(x101922,f882(f881(x101921,x101922),a870),a870)),f328(f328(f8(f882(x101922,f881(x101921,x101922)),f882(x101922,f882(f882(f881(x101921,x101922),a870),a870)),x101921),f328(f8(f881(x101921,x101922),f882(f882(f881(x101921,x101922),a870),a870),x101922),f330(f881(x101921,x101922)))),f263(x101921,x101922)))),x101926)),x101923),x101924)) % 154.70/154.56 [10178]~P1(f328(f328(f330(f881(x101782,x101783)),f328(f328(f263(x101782,x101783),x101785),x101786)),f328(f328(f41(x101781,f882(f881(x101782,x101783),a870)),f251(f882(x101781,a870))),x101784)))+P1(f328(f328(f328(f328(f41(x101781,f882(x101782,f882(x101783,a870))),f251(f882(x101781,a870))),f328(f328(f8(f882(f881(x101782,x101783),a870),f882(x101782,f882(x101783,a870)),x101781),f328(f7(x101782,f882(f881(x101782,x101783),a870),f882(x101783,a870)),f328(f328(f8(f882(x101783,f882(f882(f881(x101782,x101783),a870),a870)),f882(f882(f881(x101782,x101783),a870),f882(x101783,a870)),x101782),f7(x101783,f882(f881(x101782,x101783),a870),a870)),f328(f328(f8(f882(x101783,f881(x101782,x101783)),f882(x101783,f882(f882(f881(x101782,x101783),a870),a870)),x101782),f328(f8(f881(x101782,x101783),f882(f882(f881(x101782,x101783),a870),a870),x101783),f330(f881(x101782,x101783)))),f263(x101782,x101783))))),x101784)),x101785),x101786)) % 154.70/154.56 [10179]~P1(f328(f328(f330(f881(x101792,x101793)),f328(f328(f263(x101792,x101793),x101795),x101796)),f328(f328(f42(x101791,f882(f881(x101792,x101793),a870)),f251(f882(x101791,a870))),x101794)))+P1(f328(f328(f328(f328(f42(x101791,f882(x101792,f882(x101793,a870))),f251(f882(x101791,a870))),f328(f328(f8(f882(f881(x101792,x101793),a870),f882(x101792,f882(x101793,a870)),x101791),f328(f7(x101792,f882(f881(x101792,x101793),a870),f882(x101793,a870)),f328(f328(f8(f882(x101793,f882(f882(f881(x101792,x101793),a870),a870)),f882(f882(f881(x101792,x101793),a870),f882(x101793,a870)),x101792),f7(x101793,f882(f881(x101792,x101793),a870),a870)),f328(f328(f8(f882(x101793,f881(x101792,x101793)),f882(x101793,f882(f882(f881(x101792,x101793),a870),a870)),x101792),f328(f8(f881(x101792,x101793),f882(f882(f881(x101792,x101793),a870),a870),x101793),f330(f881(x101792,x101793)))),f263(x101792,x101793))))),x101794)),x101795),x101796)) % 154.70/154.56 [10188]P1(f328(f328(f330(f881(x101881,x101882)),f328(f328(f263(x101881,x101882),x101883),x101884)),f328(f328(f41(x101885,f882(f881(x101881,x101882),a870)),f251(f882(x101885,a870))),x101886)))+~P1(f328(f328(f328(f328(f41(x101885,f882(x101881,f882(x101882,a870))),f251(f882(x101885,a870))),f328(f328(f8(f882(f881(x101881,x101882),a870),f882(x101881,f882(x101882,a870)),x101885),f328(f7(x101881,f882(f881(x101881,x101882),a870),f882(x101882,a870)),f328(f328(f8(f882(x101882,f882(f882(f881(x101881,x101882),a870),a870)),f882(f882(f881(x101881,x101882),a870),f882(x101882,a870)),x101881),f7(x101882,f882(f881(x101881,x101882),a870),a870)),f328(f328(f8(f882(x101882,f881(x101881,x101882)),f882(x101882,f882(f882(f881(x101881,x101882),a870),a870)),x101881),f328(f8(f881(x101881,x101882),f882(f882(f881(x101881,x101882),a870),a870),x101882),f330(f881(x101881,x101882)))),f263(x101881,x101882))))),x101886)),x101883),x101884)) % 154.70/154.56 [10189]P1(f328(f328(f330(f881(x101891,x101892)),f328(f328(f263(x101891,x101892),x101893),x101894)),f328(f328(f42(x101895,f882(f881(x101891,x101892),a870)),f251(f882(x101895,a870))),x101896)))+~P1(f328(f328(f328(f328(f42(x101895,f882(x101891,f882(x101892,a870))),f251(f882(x101895,a870))),f328(f328(f8(f882(f881(x101891,x101892),a870),f882(x101891,f882(x101892,a870)),x101895),f328(f7(x101891,f882(f881(x101891,x101892),a870),f882(x101892,a870)),f328(f328(f8(f882(x101892,f882(f882(f881(x101891,x101892),a870),a870)),f882(f882(f881(x101891,x101892),a870),f882(x101892,a870)),x101891),f7(x101892,f882(f881(x101891,x101892),a870),a870)),f328(f328(f8(f882(x101892,f881(x101891,x101892)),f882(x101892,f882(f882(f881(x101891,x101892),a870),a870)),x101891),f328(f8(f881(x101891,x101892),f882(f882(f881(x101891,x101892),a870),a870),x101892),f330(f881(x101891,x101892)))),f263(x101891,x101892))))),x101896)),x101893),x101894)) % 154.70/154.56 [7405]E(f328(x74051,f328(x74052,x74053)),f328(x74054,x74053))+~E(f328(f73(x74055,x74056,x74057,x74051),x74052),x74054) % 154.70/154.56 [9632]~P24(x96323,x96324,x96321,x96325,x96326,x96327)+E(f328(f328(x96321,x96322),x96322),x96322) % 154.70/154.56 [10002]~E(f328(f237(f879(x100027),x100021,f205(x100027),x100025),f328(x100024,x100023)),f328(f235(x100027),x100022))+E(f328(f235(x100021),f771(x100022,x100023,x100024,x100025,x100026,x100027,x100021)),f328(x100024,x100023)) % 154.70/154.56 [10003]~E(f328(f237(f879(x100036),x100037,f205(x100036),x100031),f328(x100034,x100033)),f328(f235(x100036),x100032))+E(f328(x100031,f771(x100032,x100033,x100034,x100031,x100035,x100036,x100037)),f328(f235(x100036),x100032)) % 154.70/154.56 [5977]~E(f328(f328(f151(x59771,x59775),x59776),x59772),f328(f328(f151(x59773,x59775),x59777),x59774))+E(f328(f193(f876(x59771)),x59772),f328(f193(f876(x59773)),x59774)) % 154.70/154.56 [7482]E(x74821,x74822)+~E(f328(f328(f328(f72(x74823,f879(x74824)),x74825),x74826),f328(f235(x74824),x74821)),f328(f328(f328(f72(x74823,f879(x74824)),x74827),x74826),f328(f235(x74824),x74822))) % 154.70/154.56 [8452]E(f328(x84521,f328(x84522,x84523)),f328(x84524,x84523))+~E(f328(f73(x84525,x84526,x84527,x84521),x84522),f328(f73(x84526,x84526,x84527,f34(x84526)),x84524)) % 154.70/154.56 [8793]~P36(x87934,x87935,x87931,f328(f328(f148(x87934),x87932),x87936),f328(f328(f148(x87935),x87933),x87937))+P1(f328(f328(x87931,x87932),x87933)) % 154.70/154.56 [9177]P36(x91771,x91772,x91773,x91774,x91775)+~P36(x91771,x91772,x91773,f328(f328(f148(x91771),x91776),x91774),f328(f328(f148(x91772),x91777),x91775)) % 154.70/154.56 [9800]P1(f328(f328(x98001,x98002),f562(x98003,x98002,x98004,x98001)))+~P1(f328(f328(f264(x98005,x98006,x98007,x98001,x98004),x98002),x98003)) % 154.70/154.56 [9821]P1(f328(f328(x98211,f562(x98212,x98213,x98211,x98214)),x98212))+~P1(f328(f328(f264(x98215,x98216,x98217,x98214,x98211),x98213),x98212)) % 154.70/154.56 [6020]E(x60201,x60202)+~E(f328(f328(f328(f92(x60203),x60204),x60205),x60201),f328(f328(f328(f92(x60203),x60206),x60207),x60202)) % 154.70/154.56 [6021]E(x60211,x60212)+~E(f328(f328(f328(f92(x60213),x60214),x60211),x60215),f328(f328(f328(f92(x60213),x60216),x60212),x60217)) % 154.70/154.56 [6022]E(x60221,x60222)+~E(f328(f328(f328(f92(x60223),x60221),x60224),x60225),f328(f328(f328(f92(x60223),x60222),x60226),x60227)) % 154.70/154.56 [8911]~P22(x89116,x89111,x89113,x89117)+E(f328(f73(x89111,x89111,x89112,f328(x89113,x89114)),f328(f73(x89111,x89111,x89112,f328(x89113,x89114)),x89115)),f328(f73(x89111,x89111,x89112,f328(x89113,x89114)),x89115)) % 154.70/154.56 [9283]~P36(x92833,x92832,x92834,f328(f328(f151(x92831,x92833),x92835),x92836),x92837)+P36(x92831,x92832,f328(f328(f8(x92833,f882(x92832,a870),x92831),x92834),x92835),x92836,x92837) % 154.70/154.56 [9306]P36(x93061,x93062,x93063,f328(f328(f151(x93064,x93061),x93065),x93066),x93067)+~P36(x93064,x93062,f328(f328(f8(x93061,f882(x93062,a870),x93064),x93063),x93065),x93066,x93067) % 154.70/154.56 [9719]E(f185(x97191,x97192,f328(f328(f328(f72(x97191,f879(x97192)),x97193),x97194),f328(f235(x97192),x97195)),x97196,x97197),f328(f328(f328(f72(x97191,f879(x97192)),f185(x97191,x97192,x97193,x97196,x97197)),x97194),f328(f235(x97192),x97195)))+P1(f328(f328(f330(x97191),x97194),f328(f170(x97191),x97196))) % 154.70/154.56 [8910]~P1(f328(f328(f330(x89101),x89102),f328(f328(x89105,x89106),x89107)))+P1(f328(f328(f330(x89101),x89102),f328(f328(f267(x89103,x89104,f882(x89101,a870)),x89105),f328(f328(f263(x89103,x89104),x89106),x89107)))) % 154.70/154.56 [9203]P1(f328(f328(f328(x92031,x92032),x92033),x92034))+~P1(f328(f328(f328(f267(x92035,x92036,f882(x92037,a870)),x92031),f328(f328(f263(x92035,x92036),x92032),x92033)),x92034)) % 154.70/154.56 [9345]P1(f328(f328(f330(x93451),f328(f328(x93452,x93453),x93454)),f328(f307(f881(x93455,x93456),x93451,f328(f267(x93455,x93456,x93451),x93452)),x93457)))+~P1(f328(f328(f330(f881(x93455,x93456)),f328(f328(f263(x93455,x93456),x93453),x93454)),x93457)) % 154.70/154.56 [9679]P1(f328(f328(f330(f881(f876(x96791),f876(x96791))),f328(f328(f263(f876(x96791),f876(x96791)),f328(f328(f125(x96791),x96792),f328(f328(f148(x96791),x96793),x96794))),f328(f328(f125(x96791),x96792),f328(f328(f148(x96791),x96795),x96796)))),f144(x96791,x96797)))+~P1(f328(f328(f330(f881(x96791,x96791)),f328(f328(f263(x96791,x96791),x96793),x96795)),x96797)) % 154.70/154.56 [9741]~P36(x97411,x97413,x97414,x97416,f328(f328(f151(x97412,x97413),x97415),x97417))+P36(x97411,x97412,f328(f328(f7(x97411,f882(x97412,x97413),f882(x97412,a870)),f328(f328(f8(f882(x97413,a870),f882(f882(x97412,x97413),f882(x97412,a870)),x97411),f8(x97413,a870,x97412)),x97414)),x97415),x97416,x97417) % 154.70/154.56 [9825]P36(x98251,x98252,x98253,x98254,f328(f328(f151(x98255,x98252),x98256),x98257))+~P36(x98251,x98255,f328(f328(f7(x98251,f882(x98255,x98252),f882(x98255,a870)),f328(f328(f8(f882(x98252,a870),f882(f882(x98255,x98252),f882(x98255,a870)),x98251),f8(x98252,a870,x98255)),x98253)),x98256),x98254,x98257) % 154.70/154.56 [9195]E(x91951,x91952)+E(f328(f328(f328(f72(x91953,x91954),f328(f328(f328(f72(x91953,x91954),x91955),x91951),x91956)),x91952),x91957),f328(f328(f328(f72(x91953,x91954),f328(f328(f328(f72(x91953,x91954),x91955),x91952),x91957)),x91951),x91956)) % 154.70/154.56 [9439]E(f185(x94391,x94392,f328(f328(f328(f72(x94391,f879(x94392)),x94393),x94394),f328(f235(x94392),x94395)),x94396,x94397),f185(x94391,x94392,x94393,x94396,x94397))+~P1(f328(f328(f330(x94391),x94394),f328(f170(x94391),f328(f328(f173(x94391),f328(f193(f876(x94392)),x94397)),x94396)))) % 154.70/154.56 [9752]E(f185(x97521,x97522,f328(f328(f328(f72(x97521,f879(x97522)),x97523),x97524),f328(f235(x97522),x97525)),x97526,x97527),f328(f328(f328(f72(x97521,f879(x97522)),f185(x97521,x97522,x97523,x97526,x97527)),x97524),f328(f235(x97522),x97525)))+P1(f328(f328(f330(x97521),x97524),f328(f170(x97521),f328(f328(f173(x97521),f328(f193(f876(x97522)),x97527)),x97526)))) % 154.70/154.56 [10115]P1(f328(f328(f330(x101151),f834(x101152,x101153,x101154,x101155,x101156,x101157,x101151)),x101155))+P1(f328(f328(f328(f328(f42(x101151,f882(x101157,f882(x101156,a870))),x101155),x101154),x101153),x101152)) % 154.70/154.56 [10116]P1(f328(f328(f330(x101161),f743(x101162,x101163,x101164,x101165,x101166,x101167,x101161)),x101165))+~P1(f328(f328(f328(f328(f41(x101161,f882(x101167,f882(x101166,a870))),x101165),x101164),x101163),x101162)) % 154.70/154.56 [10117]P1(f328(f328(f330(x101171),f832(x101172,x101173,x101174,x101175,x101176,x101177,x101171)),x101175))+~P1(f328(f328(f328(f328(f41(x101171,f882(x101177,f882(x101176,a870))),x101175),x101174),x101173),x101172)) % 154.70/154.56 [10142]P1(f328(f328(f328(x101421,f743(x101422,x101423,x101421,x101424,x101425,x101426,x101427)),x101423),x101422))+~P1(f328(f328(f328(f328(f41(x101427,f882(x101426,f882(x101425,a870))),x101424),x101421),x101423),x101422)) % 154.70/154.56 [10143]P1(f328(f328(f328(x101431,f832(x101432,x101433,x101431,x101434,x101435,x101436,x101437)),x101433),x101432))+~P1(f328(f328(f328(f328(f41(x101437,f882(x101436,f882(x101435,a870))),x101434),x101431),x101433),x101432)) % 154.70/154.56 [10160]~P1(f328(f328(f328(x101605,f834(x101607,x101606,x101605,x101604,x101603,x101602,x101601)),x101606),x101607))+P1(f328(f328(f328(f328(f42(x101601,f882(x101602,f882(x101603,a870))),x101604),x101605),x101606),x101607)) % 154.70/154.56 [10177]~P1(f328(f328(f330(f881(x101771,x101773)),f328(f328(f263(x101771,x101773),x101776),x101777)),f328(f328(f285(x101771,x101772,x101773),x101774),x101775)))+P1(f328(f328(f264(x101771,x101772,x101773,f328(f328(f7(x101771,f882(f881(x101771,x101772),a870),f882(x101772,a870)),f328(f328(f8(f882(x101772,f882(f882(f881(x101771,x101772),a870),a870)),f882(f882(f881(x101771,x101772),a870),f882(x101772,a870)),x101771),f7(x101772,f882(f881(x101771,x101772),a870),a870)),f328(f328(f8(f882(x101772,f881(x101771,x101772)),f882(x101772,f882(f882(f881(x101771,x101772),a870),a870)),x101771),f328(f8(f881(x101771,x101772),f882(f882(f881(x101771,x101772),a870),a870),x101772),f330(f881(x101771,x101772)))),f263(x101771,x101772)))),x101774),f328(f328(f7(x101772,f882(f881(x101772,x101773),a870),f882(x101773,a870)),f328(f328(f8(f882(x101773,f882(f882(f881(x101772,x101773),a870),a870)),f882(f882(f881(x101772,x101773),a870),f882(x101773,a870)),x101772),f7(x101773,f882(f881(x101772,x101773),a870),a870)),f328(f328(f8(f882(x101773,f881(x101772,x101773)),f882(x101773,f882(f882(f881(x101772,x101773),a870),a870)),x101772),f328(f8(f881(x101772,x101773),f882(f882(f881(x101772,x101773),a870),a870),x101773),f330(f881(x101772,x101773)))),f263(x101772,x101773)))),x101775)),x101776),x101777)) % 154.70/154.56 [10187]P1(f328(f328(f330(f881(x101871,x101872)),f328(f328(f263(x101871,x101872),x101873),x101874)),f328(f328(f285(x101871,x101875,x101872),x101876),x101877)))+~P1(f328(f328(f264(x101871,x101875,x101872,f328(f328(f7(x101871,f882(f881(x101871,x101875),a870),f882(x101875,a870)),f328(f328(f8(f882(x101875,f882(f882(f881(x101871,x101875),a870),a870)),f882(f882(f881(x101871,x101875),a870),f882(x101875,a870)),x101871),f7(x101875,f882(f881(x101871,x101875),a870),a870)),f328(f328(f8(f882(x101875,f881(x101871,x101875)),f882(x101875,f882(f882(f881(x101871,x101875),a870),a870)),x101871),f328(f8(f881(x101871,x101875),f882(f882(f881(x101871,x101875),a870),a870),x101875),f330(f881(x101871,x101875)))),f263(x101871,x101875)))),x101876),f328(f328(f7(x101875,f882(f881(x101875,x101872),a870),f882(x101872,a870)),f328(f328(f8(f882(x101872,f882(f882(f881(x101875,x101872),a870),a870)),f882(f882(f881(x101875,x101872),a870),f882(x101872,a870)),x101875),f7(x101872,f882(f881(x101875,x101872),a870),a870)),f328(f328(f8(f882(x101872,f881(x101875,x101872)),f882(x101872,f882(f882(f881(x101875,x101872),a870),a870)),x101875),f328(f8(f881(x101875,x101872),f882(f882(f881(x101875,x101872),a870),a870),x101872),f330(f881(x101875,x101872)))),f263(x101875,x101872)))),x101877)),x101873),x101874)) % 154.70/154.56 [10126]~P139(x101262)+E(f328(f328(f6(x101261,x101262),f328(f328(f7(x101261,f882(x101263,a870),x101262),f328(f328(f8(f882(x101263,x101262),f882(f882(x101263,a870),x101262),x101261),f6(x101263,x101262)),f328(f328(f7(x101261,f882(x101263,x101262),f882(x101263,x101262)),f328(f328(f8(f882(x101262,x101262),f882(f882(x101263,x101262),f882(x101263,x101262)),x101261),f8(x101262,x101262,x101263)),f328(f328(f8(x101262,f882(x101262,x101262),x101261),f81(x101262)),x101264))),x101265))),x101266)),x101267),f328(f328(f81(x101262),f328(f328(f6(x101261,x101262),x101264),x101267)),f328(f328(f6(x101263,x101262),x101265),x101266))) % 154.70/154.56 [9236]~P21(x92367,x92361,x92363,x92368)+E(f328(f73(x92361,x92361,x92362,f328(x92363,x92364)),f328(f73(x92361,x92361,x92362,f328(x92363,x92365)),x92366)),f328(f73(x92361,x92361,x92362,f328(x92363,x92365)),f328(f73(x92361,x92361,x92362,f328(x92363,x92364)),x92366))) % 154.70/154.56 [10182]E(f328(f328(f263(x101821,x101822),f328(x101823,f587(x101824,x101825,x101823,x101826,x101827,x101828,x101822,x101821))),f328(x101825,f588(x101824,x101825,x101823,x101826,x101827,x101828,x101822,x101821))),x101828)+~P1(f328(f328(f330(f881(x101821,x101822)),x101828),f328(f307(f881(x101827,x101826),f881(x101821,x101822),f268(x101827,x101821,x101826,x101822,x101823,x101825)),x101824))) % 154.70/154.56 [10198]~P1(f328(f328(f330(f881(x101988,x101987)),x101986),f328(f307(f881(x101981,x101982),f881(x101988,x101987),f268(x101981,x101988,x101982,x101987,x101985,x101984)),x101983)))+P1(f328(f328(f330(f881(x101981,x101982)),f328(f328(f263(x101981,x101982),f587(x101983,x101984,x101985,x101982,x101981,x101986,x101987,x101988)),f588(x101983,x101984,x101985,x101982,x101981,x101986,x101987,x101988))),x101983)) % 154.70/154.56 [9669]P1(f328(f328(f330(f881(f881(x96691,x96692),f881(x96691,x96692))),f328(f328(f263(f881(x96691,x96692),f881(x96691,x96692)),f328(f328(f263(x96691,x96692),x96693),x96694)),f328(f328(f263(x96691,x96692),x96695),x96696))),f320(x96691,x96692,x96697,x96698)))+~P1(f328(f328(f330(f881(x96691,x96691)),f328(f328(f263(x96691,x96691),x96693),x96695)),x96697)) % 154.70/154.56 [10170]E(f328(f139(x101701,x101702,f328(f7(x101702,x101701,x101701),x101703),f328(x101704,x101705)),x101706),f328(x101704,f328(f139(x101707,x101702,f328(f7(x101702,x101707,x101707),x101708),x101705),x101706)))+P1(f328(f328(f330(x101702),f774(x101705,x101708,x101704,x101703,x101707,x101701,x101706,x101702)),f328(f170(x101702),x101706))) % 154.70/154.56 [10190]~E(f328(f73(x101901,x101901,x101907,f328(x101903,f774(x101905,x101908,x101904,x101903,x101907,x101901,x101906,x101902))),x101904),f328(f73(x101907,x101901,x101907,x101904),f328(x101908,f774(x101905,x101908,x101904,x101903,x101907,x101901,x101906,x101902))))+E(f328(f139(x101901,x101902,f328(f7(x101902,x101901,x101901),x101903),f328(x101904,x101905)),x101906),f328(x101904,f328(f139(x101907,x101902,f328(f7(x101902,x101907,x101907),x101908),x101905),x101906))) % 154.70/154.56 [8458]E(f328(x84581,f328(x84582,x84583)),f328(x84584,f328(x84585,x84583)))+~E(f328(f73(x84586,x84587,x84588,x84581),x84582),f328(f73(x84589,x84587,x84588,x84584),x84585)) % 154.70/154.56 [10054]P1(f328(f328(f330(f881(x100541,x100542)),f328(f328(f263(x100541,x100542),f328(x100543,x100544)),f328(x100545,x100546))),f328(f307(f881(x100547,x100548),f881(x100541,x100542),f268(x100547,x100541,x100548,x100542,x100543,x100545)),x100549)))+~P1(f328(f328(f330(f881(x100547,x100548)),f328(f328(f263(x100547,x100548),x100544),x100546)),x100549)) % 154.70/154.56 [8741]~E(f328(x87414,f328(x87415,x87416)),f328(x87419,f328(x874110,x874111)))+E(f328(f328(f73(x87411,x87412,x87413,x87414),x87415),x87416),f328(f328(f73(x87417,x87412,x87418,x87419),x874110),x874111)) % 154.70/154.56 [4577]~P100(x45771)+~P105(x45771)+E(f105(x45771),f240(x45771)) % 154.70/154.56 [4578]~P99(x45781)+~P105(x45781)+E(f114(x45781),f241(x45781)) % 154.70/154.56 [4820]~P121(x48201)+~P90(x48201)+E(f328(f75(x48201),f328(f107(x48201),a101)),f78(x48201)) % 154.70/154.56 [5098]E(x50981,f2(a1))+E(f82(a1,x50981),f328(f79(a1),f78(a1)))+P1(f328(f328(f243(a1),f2(a1)),x50981)) % 154.70/154.56 [5312]E(x53121,f2(a1))+E(f82(a1,x53121),f78(a1))+~P1(f328(f328(f243(a1),f2(a1)),x53121)) % 154.70/154.56 [7296]~P40(x72961)+P1(f328(f61(a1),x72961))+~P1(f328(f61(a875),f328(f307(a1,a875,a108),x72961))) % 154.70/154.56 [8567]~P9(a5000)+~P1(f328(f328(f330(f881(a873,a871)),x85671),f328(f170(f881(a873,a871)),a27)))+P1(f328(f328(f267(a873,a871,a870),f328(f16(f882(a871,a870),a873),a25)),x85671)) % 154.70/154.56 [9631]E(x96311,f192(f882(f881(a875,a875),a870)))+~P1(f328(f61(f881(a875,a875)),x96311))+P1(f328(f328(f330(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f328(f328(f263(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),f192(f882(f881(a875,a875),a870))),x96311)),a36)) % 154.70/154.56 [9801]E(x98011,f2(a875))+E(x98011,f328(a116,f2(a875)))+~P1(f328(f328(f243(a875),x98011),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 154.70/154.56 [10082]E(x100821,f2(a103))+E(f328(f328(f80(a1),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(a20,f328(f328(f38(a103),x100821),f328(f107(a103),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))))),f78(a1)),f328(a20,x100821))+E(f44(a103,x100821,f328(f107(a103),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f2(a103)) % 154.70/154.56 [9933]E(x99331,f2(a103))+~E(f44(a103,x99331,f328(f107(a103),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f2(a103))+E(f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(a20,f328(f328(f38(a103),x99331),f328(f107(a103),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))),f328(a20,x99331)) % 154.70/154.56 [4650]~P54(x46501,x46502)+P45(x46501,x46502)+~P46(a870) % 154.70/154.56 [4587]~P140(x45871)+P32(x45871,x45872)+~E(x45872,f2(x45871)) % 154.70/154.56 [4588]~P105(x45881)+P16(x45881,x45882)+~E(x45882,f117(x45881)) % 154.70/154.56 [4597]~P121(x45971)+~E(x45972,f2(x45971))+E(f82(x45971,x45972),f2(x45971)) % 154.70/154.56 [4598]~P87(x45981)+~E(x45982,f2(x45981))+E(f82(x45981,x45982),f2(x45981)) % 154.70/154.56 [4606]~P140(x46062)+~P32(x46062,x46061)+E(x46061,f2(x46062)) % 154.70/154.56 [4640]~P121(x46402)+~E(f82(x46402,x46401),f2(x46402))+E(x46401,f2(x46402)) % 154.70/154.56 [4657]~P4(x46572)+~P4(x46571)+P4(f882(x46571,x46572)) % 154.70/154.56 [4658]~P4(x46582)+~P4(x46581)+P4(f880(x46581,x46582)) % 154.70/154.56 [4659]~P4(x46592)+~P4(x46591)+P4(f881(x46591,x46592)) % 154.70/154.56 [4660]~P6(x46602)+~P6(x46601)+P6(f199(x46601,x46602)) % 154.70/154.56 [4661]~P142(x46612)+~P142(x46611)+P142(f881(x46611,x46612)) % 154.70/154.56 [4662]~P59(x46622)+~P59(x46621)+P59(f882(x46621,x46622)) % 154.70/154.56 [4663]~P59(x46632)+~P59(x46631)+P59(f880(x46631,x46632)) % 154.70/154.56 [4664]~P59(x46642)+~P59(x46641)+P59(f881(x46641,x46642)) % 154.70/154.56 [4665]~P59(x46651)+~P92(x46652)+P92(f882(x46651,x46652)) % 154.70/154.56 [4791]~P105(x47911)+~P16(x47911,x47912)+P16(x47911,f149(x47911,x47912)) % 154.70/154.56 [5029]~P6(x50292)+~P6(x50291)+P6(f44(a1,x50291,x50292)) % 154.70/154.56 [4608]~P74(x46081)+~E(x46082,f2(x46081))+E(f328(f79(x46081),x46082),x46082) % 154.70/154.56 [4612]~P89(x46121)+~E(x46122,f2(a1))+E(f328(f106(x46121),x46122),f2(x46121)) % 154.70/154.56 [4613]~P135(x46131)+~E(x46132,f2(a1))+E(f328(f106(x46131),x46132),f2(x46131)) % 154.70/154.56 [4637]~P72(x46371)+~E(f2(x46371),x46372)+E(f328(f79(x46371),x46372),f2(x46371)) % 154.70/154.56 [4638]~P83(x46381)+~E(x46382,f2(x46381))+E(f328(f75(x46381),x46382),f2(x46381)) % 154.70/154.56 [4639]~P72(x46391)+~E(x46392,f2(x46391))+E(f328(f79(x46391),x46392),f2(x46391)) % 154.70/154.56 [4667]~P74(x46672)+E(x46671,f2(x46672))+~E(f328(f79(x46672),x46671),x46671) % 154.70/154.56 [4673]E(x46731,f328(a108,x46732))+~E(x46731,f2(a875))+~E(x46732,f328(f104(a1),x46731)) % 154.70/154.56 [4674]E(f328(a108,x46741),x46742)+~E(x46742,f2(a875))+~E(x46741,f328(f104(a1),x46742)) % 154.70/154.56 [4678]~P89(x46782)+E(x46781,f2(a1))+~E(f328(f106(x46782),x46781),f2(x46782)) % 154.70/154.56 [4683]~P83(x46832)+E(x46831,f2(x46832))+~E(f328(f75(x46832),x46831),f2(x46832)) % 154.70/154.56 [4684]~P72(x46842)+E(x46841,f2(x46842))+~E(f328(f79(x46842),x46841),f2(x46842)) % 154.70/154.56 [4685]~P72(x46851)+E(f2(x46851),x46852)+~E(f328(f79(x46851),x46852),f2(x46851)) % 154.70/154.56 [4825]~P9(a5000)+~E(f328(a28,x48252),f328(f235(a871),x48251))+P1(f328(a25,x48251)) % 154.70/154.56 [4867]~P105(x48671)+~P16(x48671,x48672)+P16(x48671,f328(f169(x48671),x48672)) % 154.70/154.56 [4893]~P1(x48932)+~P1(x48931)+P1(f328(f328(a326,x48931),x48932)) % 154.70/154.56 [4925]~E(f78(a875),f2(a875))+E(f328(f37(x49251),x49252),f2(a875))+~P1(f328(f61(x49251),x49252)) % 154.70/154.56 [4958]~P139(x49581)+~P112(x49581)+E(f328(f328(f253(x49581),f2(x49581)),f328(a116,x49582)),f2(x49581)) % 154.70/154.56 [4996]~P105(x49961)+P16(x49961,f136(x49961,x49962))+~P1(f328(f61(x49961),x49962)) % 154.70/154.56 [4997]~P105(x49971)+P16(x49971,f761(x49972,x49971))+~P1(f328(f61(x49971),x49972)) % 154.70/154.56 [5019]~P105(x50191)+E(f328(f170(x50191),f136(x50191,x50192)),x50192)+~P1(f328(f61(x50191),x50192)) % 154.70/154.56 [5020]~P105(x50201)+E(f328(f170(x50201),f761(x50202,x50201)),x50202)+~P1(f328(f61(x50201),x50202)) % 154.70/154.56 [5050]P1(x50501)+P1(x50502)+~P1(f328(f328(a327,x50502),x50501)) % 154.70/154.56 [5062]E(x50621,f192(f882(x50622,a870)))+~E(f328(f37(x50622),x50621),f2(a875))+~P1(f328(f61(x50622),x50621)) % 154.70/154.56 [5067]P1(x50671)+~P1(x50672)+~P1(f328(f328(a331,x50672),x50671)) % 154.70/154.56 [5116]~P71(x51161)+E(f328(f75(x51161),x51162),x51162)+P1(f328(f328(f243(x51161),x51162),f2(x51161))) % 154.70/154.56 [5186]~P59(x51862)+~P1(f328(f57(x51862),x51861))+P1(f328(x51861,f719(x51861,x51862))) % 154.70/154.56 [5187]~P59(x51872)+~P1(f328(f57(x51872),x51871))+P1(f328(x51871,f729(x51871,x51872))) % 154.70/154.56 [5214]~P1(f328(a25,x52142))+~P1(f328(a25,x52141))+P1(f328(a25,f33(x52141,x52142))) % 154.70/154.56 [5223]E(x52231,f117(x52232))+P1(f328(f134(x52232),f118(x52232,x52231)))+~P1(f328(f134(x52232),x52231)) % 154.70/154.56 [5228]~P105(x52281)+~P1(f328(f61(x52281),x52282))+P1(f328(f134(x52281),f136(x52281,x52282))) % 154.70/154.56 [5229]~P105(x52291)+~P1(f328(f61(x52291),x52292))+P1(f328(f134(x52291),f761(x52292,x52291))) % 154.70/154.56 [5235]~P135(x52351)+E(f328(f104(x52351),f328(a108,x52352)),f328(f106(x52351),x52352))+P1(f328(f328(f243(a1),x52352),f2(a1))) % 154.70/154.56 [5263]P7(x52632,x52631)+E(f328(x52631,f510(x52631)),f328(x52631,f550(x52631)))+P1(f328(f328(x52631,f510(x52631)),f550(x52631))) % 154.70/154.56 [5278]E(f328(f104(a1),f393(x52781,x52782)),x52781)+P1(f328(x52782,f328(a108,x52781)))+~P1(f328(x52782,f2(a875))) % 154.70/154.56 [5290]~P59(x52901)+~P1(f328(x52902,f720(x52902,x52901)))+P1(f328(f58(x52901),x52902)) % 154.70/154.56 [5291]~P59(x52911)+~P1(f328(x52912,f730(x52912,x52911)))+P1(f328(f58(x52911),x52912)) % 154.70/154.56 [5305]~P59(x53052)+~P37(x53052,x53051,f55(x53052))+P1(f328(x53051,f779(x53051,x53052))) % 154.70/154.56 [5321]~P121(x53211)+~E(f82(x53211,x53212),f328(f79(x53211),f78(x53211)))+P1(f328(f328(f243(x53211),x53212),f2(x53211))) % 154.70/154.56 [5397]~E(x53972,f2(a1))+E(f222(x53971,x53972),f328(f328(f263(a1,a1),f2(a1)),f78(a1)))+P1(f328(f328(f243(a1),x53972),f2(a1))) % 154.70/154.56 [5398]~E(x53981,f2(a1))+E(f222(x53981,x53982),f328(f328(f263(a1,a1),f2(a1)),f78(a1)))+P1(f328(f328(f243(a1),x53982),f2(a1))) % 154.70/154.56 [5450]E(f328(f104(a1),f393(x54501,x54502)),x54501)+P1(f328(x54502,f328(a108,x54501)))+P1(f328(f328(f243(a1),x54501),f2(a1))) % 154.70/154.56 [5513]~P121(x55131)+E(f82(x55131,x55132),f328(f79(x55131),f78(x55131)))+~P1(f328(f328(f243(x55131),x55132),f2(x55131))) % 154.70/154.56 [5514]~P83(x55141)+E(f328(f75(x55141),x55142),f328(f79(x55141),x55142))+~P1(f328(f328(f243(x55141),x55142),f2(x55141))) % 154.70/154.56 [5515]~P83(x55151)+E(f328(f75(x55151),x55152),f328(f79(x55151),x55152))+~P1(f328(f328(f242(x55151),x55152),f2(x55151))) % 154.70/154.56 [5516]~P71(x55161)+E(f328(f75(x55161),x55162),f328(f79(x55161),x55162))+~P1(f328(f328(f243(x55161),x55162),f2(x55161))) % 154.70/154.56 [5611]~P1(f328(x56111,f393(x56112,x56111)))+P1(f328(x56111,f328(a108,x56112)))+~P1(f328(x56111,f2(a875))) % 154.70/154.56 [5618]E(x56181,f2(a875))+E(f328(a116,f807(x56182,x56181)),x56181)+~P1(f328(f328(f243(a875),x56181),f328(a116,x56182))) % 154.70/154.56 [5622]P7(x56221,x56222)+~E(f328(x56222,f510(x56222)),f328(x56222,f550(x56222)))+~P1(f328(f328(x56222,f510(x56222)),f550(x56222))) % 154.70/154.56 [5642]~P105(x56421)+P16(x56421,x56422)+P1(f328(f328(f242(a875),f745(x56422,x56421)),f746(x56422,x56421))) % 154.70/154.56 [5643]~P105(x56431)+P16(x56431,x56432)+P1(f328(f328(f242(a875),f752(x56432,x56431)),f757(x56432,x56431))) % 154.70/154.56 [5731]~P83(x57311)+~E(x57312,f2(x57311))+P1(f328(f328(f242(x57311),f328(f75(x57311),x57312)),f2(x57311))) % 154.70/154.56 [5810]~P59(x58102)+~P59(x58101)+E(f59(x58101,x58102,f55(x58101),f55(x58102)),f55(f881(x58101,x58102))) % 154.70/154.56 [5814]~P1(f328(x58141,f393(x58142,x58141)))+P1(f328(x58141,f328(a108,x58142)))+P1(f328(f328(f243(a1),x58142),f2(a1))) % 154.70/154.56 [5837]~P1(f328(x58371,f328(a108,x58372)))+P1(f328(x58371,f2(a875)))+~P1(f328(f328(f243(a1),x58372),f2(a1))) % 154.70/154.56 [6178]~P121(x61781)+~P1(f328(f328(f243(x61781),x61782),f2(x61781)))+P1(f328(f328(f243(x61781),f82(x61781,x61782)),f2(x61781))) % 154.70/154.56 [6292]~P121(x62921)+P1(f328(f328(f243(x62921),f328(f106(x62921),x62922)),f2(x62921)))+~P1(f328(f328(f243(a1),x62922),f2(a1))) % 154.70/154.56 [6293]~P121(x62931)+P1(f328(f328(f242(x62931),f328(f106(x62931),x62932)),f2(x62931)))+~P1(f328(f328(f242(a1),x62932),f2(a1))) % 154.70/154.56 [6300]~P83(x63002)+E(x63001,f2(x63002))+~P1(f328(f328(f242(x63002),f328(f75(x63002),x63001)),f2(x63002))) % 154.70/154.56 [6375]~P135(x63751)+~P1(f328(f328(f330(x63751),x63752),f113(x63751)))+P1(f328(f328(f330(x63751),f328(f79(x63751),x63752)),f113(x63751))) % 154.70/154.56 [6407]~P121(x64071)+~P1(f328(f328(f243(x64071),f82(x64071,x64072)),f2(x64071)))+P1(f328(f328(f243(x64071),x64072),f2(x64071))) % 154.70/154.56 [6576]~P121(x65762)+~P1(f328(f328(f243(x65762),f328(f106(x65762),x65761)),f2(x65762)))+P1(f328(f328(f243(a1),x65761),f2(a1))) % 154.70/154.56 [6577]~P121(x65772)+~P1(f328(f328(f242(x65772),f328(f106(x65772),x65771)),f2(x65772)))+P1(f328(f328(f242(a1),x65771),f2(a1))) % 154.70/154.56 [7081]~P74(x70811)+~P1(f328(f328(f243(x70811),x70812),f2(x70811)))+P1(f328(f328(f243(x70811),f328(f328(f80(x70811),x70812),x70812)),f2(x70811))) % 154.70/154.56 [7082]~P121(x70821)+~P1(f328(f328(f243(x70821),x70822),f2(x70821)))+P1(f328(f328(f243(x70821),f328(f328(f80(x70821),x70822),x70822)),f2(x70821))) % 154.70/154.56 [7083]~P74(x70831)+~P1(f328(f328(f242(x70831),x70832),f2(x70831)))+P1(f328(f328(f242(x70831),f328(f328(f80(x70831),x70832),x70832)),f2(x70831))) % 154.70/154.56 [7654]~P74(x76541)+~P1(f328(f328(f243(x76541),f328(f328(f80(x76541),x76542),x76542)),f2(x76541)))+P1(f328(f328(f243(x76541),x76542),f2(x76541))) % 154.70/154.56 [7655]~P121(x76551)+~P1(f328(f328(f243(x76551),f328(f328(f80(x76551),x76552),x76552)),f2(x76551)))+P1(f328(f328(f243(x76551),x76552),f2(x76551))) % 154.70/154.56 [7656]~P74(x76561)+~P1(f328(f328(f242(x76561),f328(f328(f80(x76561),x76562),x76562)),f2(x76561)))+P1(f328(f328(f242(x76561),x76562),f2(x76561))) % 154.70/154.56 [4723]~E(x47232,f2(a875))+~E(x47231,f2(a875))+E(f328(f328(f80(a875),x47231),x47232),f2(a875)) % 154.70/154.56 [4724]~E(x47242,f78(a875))+~E(x47241,f78(a875))+E(f328(f328(f81(a875),x47241),x47242),f78(a875)) % 154.70/154.56 [4725]~E(x47252,f78(a1))+~E(x47251,f78(a1))+E(f328(f328(f81(a1),x47251),x47252),f78(a1)) % 154.70/154.56 [4777]~P117(x47772)+E(x47771,f2(x47772))+E(f328(f328(f286(x47772),x47771),x47771),f78(x47772)) % 154.70/154.56 [4778]~P57(x47782)+E(x47781,f2(x47782))+E(f328(f328(f38(x47782),x47781),x47781),f78(x47782)) % 154.70/154.56 [4779]~P118(x47792)+E(x47791,f2(x47792))+E(f328(f328(f286(x47792),x47791),x47791),f78(x47792)) % 154.70/154.56 [4796]~P74(x47961)+~E(x47962,f2(x47961))+E(f328(f328(f80(x47961),x47962),x47962),f2(x47961)) % 154.70/154.56 [4799]~P137(x47991)+~E(x47992,f78(x47991))+E(f328(f328(f81(x47991),x47992),x47992),f78(x47991)) % 154.70/154.56 [4800]~P118(x48001)+~E(x48002,f2(x48001))+E(f328(f328(f286(x48001),x48002),x48002),f2(x48001)) % 154.70/154.56 [4846]~E(x48462,f2(a875))+~E(x48461,f2(a875))+E(f328(f79(a1),f328(f104(a1),x48461)),f328(f104(a1),x48462)) % 154.70/154.56 [4864]E(x48641,f78(a875))+E(x48642,f2(a875))+~E(f328(f328(f81(a875),x48642),x48641),x48642) % 154.70/154.56 [4874]E(x48741,f2(a875))+E(x48742,f2(a875))+~E(f328(f328(f81(a875),x48742),x48741),f2(a875)) % 154.70/154.56 [4902]~E(x49022,f2(a875))+~E(x49021,f328(a116,f2(a875)))+E(f328(f328(f80(a875),x49021),x49022),f328(a116,f2(a875))) % 154.70/154.56 [4903]~E(x49031,f2(a875))+~E(x49032,f328(a116,f2(a875)))+E(f328(f328(f80(a875),x49031),x49032),f328(a116,f2(a875))) % 154.70/154.56 [4908]E(x49081,f78(a1))+E(x49082,f328(f107(a1),a101))+~E(f328(f328(f81(a1),x49081),x49082),f78(a1)) % 154.70/154.56 [4909]E(x49091,f78(a1))+E(x49092,f328(f107(a1),a101))+~E(f328(f328(f81(a1),x49092),x49091),f78(a1)) % 154.70/154.56 [4910]E(x49101,f78(a1))+E(x49101,f328(f107(a1),a101))+~E(f328(f328(f81(a1),x49102),x49101),f78(a1)) % 154.70/154.56 [4912]E(x49121,f78(a1))+E(x49121,f328(f107(a1),a101))+~E(f328(f328(f81(a1),x49121),x49122),f78(a1)) % 154.70/154.56 [4929]~P74(x49292)+E(x49291,f2(x49292))+~E(f328(f328(f80(x49292),x49291),x49291),f2(x49292)) % 154.70/154.56 [4935]~E(x49351,f328(f107(a1),a101))+~E(x49352,f328(f107(a1),a101))+E(f328(f328(f81(a1),x49351),x49352),f78(a1)) % 154.70/154.56 [4947]E(x49471,f2(a875))+E(x49472,f2(a875))+~E(f328(f328(f80(a875),x49472),x49471),f328(a116,f2(a875))) % 154.70/154.56 [4957]~P60(x49571)+~P90(x49571)+E(f328(f328(f286(x49571),x49572),f328(f107(x49571),a83)),f2(x49571)) % 154.70/154.56 [4963]~P137(x49631)+~E(x49632,f328(f79(x49631),f78(x49631)))+E(f328(f328(f81(x49631),x49632),x49632),f78(x49631)) % 154.70/154.56 [4968]~P6(x49682)+~P6(x49681)+P6(f328(f328(f80(a1),x49681),x49682)) % 154.70/154.56 [4969]~P6(x49692)+~P6(x49691)+P6(f328(f328(f81(a1),x49691),x49692)) % 154.70/154.56 [4970]~P6(x49702)+~P6(x49701)+P6(f328(f328(f38(a1),x49701),x49702)) % 154.70/154.56 [4972]~E(x49722,f2(a1))+E(x49721,f2(a1))+E(f45(x49721,x49722),f328(f328(f263(a1,a1),f2(a1)),x49721)) % 154.70/154.56 [4994]~E(x49942,f328(a116,f2(a875)))+~E(x49941,f328(a116,f2(a875)))+E(f328(f328(f81(a875),x49941),x49942),f328(a116,f2(a875))) % 154.70/154.56 [5009]E(x50091,f2(a875))+E(x50092,f328(a116,f2(a875)))+~E(f328(f328(f253(a875),x50092),x50091),f328(a116,f2(a875))) % 154.70/154.56 [5010]E(x50101,f2(a875))+E(x50101,f328(a116,f2(a875)))+~E(f328(f328(f80(a875),x50102),x50101),f328(a116,f2(a875))) % 154.70/154.56 [5011]E(x50111,f2(a875))+E(x50111,f328(a116,f2(a875)))+~E(f328(f328(f80(a875),x50111),x50112),f328(a116,f2(a875))) % 154.70/154.56 [5021]~P60(x50211)+~P90(x50211)+E(f328(f328(f286(x50211),x50212),f328(f107(x50211),a101)),f328(f79(x50211),x50212)) % 154.70/154.56 [5042]E(x50421,f328(a108,x50422))+~E(x50421,f2(a875))+P1(f328(f328(f242(a1),f2(a1)),x50422)) % 154.70/154.56 [5043]E(f328(a108,x50431),x50432)+~E(x50432,f2(a875))+P1(f328(f328(f242(a1),f2(a1)),x50431)) % 154.70/154.56 [5058]E(x50581,f328(a116,f2(a875)))+E(x50582,f328(a116,f2(a875)))+~E(f328(f328(f80(a875),x50581),x50582),f328(a116,f2(a875))) % 154.70/154.56 [5069]~E(x50691,f328(a108,x50692))+E(x50691,f2(a875))+P1(f328(f328(f242(a1),f2(a1)),x50692)) % 154.70/154.56 [5070]~E(f328(a108,x50702),x50701)+E(x50701,f2(a875))+P1(f328(f328(f242(a1),f2(a1)),x50702)) % 154.70/154.56 [5092]~P2(x50921)+E(f328(f63(x50921,f114(x50921)),x50922),f10(x50921,x50922))+~P1(f328(f61(x50921),x50922)) % 154.70/154.56 [5093]~P2(x50931)+E(f328(f63(x50931,f105(x50931)),x50932),f11(x50931,x50932))+~P1(f328(f61(x50931),x50932)) % 154.70/154.56 [5094]~P105(x50941)+E(f328(f63(x50941,f240(x50941)),x50942),f14(x50941,x50942))+~P1(f328(f61(x50941),x50942)) % 154.70/154.56 [5095]~P105(x50951)+E(f328(f63(x50951,f241(x50951)),x50952),f15(x50951,x50952))+~P1(f328(f61(x50951),x50952)) % 154.70/154.56 [5097]~P59(x50971)+~P1(f328(x50972,f205(x50971)))+P1(f328(f57(f879(x50971)),x50972)) % 154.70/154.56 [5179]~P59(x51792)+P1(f328(x51791,f205(x51792)))+~P1(f328(f58(f879(x51792)),x51791)) % 154.70/154.56 [5180]E(x51801,x51802)+~E(f328(f328(f22(a875),x51802),x51801),f2(a875))+~E(f328(f328(f22(a875),x51801),x51802),f2(a875)) % 154.70/154.56 [5194]P6(x51941)+~P40(x51942)+~P1(f328(f328(f330(a1),x51941),x51942)) % 154.70/154.56 [5224]~P121(x52241)+~E(f82(x52241,x52242),f78(x52241))+P1(f328(f328(f243(x52241),f2(x52241)),x52242)) % 154.70/154.56 [5236]~P90(x52361)+E(f328(f104(x52361),f328(f107(a875),x52362)),f328(f107(x52361),x52362))+P1(f328(a197,f328(f107(a1),x52362))) % 154.70/154.56 [5242]~P45(x52421,x52422)+P46(a870)+P1(f328(f61(f881(x52421,x52421)),x52422)) % 154.70/154.56 [5314]~P105(x53141)+E(f328(f63(x53141,f241(x53141)),x53142),f12(x53141,f241(x53141),x53142))+~P1(f328(f61(x53141),x53142)) % 154.70/154.56 [5315]~P105(x53151)+E(f328(f63(x53151,f240(x53151)),x53152),f13(x53151,f240(x53151),x53152))+~P1(f328(f61(x53151),x53152)) % 154.70/154.56 [5328]E(x53281,x53282)+P1(f328(f328(f243(a875),x53282),x53281))+P1(f328(f328(f243(a875),x53281),x53282)) % 154.70/154.56 [5329]E(x53291,x53292)+P1(f328(f328(f243(a1),x53292),x53291))+P1(f328(f328(f243(a1),x53291),x53292)) % 154.70/154.56 [5384]~P90(x53841)+E(f328(f104(x53841),f328(f107(a875),x53842)),f2(x53841))+~P1(f328(a197,f328(f107(a1),x53842))) % 154.70/154.56 [5387]~E(x53872,f328(a108,x53871))+E(x53871,f328(f104(a1),x53872))+~P1(f328(f328(f242(a1),f2(a1)),x53871)) % 154.70/154.56 [5388]~E(f328(a108,x53881),x53882)+E(x53881,f328(f104(a1),x53882))+~P1(f328(f328(f242(a1),f2(a1)),x53881)) % 154.70/154.56 [5389]~E(x53891,f328(a108,x53892))+E(f328(f104(a1),x53891),x53892)+~P1(f328(f328(f242(a1),f2(a1)),x53892)) % 154.70/154.56 [5399]E(x53991,f328(a108,x53992))+~E(x53992,f328(f104(a1),x53991))+~P1(f328(f328(f242(a1),f2(a1)),x53992)) % 154.70/154.56 [5400]E(f328(a108,x54001),x54002)+~E(x54001,f328(f104(a1),x54002))+~P1(f328(f328(f242(a1),f2(a1)),x54001)) % 154.70/154.56 [5439]~P83(x54392)+E(x54391,f2(x54392))+P1(f328(f328(f243(x54392),f2(x54392)),f328(f75(x54392),x54391))) % 154.70/154.56 [5506]~P121(x55061)+E(f82(x55061,x55062),f78(x55061))+~P1(f328(f328(f243(x55061),f2(x55061)),x55062)) % 154.70/154.56 [5510]~P90(x55101)+E(f328(f104(x55101),f328(f107(a875),x55102)),f2(x55101))+P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x55102))) % 154.70/154.56 [5517]~P83(x55171)+E(f328(f75(x55171),x55172),x55172)+~P1(f328(f328(f243(x55171),f2(x55171)),x55172)) % 154.70/154.56 [5518]~P83(x55181)+E(f328(f75(x55181),x55182),x55182)+~P1(f328(f328(f242(x55181),f2(x55181)),x55182)) % 154.70/154.56 [5525]E(x55251,f2(a875))+~E(f136(a875,f328(f298(a875,x55252),x55251)),f117(a875))+P1(f328(f328(f242(a875),x55251),x55252)) % 154.70/154.56 [5535]~P66(x55351)+E(f328(f328(f6(x55351,x55351),f5(x55351)),f328(f170(x55351),x55352)),f328(f163(x55351),x55352))+~P1(f328(f134(x55351),x55352)) % 154.70/154.56 [5538]~P135(x55381)+E(f328(f104(x55381),f328(a108,x55382)),f328(f106(x55381),x55382))+~P1(f328(f328(f242(a1),f2(a1)),x55382)) % 154.70/154.56 [5565]E(x55651,x55652)+P1(f328(f328(f243(a875),x55651),x55652))+~P1(f328(f328(f242(a875),x55651),x55652)) % 154.70/154.56 [5566]E(x55661,x55662)+P1(f328(f328(f243(a1),x55661),x55662))+~P1(f328(f328(f242(a1),x55661),x55662)) % 154.70/154.56 [5569]E(x55691,f78(a1))+~E(f328(f328(f81(a1),x55692),x55691),f78(a1))+~P1(f328(f328(f243(a1),f2(a1)),x55692)) % 154.70/154.56 [5570]E(x55701,f78(a1))+~E(f328(f328(f81(a1),x55701),x55702),f78(a1))+~P1(f328(f328(f243(a1),f2(a1)),x55701)) % 154.70/154.56 [5608]~P40(x56082)+P1(f328(f328(f242(a1),f2(a1)),x56081))+~P1(f328(f328(f330(a1),x56081),x56082)) % 154.70/154.56 [5627]~P54(x56271,x56272)+P39(x56271,x56272)+~P1(f328(f61(f881(x56271,x56271)),x56272)) % 154.70/154.56 [5629]~P54(x56291,x56292)+P45(x56291,x56292)+~P1(f328(f61(f881(x56291,x56291)),x56292)) % 154.70/154.56 [5673]E(x56731,f192(f882(x56732,a870)))+~P1(f328(f61(x56732),x56731))+P1(f328(f328(f243(a875),f2(a875)),f328(f37(x56732),x56731))) % 154.70/154.56 [5700]~P1(f328(x57001,x57002))+P1(f328(x57001,f2(a875)))+P1(f328(f328(f243(a875),f411(x57002,x57001)),x57002)) % 154.70/154.56 [5725]E(x57251,f2(a875))+~E(f328(f163(a875),x57252),f2(a875))+~P1(f328(f328(f330(a875),x57251),f328(f170(a875),x57252))) % 154.70/154.56 [5791]E(x57911,x57912)+~P1(f328(f328(f242(a875),x57912),x57911))+~P1(f328(f328(f242(a875),x57911),x57912)) % 154.70/154.56 [5792]E(x57921,x57922)+~P1(f328(f328(f242(a1),x57922),x57921))+~P1(f328(f328(f242(a1),x57921),x57922)) % 154.70/154.56 [5793]E(f328(f37(x57931),x57932),f2(a875))+~P1(f328(f61(x57931),x57932))+P1(f328(f328(f330(x57931),f511(x57932,x57931)),x57932)) % 154.70/154.56 [5802]E(f49(x58021,x58022),f45(x58021,x58022))+P1(f328(f328(f242(a1),f2(a1)),x58021))+~P1(f328(f328(f243(a1),f2(a1)),x58022)) % 154.70/154.56 [5826]~P1(f328(x58261,f390(x58261)))+P1(f328(x58261,f328(a108,x58262)))+~P1(f328(f328(f242(a1),f2(a1)),x58262)) % 154.70/154.56 [5828]P1(f328(f328(f243(a875),x58281),f342(x58282)))+~P1(f328(f61(a875),x58282))+~P1(f328(f328(f330(a875),x58281),x58282)) % 154.70/154.56 [5829]P1(f328(f328(f242(a875),x58291),f357(x58292)))+~P1(f328(f61(a875),x58292))+~P1(f328(f328(f330(a875),x58291),x58292)) % 154.70/154.56 [5858]E(x58581,x58582)+~P1(f328(f328(f243(a875),x58581),f328(a116,x58582)))+P1(f328(f328(f243(a875),x58581),x58582)) % 154.70/154.56 [5892]E(x58921,f328(a116,x58922))+~P1(f328(f328(f242(a875),x58921),f328(a116,x58922)))+P1(f328(f328(f242(a875),x58921),x58922)) % 154.70/154.56 [5905]P1(f328(x59051,f391(x59051)))+~P1(f328(x59051,f328(a108,x59052)))+~P1(f328(f328(f242(a1),f2(a1)),x59052)) % 154.70/154.56 [5919]~P1(f328(x59191,x59192))+~P1(f328(f328(f242(a1),f2(a1)),x59192))+P1(f328(x59191,f328(f104(a1),f367(x59191)))) % 154.70/154.56 [5933]~P83(x59332)+~E(x59331,f2(x59332))+~P1(f328(f328(f243(x59332),f2(x59332)),f328(f75(x59332),x59331))) % 154.70/154.56 [5958]~P54(x59581,x59582)+P39(x59581,f328(f283(x59581,x59581),x59582))+~P1(f328(f61(f881(x59581,x59581)),x59582)) % 154.70/154.56 [5966]~P90(x59661)+E(f328(f104(x59661),f328(f107(a875),x59662)),f328(f107(x59661),x59662))+~P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x59662))) % 154.70/154.56 [5969]E(f328(a116,x59691),x59692)+~P1(f328(f328(f243(a875),x59691),x59692))+P1(f328(f328(f243(a875),f328(a116,x59691)),x59692)) % 154.70/154.56 [5982]E(f328(f328(f38(a1),x59821),x59822),f2(a1))+~P1(f328(f328(f242(a1),x59821),f2(a1)))+~P1(f328(f328(f243(a1),x59822),x59821)) % 154.70/154.56 [5993]E(f44(a1,x59931,x59932),x59931)+~P1(f328(f328(f242(a1),x59931),f2(a1)))+~P1(f328(f328(f243(a1),x59932),x59931)) % 154.70/154.56 [6006]E(f46(x60061,x60062),f45(x60061,x60062))+~P1(f328(f328(f242(a1),f2(a1)),x60061))+~P1(f328(f328(f242(a1),f2(a1)),x60062)) % 154.70/154.56 [6014]E(f328(f328(f38(a1),x60141),x60142),f2(a1))+~P1(f328(f328(f242(a1),f2(a1)),x60141))+~P1(f328(f328(f243(a1),x60141),x60142)) % 154.70/154.56 [6026]E(f44(a875,f328(f107(a875),x60261),f328(f107(a875),x60262)),f328(f107(a875),x60261))+P1(f328(a197,f328(f107(a1),x60261)))+~P1(f328(a197,f328(f107(a1),x60262))) % 154.70/154.56 [6028]E(f44(a1,x60281,x60282),x60281)+~P1(f328(f328(f242(a1),f2(a1)),x60281))+~P1(f328(f328(f243(a1),x60281),x60282)) % 154.70/154.56 [6029]E(x60291,x60292)+~P1(f328(f328(f243(a875),x60291),f328(a116,x60292)))+~P1(f328(f328(f242(a875),x60292),x60291)) % 154.70/154.56 [6046]~P121(x60461)+~P1(f328(f328(f243(x60461),x60462),f2(x60461)))+P1(f328(f328(f243(x60461),x60462),f328(f79(x60461),x60462))) % 154.70/154.56 [6047]~P74(x60471)+~P1(f328(f328(f242(x60471),x60472),f2(x60471)))+P1(f328(f328(f242(x60471),x60472),f328(f79(x60471),x60472))) % 154.70/154.56 [6057]~P5(x60571)+E(f328(f328(f64(x60571,x60571,f114(x60571)),f192(x60571)),x60572),f39(x60571,x60572))+~P1(f328(f61(x60571),x60572)) % 154.70/154.56 [6058]~P5(x60581)+E(f328(f328(f64(x60581,x60581,f105(x60581)),f251(x60581)),x60582),f40(x60581,x60582))+~P1(f328(f61(x60581),x60582)) % 154.70/154.56 [6072]~P123(x60721)+~P1(f328(f328(f243(a875),f2(a875)),x60722))+P1(f328(f328(f243(x60721),f2(x60721)),f328(f104(x60721),x60722))) % 154.70/154.56 [6073]~P121(x60731)+~P1(f328(f328(f243(a1),f2(a1)),x60732))+P1(f328(f328(f243(x60731),f2(x60731)),f328(f106(x60731),x60732))) % 154.70/154.56 [6074]~P121(x60741)+~P1(f328(f328(f242(a1),f2(a1)),x60742))+P1(f328(f328(f242(x60741),f2(x60741)),f328(f106(x60741),x60742))) % 154.70/154.56 [6077]~P6(x60772)+~P6(x60771)+E(f328(f307(a875,a1,f104(a1)),f299(a875,f328(a108,x60771),f328(a108,x60772))),f299(a1,x60771,x60772)) % 154.70/154.56 [6083]P1(f328(x60831,x60832))+~P1(f328(f328(f242(a1),f2(a1)),x60832))+~P1(f328(x60831,f328(f104(a1),f370(x60831)))) % 154.70/154.56 [6108]E(f328(f328(f80(a875),f328(f107(a875),x61081)),f328(f107(a875),x61082)),f328(f107(a875),x61081))+P1(f328(f328(f243(a1),x61081),a83))+~P1(f328(f328(f243(a1),x61082),a83)) % 154.70/154.56 [6112]~P121(x61121)+P1(f328(f328(f243(x61121),f2(x61121)),f82(x61121,x61122)))+~P1(f328(f328(f243(x61121),f2(x61121)),x61122)) % 154.70/154.56 [6123]~P81(x61231)+~P1(f328(f328(f243(x61231),x61232),f2(x61231)))+P1(f328(f328(f243(x61231),f2(x61231)),f328(f79(x61231),x61232))) % 154.70/154.56 [6124]~P81(x61241)+~P1(f328(f328(f242(x61241),x61242),f2(x61241)))+P1(f328(f328(f242(x61241),f2(x61241)),f328(f79(x61241),x61242))) % 154.70/154.56 [6127]E(x61271,f251(f882(x61272,a870)))+~E(f328(f37(x61272),x61271),f328(f37(x61272),f251(f882(x61272,a870))))+~P1(f328(f61(x61272),f251(f882(x61272,a870)))) % 154.70/154.56 [6169]~P121(x61691)+P1(f328(f328(f243(x61691),x61692),f2(x61691)))+~P1(f328(f328(f243(x61691),x61692),f328(f79(x61691),x61692))) % 154.70/154.56 [6170]~P74(x61701)+P1(f328(f328(f242(x61701),x61702),f2(x61701)))+~P1(f328(f328(f242(x61701),x61702),f328(f79(x61701),x61702))) % 154.70/154.56 [6180]~P90(x61801)+P1(f328(f328(f330(x61801),f328(f107(x61801),x61802)),f190(x61801)))+~P1(f328(f328(f242(a1),a83),x61802)) % 154.70/154.56 [6211]E(x62111,f2(a875))+~P1(f328(f328(f243(a875),x62111),f328(a116,x62112)))+P1(f328(f328(f243(a875),f807(x62112,x62111)),x62112)) % 154.70/154.56 [6233]~P121(x62331)+~P1(f328(f328(f243(x62331),f2(x62331)),f82(x62331,x62332)))+P1(f328(f328(f243(x62331),f2(x62331)),x62332)) % 154.70/154.56 [6235]~E(f328(f107(a875),x62352),f328(f107(a875),x62351))+P1(f328(f328(f242(a1),f328(f107(a1),x62351)),f2(a1)))+~P1(f328(a197,f328(f107(a1),x62352))) % 154.70/154.56 [6265]E(f328(f262(a1,a1),f49(x62651,x62652)),f328(f328(f38(a1),x62651),x62652))+~P1(f328(f328(f243(a1),x62651),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x62652)) % 154.70/154.56 [6298]E(f328(f266(a1,a1),f49(x62981,x62982)),f44(a1,x62981,x62982))+~P1(f328(f328(f243(a1),x62981),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x62982)) % 154.70/154.56 [6301]~P123(x63012)+~P1(f328(f328(f243(x63012),f2(x63012)),f328(f104(x63012),x63011)))+P1(f328(f328(f243(a875),f2(a875)),x63011)) % 154.70/154.56 [6302]~P121(x63022)+~P1(f328(f328(f243(x63022),f2(x63022)),f328(f106(x63022),x63021)))+P1(f328(f328(f243(a1),f2(a1)),x63021)) % 154.70/154.56 [6303]~P121(x63032)+~P1(f328(f328(f242(x63032),f2(x63032)),f328(f106(x63032),x63031)))+P1(f328(f328(f242(a1),f2(a1)),x63031)) % 154.70/154.56 [6306]E(f328(f262(a1,a1),f46(x63061,x63062)),f328(f328(f38(a1),x63061),x63062))+~P1(f328(f328(f243(a1),f2(a1)),x63061))+~P1(f328(f328(f242(a1),f2(a1)),x63062)) % 154.70/154.56 [6321]E(f328(f266(a1,a1),f46(x63211,x63212)),f44(a1,x63211,x63212))+~P1(f328(f328(f243(a1),f2(a1)),x63211))+~P1(f328(f328(f242(a1),f2(a1)),x63212)) % 154.70/154.56 [6336]~P81(x63361)+P1(f328(f328(f243(x63361),x63362),f2(x63361)))+~P1(f328(f328(f243(x63361),f2(x63361)),f328(f79(x63361),x63362))) % 154.70/154.56 [6337]~P81(x63371)+P1(f328(f328(f242(x63371),x63372),f2(x63371)))+~P1(f328(f328(f242(x63371),f2(x63371)),f328(f79(x63371),x63372))) % 154.70/154.56 [6362]P1(f328(f48(x63621,x63622),f49(x63621,x63622)))+~P1(f328(f328(f243(a1),x63621),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x63622)) % 154.70/154.56 [6387]P1(f328(f48(x63871,x63872),f46(x63871,x63872)))+~P1(f328(f328(f243(a1),f2(a1)),x63872))+~P1(f328(f328(f242(a1),f2(a1)),x63871)) % 154.70/154.56 [6430]~P81(x64301)+P1(f328(f328(f243(x64301),f328(f79(x64301),x64302)),f2(x64301)))+~P1(f328(f328(f243(x64301),f2(x64301)),x64302)) % 154.70/154.56 [6431]~P81(x64311)+P1(f328(f328(f242(x64311),f328(f79(x64311),x64312)),f2(x64311)))+~P1(f328(f328(f242(x64311),f2(x64311)),x64312)) % 154.70/154.56 [6448]E(f328(f328(f22(a875),f328(a108,x64481)),f328(a108,x64482)),f328(a108,f199(x64481,x64482)))+~P1(f328(f328(f242(a1),f2(a1)),x64482))+~P1(f328(f328(f242(a1),f2(a1)),x64481)) % 154.70/154.56 [6465]P1(f328(f328(f242(a1),f2(a1)),f199(x64651,x64652)))+~P1(f328(f328(f242(a1),f2(a1)),x64652))+~P1(f328(f328(f242(a1),f2(a1)),x64651)) % 154.70/154.56 [6502]~P1(f328(x65021,x65022))+P1(f328(x65021,f2(a875)))+P1(f328(x65021,f328(f328(f80(a875),f411(x65022,x65021)),f78(a875)))) % 154.70/154.56 [6583]E(f328(f107(a875),x65831),f328(f107(a875),x65832))+~P1(f328(f328(f242(a1),f328(f107(a1),x65832)),f2(a1)))+~P1(f328(a197,f328(f107(a1),x65831))) % 154.70/154.56 [6593]~E(x65931,f2(a875))+~E(f706(x65932,x65931),f2(a875))+E(f328(f139(a875,a875,f80(a875),x65931),x65932),f2(a875)) % 154.70/154.56 [6619]~P1(f328(f61(x66191),f797(x66192,x66191)))+~P1(f328(f61(f882(x66191,a870)),x66192))+P1(f328(f61(x66191),f39(f882(x66191,a870),x66192))) % 154.70/154.56 [6625]E(x66251,x66252)+P1(f328(f328(f243(a1),x66251),x66252))+~P1(f328(f328(f243(a1),x66251),f328(f328(f80(a1),x66252),f78(a1)))) % 154.70/154.56 [6627]P1(f328(f328(f243(a875),f328(a108,x66271)),f328(a108,x66272)))+~P1(f328(f328(f243(a1),f2(a1)),x66272))+~P1(f328(f328(f243(a1),x66271),x66272)) % 154.70/154.56 [6628]P1(f328(f328(f243(a875),f328(a108,x66281)),f328(a108,x66282)))+~P1(f328(f328(f242(a1),f2(a1)),x66281))+~P1(f328(f328(f243(a1),x66281),x66282)) % 154.70/154.56 [6629]P1(f328(f328(f242(a875),f328(a108,x66291)),f328(a108,x66292)))+~P1(f328(f328(f243(a1),f2(a1)),x66291))+~P1(f328(f328(f242(a1),x66291),x66292)) % 154.70/154.56 [6630]P1(f328(f328(f242(a875),f328(a108,x66301)),f328(a108,x66302)))+~P1(f328(f328(f242(a1),f2(a1)),x66302))+~P1(f328(f328(f242(a1),x66301),x66302)) % 154.70/154.56 [6642]E(f44(a875,f328(a108,x66421),f328(a108,x66422)),f328(a108,f44(a1,x66421,x66422)))+~P1(f328(f328(f242(a1),f2(a1)),x66422))+~P1(f328(f328(f242(a1),f2(a1)),x66421)) % 154.70/154.56 [6664]~P81(x66641)+~P1(f328(f328(f243(x66641),f328(f79(x66641),x66642)),f2(x66641)))+P1(f328(f328(f243(x66641),f2(x66641)),x66642)) % 154.70/154.56 [6665]~P81(x66651)+~P1(f328(f328(f242(x66651),f328(f79(x66651),x66652)),f2(x66651)))+P1(f328(f328(f242(x66651),f2(x66651)),x66652)) % 154.70/154.56 [6680]~P1(f328(f328(f243(a1),a83),x66802))+~P1(f328(f328(f243(a1),x66801),x66802))+P1(f328(f328(f243(a875),f328(f107(a875),x66801)),f328(f107(a875),x66802))) % 154.70/154.56 [6771]~P1(f328(f328(f242(a1),f2(a1)),x67711))+P1(f328(f328(f243(a875),f328(a108,x67711)),x67712))+~P1(f328(f328(f243(a1),x67711),f328(f104(a1),x67712))) % 154.70/154.56 [6788]E(x67881,f2(a1))+E(f44(a1,x67882,x67881),f2(a1))+E(f328(f328(f22(a1),f328(f79(a1),f328(f328(f38(a1),x67882),x67881))),f78(a1)),f328(f328(f38(a1),x67882),f328(f79(a1),x67881))) % 154.70/154.56 [6804]~P1(f328(f328(f242(a1),f2(a1)),x68041))+~P1(f328(f328(f243(a875),f328(a108,x68041)),x68042))+P1(f328(f328(f243(a1),x68041),f328(f104(a1),x68042))) % 154.70/154.56 [6841]~P1(f328(f328(f242(a875),f328(a108,x68411)),f328(a108,x68412)))+~P1(f328(f328(f243(a1),f2(a1)),x68411))+P1(f328(f328(f242(a1),x68411),x68412)) % 154.70/154.56 [6842]~P1(f328(f328(f242(a875),f328(a108,x68421)),f328(a108,x68422)))+~P1(f328(f328(f242(a1),f2(a1)),x68422))+P1(f328(f328(f242(a1),x68421),x68422)) % 154.70/154.56 [6869]P1(f328(f328(f242(a1),x68691),x68692))+~P1(f328(f328(f242(a875),f328(f107(a875),x68691)),f328(f107(a875),x68692)))+P1(f328(f328(f242(a1),x68691),a83)) % 154.70/154.56 [6894]P1(f328(f328(f242(a1),f2(a1)),f44(a1,x68941,x68942)))+~P1(f328(f328(f242(a1),f2(a1)),x68942))+~P1(f328(f328(f242(a1),f2(a1)),x68941)) % 154.70/154.56 [6992]P1(f328(f328(f243(a1),a83),x69921))+~P1(f328(f328(f243(a1),x69922),x69921))+~P1(f328(f328(f243(a875),f328(f107(a875),x69922)),f328(f107(a875),x69921))) % 154.70/154.56 [7043]E(f328(f328(f263(a1,a1),f328(f328(f38(a1),x70431),x70432)),f44(a1,x70431,x70432)),f49(x70431,x70432))+~P1(f328(f328(f243(a1),x70431),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x70432)) % 154.70/154.56 [7064]E(f328(f328(f263(a1,a1),f328(f328(f38(a1),x70641),x70642)),f44(a1,x70641,x70642)),f46(x70641,x70642))+~P1(f328(f328(f242(a1),f2(a1)),x70642))+~P1(f328(f328(f242(a1),f2(a1)),x70641)) % 154.70/154.56 [7115]~P94(x71152)+E(x71151,f117(x71152))+E(f328(f139(x71152,x71152,f81(x71152),f328(f138(x71152),x71151)),f328(f169(x71152),x71151)),f328(f63(x71152,f81(x71152)),f328(f170(x71152),x71151))) % 154.70/154.56 [7229]~E(x72291,f2(a875))+E(f328(f139(a875,a875,f80(a875),x72291),x72292),f2(a875))+P1(f328(f328(f330(a875),f706(x72292,x72291)),f328(f170(a875),x72292))) % 154.70/154.56 [7276]~P1(f328(f328(f243(a1),x72762),f2(a1)))+P1(f328(f328(f243(a1),f328(f328(f38(a1),x72761),x72762)),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x72761)) % 154.70/154.56 [7278]~P1(f328(f328(f243(a1),x72781),f2(a1)))+P1(f328(f328(f243(a1),f328(f328(f38(a1),x72781),x72782)),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x72782)) % 154.70/154.56 [7279]~P1(f328(f328(f243(a1),x72792),f2(a1)))+P1(f328(f328(f242(a1),f328(f328(f38(a1),x72791),x72792)),f2(a1)))+~P1(f328(f328(f242(a1),f2(a1)),x72791)) % 154.70/154.56 [7280]~P1(f328(f328(f242(a1),x72801),f2(a1)))+P1(f328(f328(f242(a1),f328(f328(f38(a1),x72801),x72802)),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x72802)) % 154.70/154.56 [7286]P1(f328(f328(f330(f882(x72861,a870)),f797(x72862,x72861)),x72862))+~P1(f328(f61(f882(x72861,a870)),x72862))+P1(f328(f61(x72861),f39(f882(x72861,a870),x72862))) % 154.70/154.56 [7383]P27(x73831,x73831,x73832,f251(f882(x73831,a870)))+~E(f328(f307(x73831,x73831,x73832),f251(f882(x73831,a870))),f251(f882(x73831,a870)))+~P1(f328(f61(x73831),f251(f882(x73831,a870)))) % 154.70/154.56 [7510]~P27(x75101,x75101,x75102,f251(f882(x75101,a870)))+E(f328(f307(x75101,x75101,x75102),f251(f882(x75101,a870))),f251(f882(x75101,a870)))+~P1(f328(f61(x75101),f251(f882(x75101,a870)))) % 154.70/154.56 [7648]E(f328(f328(f38(a1),x76481),x76482),f328(f107(a1),a101))+~P1(f328(f328(f242(a1),f328(f328(f80(a1),x76481),x76482)),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x76481)) % 154.70/154.56 [7707]~P1(f328(f328(f243(a1),x77072),f2(a1)))+~P1(f328(f328(f243(a1),f328(f328(f38(a1),x77071),x77072)),f2(a1)))+P1(f328(f328(f243(a1),f2(a1)),x77071)) % 154.70/154.56 [7712]E(f328(f328(f80(a1),x77121),x77122),f44(a1,x77121,x77122))+~P1(f328(f328(f242(a1),f328(f328(f80(a1),x77121),x77122)),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x77121)) % 154.70/154.56 [7715]P1(f328(f328(f243(a1),x77151),f2(a1)))+~P1(f328(f328(f243(a1),f328(f328(f38(a1),x77151),x77152)),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x77152)) % 154.70/154.56 [8104]~P59(x81041)+~P1(f328(f58(f879(x81041)),x81042))+P1(f328(f58(x81041),f328(f328(f8(f879(x81041),a870,x81041),x81042),f235(x81041)))) % 154.70/154.56 [8424]~P105(x84241)+P16(x84241,x84242)+~P1(f328(f328(f242(x84241),f328(f328(f162(x84241),x84242),f745(x84242,x84241))),f328(f328(f162(x84241),x84242),f746(x84242,x84241)))) % 154.70/154.56 [8425]~P105(x84251)+P16(x84251,x84252)+~P1(f328(f328(f242(x84251),f328(f328(f162(x84251),x84252),f752(x84252,x84251))),f328(f328(f162(x84251),x84252),f757(x84252,x84251)))) % 154.70/154.56 [8581]~P59(x85811)+P1(f328(f57(f879(x85811)),x85812))+~P1(f328(f57(x85811),f328(f328(f8(f879(x85811),a870,x85811),x85812),f235(x85811)))) % 154.70/154.56 [9749]~P59(x97491)+~P59(x97492)+E(f328(f328(f151(f876(x97491),f882(x97492,x97491)),f328(f328(f8(f882(x97492,f879(x97491)),f882(x97492,x97491),f876(x97491)),f73(f879(x97491),x97491,x97492,f239(x97491))),f328(f328(f8(f876(f881(x97492,x97491)),f882(x97492,f879(x97491)),f876(x97491)),f176(x97492,x97491)),f328(f180(x97492,x97491),f55(x97492))))),f54(x97491,f328(f193(f876(x97492)),f55(x97492)),f55(x97491))),f55(f882(x97492,x97491))) % 154.70/154.56 [5666]E(x56661,f2(a1))+~E(f44(a1,x56662,x56661),f2(a1))+E(f328(f328(f38(a1),x56662),f328(f79(a1),x56661)),f328(f79(a1),f328(f328(f38(a1),x56662),x56661))) % 154.70/154.56 [5684]~P40(x56842)+~P40(x56841)+P40(f328(f328(f114(f882(a1,a870)),x56841),x56842)) % 154.70/154.56 [5685]~P40(x56852)+~P40(x56851)+P40(f328(f328(f105(f882(a1,a870)),x56851),x56852)) % 154.70/154.56 [5703]~P60(x57031)+~P90(x57031)+E(f328(f79(x57031),f328(f328(f286(x57031),f78(x57031)),x57032)),f328(f328(f286(x57031),f328(f107(x57031),a101)),x57032)) % 154.70/154.56 [5818]E(x58181,f2(a1))+~E(f44(a1,x58182,x58181),f2(a1))+E(f328(f328(f38(a1),f328(f79(a1),x58182)),x58181),f328(f79(a1),f328(f328(f38(a1),x58182),x58181))) % 154.70/154.56 [5952]~P105(x59521)+P16(x59521,x59522)+P1(f328(f328(f243(a875),f746(x59522,x59521)),f328(f193(f876(x59521)),x59522))) % 154.70/154.56 [5953]~P105(x59531)+P16(x59531,x59532)+P1(f328(f328(f243(a875),f757(x59532,x59531)),f328(f193(f876(x59531)),x59532))) % 154.70/154.56 [6104]~P90(x61041)+~E(f328(f107(x61041),x61042),f2(x61041))+P32(x61041,f328(f107(x61041),f328(f328(f80(a1),x61042),f328(f79(a1),a83)))) % 154.70/154.56 [6105]~P90(x61051)+~E(f328(f107(x61051),x61052),f2(x61051))+P32(x61051,f328(f107(x61051),f328(f328(f80(a1),a83),f328(f79(a1),x61052)))) % 154.70/154.56 [6107]E(f328(a50,f46(f328(f79(a1),x61071),f328(f79(a1),x61072))),f45(x61071,x61072))+P1(f328(f328(f243(a1),f2(a1)),x61072))+P1(f328(f328(f242(a1),f2(a1)),x61071)) % 154.70/154.56 [6241]~E(x62412,f2(a875))+~E(x62411,f2(a875))+P1(f328(f328(f242(a1),f328(f104(a1),x62411)),f328(f79(a1),f328(f104(a1),x62412)))) % 154.70/154.56 [6269]E(f328(f328(f80(a875),f328(f107(a875),x62691)),f328(f107(a875),x62692)),f328(f107(a875),f328(f328(f80(a1),x62691),x62692)))+P1(f328(f328(f243(a1),x62691),a83))+P1(f328(f328(f243(a1),x62692),a83)) % 154.70/154.56 [6396]~P74(x63961)+~P1(f328(f328(f243(x63961),f2(x63961)),x63962))+P1(f328(f328(f243(x63961),f328(f79(x63961),x63962)),x63962)) % 154.70/154.56 [6397]~P74(x63971)+~P1(f328(f328(f242(x63971),f2(x63971)),x63972))+P1(f328(f328(f242(x63971),f328(f79(x63971),x63972)),x63972)) % 154.70/154.56 [6569]E(f328(f328(f22(a875),f328(a108,x65691)),f328(a108,x65692)),f328(a108,f328(f328(f22(a1),x65691),x65692)))+~P1(f328(f328(f242(a1),f2(a1)),x65692))+~P1(f328(f328(f242(a1),x65692),x65691)) % 154.70/154.56 [6602]E(f328(a108,f44(a1,f328(f107(a1),x66021),f328(f107(a1),x66022))),f44(a875,f328(f107(a875),x66021),f328(f107(a875),x66022)))+P1(f328(a197,f328(f107(a1),x66021)))+P1(f328(a197,f328(f107(a1),x66022))) % 154.70/154.56 [6620]~P74(x66201)+P1(f328(f328(f243(x66201),f2(x66201)),x66202))+~P1(f328(f328(f243(x66201),f328(f79(x66201),x66202)),x66202)) % 154.70/154.56 [6621]~P74(x66211)+P1(f328(f328(f242(x66211),f2(x66211)),x66212))+~P1(f328(f328(f242(x66211),f328(f79(x66211),x66212)),x66212)) % 154.70/154.56 [6633]~P74(x66331)+~P1(f328(f328(f243(x66331),f2(x66331)),x66332))+P1(f328(f328(f243(x66331),f2(x66331)),f328(f328(f80(x66331),x66332),x66332))) % 154.70/154.56 [6635]~P74(x66351)+~P1(f328(f328(f242(x66351),f2(x66351)),x66352))+P1(f328(f328(f242(x66351),f2(x66351)),f328(f328(f80(x66351),x66352),x66352))) % 154.70/154.56 [6647]E(f328(f328(f80(a875),f328(a108,x66471)),f328(a108,x66472)),f328(a108,f328(f328(f80(a1),x66471),x66472)))+~P1(f328(f328(f242(a1),f2(a1)),x66472))+~P1(f328(f328(f242(a1),f2(a1)),x66471)) % 154.70/154.56 [6659]E(x66591,f2(a875))+P1(f328(f328(f243(a875),f2(a875)),x66592))+~P1(f328(f328(f243(a875),f2(a875)),f328(f328(f253(a875),x66592),x66591))) % 154.70/154.56 [6689]~P90(x66891)+E(f328(f107(x66891),x66892),f2(x66891))+~P32(x66891,f328(f107(x66891),f328(f328(f80(a1),a83),f328(f79(a1),x66892)))) % 154.70/154.56 [6690]~P90(x66901)+E(f328(f107(x66901),x66902),f2(x66901))+~P32(x66901,f328(f107(x66901),f328(f328(f80(a1),x66902),f328(f79(a1),a83)))) % 154.70/154.56 [6749]~P1(f328(f61(x67491),x67492))+~P1(f328(f61(x67491),f251(f882(x67491,a870))))+P1(f328(f61(x67491),f328(f79(f882(x67491,a870)),x67492))) % 154.70/154.56 [6772]~P1(f328(f328(f243(a1),f2(a1)),x67722))+~P1(f328(f328(f242(a1),x67722),x67721))+P1(f328(f328(f243(a1),f2(a1)),f328(f328(f38(a1),x67721),x67722))) % 154.70/154.56 [6773]~P1(f328(f328(f243(a1),x67732),f2(a1)))+~P1(f328(f328(f242(a1),x67731),f2(a1)))+P1(f328(f328(f242(a1),f2(a1)),f328(f328(f38(a1),x67731),x67732))) % 154.70/154.56 [6812]~P1(f328(f328(f243(a875),f2(a875)),x68122))+~P1(f328(f328(f243(a875),f2(a875)),x68121))+P1(f328(f328(f243(a875),f2(a875)),f328(f328(f81(a875),x68121),x68122))) % 154.70/154.56 [6813]~P1(f328(f328(f242(a1),f2(a1)),x68132))+~P1(f328(f328(f242(a1),f2(a1)),x68131))+P1(f328(f328(f242(a1),f2(a1)),f328(f328(f80(a1),x68131),x68132))) % 154.70/154.56 [6814]~P1(f328(f328(f242(a1),f2(a1)),x68142))+~P1(f328(f328(f242(a1),f2(a1)),x68141))+P1(f328(f328(f242(a1),f2(a1)),f328(f328(f81(a1),x68141),x68142))) % 154.70/154.56 [6815]~P1(f328(f328(f243(a1),f2(a1)),x68152))+~P1(f328(f328(f242(a1),f2(a1)),x68151))+P1(f328(f328(f242(a1),f2(a1)),f328(f328(f38(a1),x68151),x68152))) % 154.70/154.56 [6816]~P1(f328(f328(f242(a1),f2(a1)),x68162))+~P1(f328(f328(f242(a1),f2(a1)),x68161))+P1(f328(f328(f242(a1),f2(a1)),f328(f328(f38(a1),x68161),x68162))) % 154.70/154.56 [6882]E(x68821,f2(a1))+E(f44(a1,x68822,x68821),f2(a1))+E(f328(f328(f22(a1),f328(f79(a1),f328(f328(f38(a1),x68822),x68821))),f78(a1)),f328(f328(f38(a1),f328(f79(a1),x68822)),x68821)) % 154.70/154.56 [6935]P1(f328(f328(f243(a875),f2(a875)),x69351))+P1(f328(f328(f243(a875),f2(a875)),x69352))+~P1(f328(f328(f243(a875),f2(a875)),f328(f328(f80(a875),x69352),x69351))) % 154.70/154.56 [6939]~P74(x69391)+P1(f328(f328(f243(x69391),f2(x69391)),x69392))+~P1(f328(f328(f243(x69391),f2(x69391)),f328(f328(f80(x69391),x69392),x69392))) % 154.70/154.56 [6940]~P74(x69401)+P1(f328(f328(f242(x69401),f2(x69401)),x69402))+~P1(f328(f328(f242(x69401),f2(x69401)),f328(f328(f80(x69401),x69402),x69402))) % 154.70/154.56 [6993]~P1(f328(f61(x69931),x69932))+P1(f328(f61(x69931),f251(f882(x69931,a870))))+~P1(f328(f61(x69931),f328(f79(f882(x69931,a870)),x69932))) % 154.70/154.56 [7056]P1(f328(f328(f242(a1),x70561),f2(a1)))+~P1(f328(f328(f243(a1),x70562),f2(a1)))+~P1(f328(f328(f242(a1),f2(a1)),f328(f328(f38(a1),x70561),x70562))) % 154.70/154.56 [7062]~P1(f328(f328(f243(a1),f2(a1)),x70621))+P1(f328(f328(f242(a1),x70621),x70622))+~P1(f328(f328(f243(a1),f2(a1)),f328(f328(f38(a1),x70622),x70621))) % 154.70/154.56 [7063]~P1(f328(f328(f242(a1),f2(a1)),x70632))+P1(f328(f328(f242(a1),x70631),x70632))+~P1(f328(f328(f243(a1),f2(a1)),f328(f328(f38(a1),x70632),x70631))) % 154.70/154.56 [7092]P1(f328(f328(f243(a1),f2(a1)),x70921))+~P1(f328(f328(f242(a1),f2(a1)),x70922))+~P1(f328(f328(f243(a1),f2(a1)),f328(f328(f38(a1),x70922),x70921))) % 154.70/154.56 [7093]P1(f328(f328(f242(a1),f2(a1)),x70931))+~P1(f328(f328(f243(a1),f2(a1)),x70932))+~P1(f328(f328(f242(a1),f2(a1)),f328(f328(f38(a1),x70931),x70932))) % 154.70/154.56 [7540]~P1(f328(f61(x75402),f251(f882(x75402,a870))))+~P1(f328(f61(x75401),f251(f882(x75401,a870))))+P1(f328(f61(f880(x75401,x75402)),f251(f882(f880(x75401,x75402),a870)))) % 154.70/154.56 [7541]~P1(f328(f61(x75412),f251(f882(x75412,a870))))+~P1(f328(f61(x75411),f251(f882(x75411,a870))))+P1(f328(f61(f881(x75411,x75412)),f251(f882(f881(x75411,x75412),a870)))) % 154.70/154.56 [7612]~P1(f328(f328(f243(a875),f328(a116,f2(a875))),x76121))+~P1(f328(f328(f243(a875),f328(a116,f2(a875))),x76122))+P1(f328(f328(f243(a875),x76121),f328(f328(f81(a875),x76122),x76121))) % 154.70/154.56 [7613]~P1(f328(f328(f243(a875),f328(a116,f2(a875))),x76131))+~P1(f328(f328(f243(a875),f328(a116,f2(a875))),x76132))+P1(f328(f328(f243(a875),x76131),f328(f328(f81(a875),x76131),x76132))) % 154.70/154.56 [7647]E(f328(f37(x76471),f251(f882(x76471,a870))),f328(a116,f2(a875)))+P1(f328(f61(x76472),f251(f882(x76472,a870))))+~P1(f328(f61(f882(x76472,x76471)),f251(f882(f882(x76472,x76471),a870)))) % 154.70/154.56 [7777]~P1(f328(f328(f243(a875),f328(a116,f2(a875))),x77772))+~P1(f328(f328(f243(a875),f328(a116,f2(a875))),x77771))+P1(f328(f328(f243(a875),f328(a116,f2(a875))),f328(f328(f81(a875),x77771),x77772))) % 154.70/154.56 [7778]~P1(f328(f328(f242(a875),f328(a116,f2(a875))),x77781))+~P1(f328(f328(f242(a875),f328(a116,f2(a875))),x77782))+P1(f328(f328(f242(a875),f328(a116,f2(a875))),f328(f328(f81(a875),x77781),x77782))) % 154.70/154.56 [8469]E(x84691,f117(x84692))+~P1(f328(f134(x84692),x84691))+E(f175(x84692,f328(f328(f8(a870,a870,x84692),a323),f328(f328(f7(x84692,x84692,a870),a325),f141(x84692,x84691))),x84691),f118(x84692,x84691)) % 154.70/154.56 [8572]~P40(x85722)+~P40(x85721)+E(f328(f307(a875,a1,f104(a1)),f328(f328(f114(f882(a875,a870)),f328(f307(a1,a875,a108),x85721)),f328(f307(a1,a875,a108),x85722))),f328(f328(f114(f882(a1,a870)),x85721),x85722)) % 154.70/154.56 [8573]~P40(x85732)+~P40(x85731)+E(f328(f307(a875,a1,f104(a1)),f328(f328(f105(f882(a875,a870)),f328(f307(a1,a875,a108),x85731)),f328(f307(a1,a875,a108),x85732))),f328(f328(f105(f882(a1,a870)),x85731),x85732)) % 154.70/154.56 [9230]~P90(x92301)+~E(f328(f107(x92301),x92302),f78(x92301))+P32(x92301,f328(f107(x92301),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f79(a1),x92302)))) % 154.70/154.56 [9463]~P90(x94631)+E(f328(f107(x94631),x94632),f78(x94631))+~P32(x94631,f328(f107(x94631),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f79(a1),x94632)))) % 154.70/154.56 [10195]E(x101951,f2(a1))+E(x101952,f2(a1))+E(f328(f268(a1,a1,a1,a1,f34(a1),f328(f81(a1),f82(a1,x101952))),f328(f328(f328(f100(f881(a1,a1)),f328(f328(a325,f82(a1,x101951)),f82(a1,x101952))),f52(x101951,x101952)),f328(f328(f267(a1,a1,f881(a1,a1)),f328(f328(f18(a1,f882(a1,f881(a1,a1)),f882(a1,f881(a1,a1))),f328(f328(f8(f882(a1,f882(f881(a1,a1),f881(a1,a1))),f882(f882(a1,f881(a1,a1)),f882(a1,f881(a1,a1))),a1),f18(a1,f881(a1,a1),f881(a1,a1))),f328(f328(f8(f881(a1,a1),f882(a1,f882(f881(a1,a1),f881(a1,a1))),a1),f328(f7(a1,f881(a1,a1),f882(f881(a1,a1),f881(a1,a1))),f328(f328(f8(a870,f882(f881(a1,a1),f882(f881(a1,a1),f881(a1,a1))),a1),f100(f881(a1,a1))),f328(f328(f7(a1,a1,a870),a325),f2(a1))))),f328(f328(f7(a1,a1,f881(a1,a1)),f328(f328(f8(a1,f882(a1,f881(a1,a1)),a1),f263(a1,a1)),f79(a1))),f2(a1))))),f328(f328(f7(a1,f882(a1,a1),f882(a1,f881(a1,a1))),f328(f328(f8(f882(a1,f881(a1,a1)),f882(f882(a1,a1),f882(a1,f881(a1,a1))),a1),f8(a1,f881(a1,a1),a1)),f328(f328(f8(a1,f882(a1,f881(a1,a1)),a1),f263(a1,a1)),f328(f328(f7(a1,a1,a1),f328(f328(f8(a1,f882(a1,a1),a1),f22(a1)),f79(a1))),f78(a1))))),f328(f22(a1),f328(f75(a1),x101952))))),f52(x101951,x101952)))),f45(x101951,x101952)) % 154.70/154.56 [10196]E(x101961,f2(a1))+E(x101962,f2(a1))+E(f328(f268(a1,a1,a1,a1,f34(a1),f328(f81(a1),f82(a1,x101962))),f328(f328(f328(f100(f881(a1,a1)),f328(f328(a327,f328(f328(a326,f328(f328(f243(a1),f2(a1)),x101962)),f328(f328(f242(a1),f2(a1)),x101961))),f328(f328(a326,f328(f328(f243(a1),x101962),f2(a1))),f328(f328(f243(a1),x101961),f2(a1))))),f52(x101961,x101962)),f328(f328(f267(a1,a1,f881(a1,a1)),f328(f328(f18(a1,f882(a1,f881(a1,a1)),f882(a1,f881(a1,a1))),f328(f328(f8(f882(a1,f882(f881(a1,a1),f881(a1,a1))),f882(f882(a1,f881(a1,a1)),f882(a1,f881(a1,a1))),a1),f18(a1,f881(a1,a1),f881(a1,a1))),f328(f328(f8(f881(a1,a1),f882(a1,f882(f881(a1,a1),f881(a1,a1))),a1),f328(f7(a1,f881(a1,a1),f882(f881(a1,a1),f881(a1,a1))),f328(f328(f8(a870,f882(f881(a1,a1),f882(f881(a1,a1),f881(a1,a1))),a1),f100(f881(a1,a1))),f328(f328(f7(a1,a1,a870),a325),f2(a1))))),f328(f328(f7(a1,a1,f881(a1,a1)),f328(f328(f8(a1,f882(a1,f881(a1,a1)),a1),f263(a1,a1)),f79(a1))),f2(a1))))),f328(f328(f7(a1,f882(a1,a1),f882(a1,f881(a1,a1))),f328(f328(f8(f882(a1,f881(a1,a1)),f882(f882(a1,a1),f882(a1,f881(a1,a1))),a1),f8(a1,f881(a1,a1),a1)),f328(f328(f8(a1,f882(a1,f881(a1,a1)),a1),f263(a1,a1)),f328(f328(f7(a1,a1,a1),f328(f328(f8(a1,f882(a1,a1),a1),f22(a1)),f79(a1))),f78(a1))))),f328(f22(a1),f328(f75(a1),x101962))))),f52(x101961,x101962)))),f45(x101961,x101962)) % 154.70/154.56 [10197]~P31(a5000)+P26(a872,x101971,f328(f328(f306(f874(a872)),f328(f328(f328(f92(a872),a325),x101972),f328(a198,x101972))),f192(f882(f874(a872),a870))))+~P26(a872,x101971,f328(f328(f306(f874(a872)),f328(f328(f328(f92(a872),f328(f328(f8(f882(a872,f882(a872,a870)),f882(a872,a870),a872),f328(f8(f882(a872,a870),a870,a872),f88(a872))),f328(f328(f8(f882(a872,a870),f882(a872,f882(a872,a870)),a872),f328(f7(a872,f882(a872,a870),f882(a872,a870)),f328(f328(f8(f882(a872,f882(a870,a870)),f882(f882(a872,a870),f882(a872,a870)),a872),f18(a872,a870,a870)),f328(f328(f8(f882(a872,a870),f882(a872,f882(a870,a870)),a872),f328(f8(a870,f882(a870,a870),a872),a331)),f328(a198,x101972))))),a325))),x101972),a325)),f192(f882(f874(a872),a870)))) % 154.70/154.56 [5692]~P121(x56921)+~P90(x56921)+E(f328(f75(x56921),f328(f328(f253(x56921),f328(f107(x56921),a101)),x56922)),f78(x56921)) % 154.70/154.56 [6181]~P135(x61811)+~P1(f328(f328(f243(a1),x61812),f2(a1)))+E(f328(f79(x61811),f328(f104(x61811),f328(a108,f328(f79(a1),x61812)))),f328(f106(x61811),x61812)) % 154.70/154.56 [6380]P1(f328(f328(f242(a103),x63801),f78(a103)))+E(f328(f328(f80(a103),f78(a103)),f276(x63801,f328(f328(f38(a103),x63802),x63801))),f276(x63801,x63802))+P1(f328(f328(f243(a103),x63802),x63801)) % 154.70/154.56 [6980]~P89(x69801)+~P1(f328(f328(f330(x69801),x69802),f113(x69801)))+~E(f328(f328(f80(x69801),f328(f328(f80(x69801),f78(x69801)),x69802)),x69802),f2(x69801)) % 154.70/154.56 [7094]~P1(f328(f328(f243(a1),x70941),f2(a1)))+~P1(f328(f328(f242(a1),x70942),f2(a1)))+E(f328(f262(a1,a1),f328(a50,f46(f328(f79(a1),x70941),f328(f79(a1),x70942)))),f328(f328(f38(a1),x70941),x70942)) % 154.70/154.56 [7111]~P1(f328(f328(f243(a1),x71111),f2(a1)))+~P1(f328(f328(f242(a1),x71112),f2(a1)))+E(f328(f266(a1,a1),f328(a50,f46(f328(f79(a1),x71111),f328(f79(a1),x71112)))),f44(a1,x71111,x71112)) % 154.70/154.56 [7117]~P1(f328(f328(f243(a1),x71172),f2(a1)))+E(f328(f262(a1,a1),f328(a50,f49(f328(f79(a1),x71171),f328(f79(a1),x71172)))),f328(f328(f38(a1),x71171),x71172))+~P1(f328(f328(f243(a1),f2(a1)),x71171)) % 154.70/154.56 [7135]~P1(f328(f328(f243(a1),x71352),f2(a1)))+E(f328(f266(a1,a1),f328(a50,f49(f328(f79(a1),x71351),f328(f79(a1),x71352)))),f44(a1,x71351,x71352))+~P1(f328(f328(f243(a1),f2(a1)),x71351)) % 154.70/154.56 [7190]E(f328(f328(f38(a1),f328(f328(f253(a1),x71901),x71902)),x71901),f328(f328(f253(a1),x71901),f328(f328(f22(a875),x71902),f328(a116,f2(a875)))))+~P1(f328(f328(f243(a875),f2(a875)),x71902))+~P1(f328(f328(f243(a1),f2(a1)),x71901)) % 154.70/154.56 [7283]~P1(f328(f328(f243(a875),f2(a875)),x72831))+~P1(f328(f328(f243(a875),f2(a875)),x72832))+P1(f328(f328(f243(a875),f328(f328(f22(a875),x72831),x72832)),x72831)) % 154.70/154.56 [7284]~P1(f328(f328(f243(a875),f2(a875)),x72841))+~P1(f328(f328(f243(a875),f78(a875)),x72842))+P1(f328(f328(f243(a875),f328(f328(f38(a875),x72841),x72842)),x72841)) % 154.70/154.56 [7285]~P1(f328(f328(f243(a1),f2(a1)),x72851))+~P1(f328(f328(f243(a1),f78(a1)),x72852))+P1(f328(f328(f243(a1),f328(f328(f38(a1),x72851),x72852)),x72851)) % 154.70/154.56 [7432]E(x74321,f2(a875))+~E(x74322,f2(a1))+~P1(f328(f328(f243(a1),f2(a1)),f328(f328(f253(a1),f328(f75(a1),x74322)),x74321))) % 154.70/154.56 [7857]~E(x78572,f117(f876(x78571)))+E(f328(f193(f876(f876(x78571))),f178(x78571,x78572)),f2(a875))+~P16(a875,f328(f166(a875),f328(f328(f151(f876(x78571),a875),f193(f876(x78571))),x78572))) % 154.70/154.56 [8103]P1(f328(x81031,x81032))+~P1(f328(x81031,f328(a110,f585(x81031,x81032))))+~P1(f328(f328(f330(f882(f881(a875,a875),a870)),x81032),a102)) % 154.70/154.56 [8122]E(x81221,f117(f876(x81222)))+E(f328(f193(f876(x81222)),f328(f328(f162(f876(x81222)),x81221),f2(a875))),f328(f193(f876(f876(x81222))),f178(x81222,x81221)))+~P16(a875,f328(f166(a875),f328(f328(f151(f876(x81222),a875),f193(f876(x81222))),x81221))) % 154.70/154.56 [8836]~P1(f328(f61(x88361),f328(f248(x88361),x88362)))+~P1(f328(f61(x88361),f251(f882(x88361,a870))))+P1(f328(f61(x88361),f328(f248(x88361),f328(f328(f8(a870,a870,x88361),a323),x88362)))) % 154.70/154.56 [8897]E(f328(f328(f263(a875,a875),f328(a116,f328(f328(f38(a875),f328(f328(f22(a875),x88971),x88972)),x88972))),f44(a875,f328(f328(f22(a875),x88971),x88972),x88972)),f85(f881(a875,a875),f47(x88971,x88972)))+~P1(f328(f328(f243(a875),f2(a875)),x88972))+~P1(f328(f328(f242(a875),x88972),x88971)) % 154.70/154.56 [9193]~P1(f328(f61(x91931),f328(f248(x91931),x91932)))+P1(f328(f61(x91931),f251(f882(x91931,a870))))+~P1(f328(f61(x91931),f328(f248(x91931),f328(f328(f8(a870,a870,x91931),a323),x91932)))) % 154.70/154.56 [9916]P28(x99161,x99162)+~P39(x99161,f328(f262(f882(f881(x99161,x99161),a870),f882(f881(x99161,x99161),a870)),x99162))+~P1(f328(f328(f242(f882(f881(x99161,x99161),a870)),f328(f328(f285(x99161,x99161,x99161),f328(f262(f882(f881(x99161,x99161),a870),f882(f881(x99161,x99161),a870)),x99162)),f328(f266(f882(f881(x99161,x99161),a870),f882(f881(x99161,x99161),a870)),x99162))),f328(f262(f882(f881(x99161,x99161),a870),f882(f881(x99161,x99161),a870)),x99162))) % 154.70/154.56 [7216]~P1(f328(f328(f243(a875),f2(a875)),x72162))+P1(f328(f328(f243(a875),x72161),x72162))+E(f328(a116,f328(f328(f38(a875),f328(f328(f22(a875),x72161),x72162)),x72162)),f328(f328(f38(a875),x72161),x72162)) % 154.70/154.56 [7353]~P1(f328(f328(f243(a875),f2(a875)),x73532))+~P1(f328(f328(f242(a875),x73532),x73531))+E(f328(a116,f328(f328(f38(a875),f328(f328(f22(a875),x73531),x73532)),x73532)),f328(f328(f38(a875),x73531),x73532)) % 154.70/154.56 [8341]~P90(x83411)+~P89(x83411)+~P32(x83411,f328(f107(x83411),f328(f328(f22(a1),f328(f328(f80(a1),x83412),x83412)),a101))) % 154.70/154.56 [9100]E(x91001,f2(a875))+E(f328(f328(f267(a875,a875,f881(a875,a875)),f328(f328(f8(a875,f882(a875,f881(a875,a875)),a875),f263(a875,a875)),a116)),f85(f881(a875,a875),f47(f328(f328(f22(a875),x91002),x91001),x91001))),f85(f881(a875,a875),f47(x91002,x91001)))+P1(f328(f328(f243(a875),x91002),x91001)) % 154.70/154.56 [9526]P1(f328(x95262,f657(x95262,x95261)))+P1(f328(x95261,f657(x95262,x95261)))+E(f328(f248(a1),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a326),f328(f242(a1),f2(a1)))),x95261)),f328(f248(a1),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a326),f328(f242(a1),f2(a1)))),x95262))) % 154.70/154.56 [9530]~P1(f328(x95302,f657(x95302,x95301)))+~P1(f328(x95301,f657(x95302,x95301)))+E(f328(f248(a1),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a326),f328(f242(a1),f2(a1)))),x95301)),f328(f248(a1),f328(f328(f18(a1,a870,a870),f328(f328(f8(a870,f882(a870,a870),a1),a326),f328(f242(a1),f2(a1)))),x95302))) % 154.70/154.56 [7568]~P61(x75681)+~P90(x75681)+E(f328(f328(f286(x75681),x75682),f328(f107(x75681),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))),x75682) % 154.70/154.56 [9229]~P90(x92291)+~E(f328(f107(x92291),x92292),f78(x92291))+P32(x92291,f328(f107(x92291),f328(f328(f80(a1),x92292),f328(f79(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 154.70/154.56 [9406]~P137(x94061)+~E(x94062,f2(x94061))+E(f328(f328(f253(x94061),x94062),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f2(x94061)) % 154.70/154.56 [9407]~P137(x94071)+~E(x94072,f78(x94071))+E(f328(f328(f253(x94071),x94072),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f78(x94071)) % 154.70/154.56 [9420]~P137(x94201)+~E(x94202,f328(f79(x94201),f78(x94201)))+E(f328(f328(f253(x94201),x94202),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f78(x94201)) % 154.70/154.56 [9464]~P90(x94641)+E(f328(f107(x94641),x94642),f78(x94641))+~P32(x94641,f328(f107(x94641),f328(f328(f80(a1),x94642),f328(f79(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 154.70/154.56 [9850]~P121(x98502)+E(x98501,f2(x98502))+P1(f328(f328(f243(x98502),f2(x98502)),f328(f328(f253(x98502),x98501),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))) % 154.70/154.56 [9915]~P121(x99152)+~E(x99151,f2(x99152))+~P1(f328(f328(f243(x99152),f2(x99152)),f328(f328(f253(x99152),x99151),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))) % 154.70/154.56 [9941]P1(f328(f328(f242(a1),x99411),f2(a1)))+P1(f328(f328(f243(a1),x99412),x99411))+E(f328(f43(x99411),f46(x99412,f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x99411))),f46(x99412,x99411)) % 154.70/154.56 [9942]~P1(f328(f328(f243(a1),f2(a1)),x99421))+P1(f328(f328(f243(a1),x99422),x99421))+E(f328(f43(x99421),f46(x99422,f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x99421))),f46(x99422,x99421)) % 154.70/154.56 [9943]P1(f328(f328(f242(a1),x99431),f2(a1)))+P1(f328(f328(f242(a1),f2(a1)),f328(f328(f80(a1),x99432),x99431)))+E(f328(f43(x99431),f49(x99432,f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x99431))),f49(x99432,x99431)) % 154.70/154.56 [9944]~P1(f328(f328(f243(a1),f2(a1)),x99441))+P1(f328(f328(f242(a1),f2(a1)),f328(f328(f80(a1),x99442),x99441)))+E(f328(f43(x99441),f49(x99442,f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x99441))),f49(x99442,x99441)) % 154.70/154.56 [9945]~P140(x99451)+~P1(f328(f328(f242(a1),f2(a1)),x99452))+E(f328(f104(x99451),f328(a108,f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x99452))),f328(f328(f80(x99451),f328(f104(x99451),f328(a108,x99452))),f328(f104(x99451),f328(a108,x99452)))) % 154.70/154.56 [5030]~P143(x50301,x50303,x50302)+~E(x50303,f2(a1))+P1(f328(x50301,x50302)) % 154.70/154.56 [5152]~P105(x51521)+~P16(x51521,x51523)+P16(x51521,f167(x51521,x51522,x51523)) % 154.70/154.56 [5153]~P105(x51531)+~P16(x51531,x51533)+P16(x51531,f175(x51531,x51532,x51533)) % 154.70/154.56 [4734]~P72(x47342)+~E(x47343,f328(f79(x47342),x47341))+E(x47341,f328(f79(x47342),x47343)) % 154.70/154.56 [4736]~P72(x47361)+~E(f328(f79(x47361),x47363),x47362)+E(f328(f79(x47361),x47362),x47363) % 154.70/154.56 [4810]~P105(x48103)+E(x48101,x48102)+~E(f328(f249(x48103),x48101),f328(f249(x48103),x48102)) % 154.70/154.56 [4811]~P101(x48113)+E(x48111,x48112)+~E(f328(f104(x48113),x48111),f328(f104(x48113),x48112)) % 154.70/154.56 [4812]~P105(x48123)+E(x48121,x48122)+~E(f328(f300(x48123),x48121),f328(f300(x48123),x48122)) % 154.70/154.56 [4813]~P105(x48133)+E(x48131,x48132)+~E(f328(f297(x48133),x48131),f328(f297(x48133),x48132)) % 154.70/154.56 [4814]~P105(x48143)+E(x48141,x48142)+~E(f328(f250(x48143),x48141),f328(f250(x48143),x48142)) % 154.70/154.56 [4815]~P72(x48153)+E(x48151,x48152)+~E(f328(f79(x48153),x48151),f328(f79(x48153),x48152)) % 154.70/154.56 [4816]~P93(x48163)+E(x48161,x48162)+~E(f328(f79(x48163),x48161),f328(f79(x48163),x48162)) % 154.70/154.56 [4817]~P89(x48173)+E(x48171,x48172)+~E(f328(f106(x48173),x48171),f328(f106(x48173),x48172)) % 154.70/154.56 [4916]~P59(x49161)+~P1(f328(x49162,x49163))+P1(f328(f57(x49161),x49162)) % 154.70/154.56 [4949]~P59(x49493)+P1(f328(x49491,x49492))+~P1(f328(f58(x49493),x49491)) % 154.70/154.56 [5049]~P144(x50491,x50492,x50493)+~E(x50492,f2(a1))+P1(f328(x50491,f2(a1))) % 154.70/154.56 [5087]~E(x50871,f2(a875))+E(f778(x50871,x50872,x50873),f192(f882(x50873,a870)))+~E(f328(f37(x50873),x50872),f328(a116,x50871)) % 154.70/154.56 [5241]~E(x52412,f2(a875))+E(f328(f262(a875,a875),x52411),f2(a875))+~P1(f328(f47(x52413,x52412),x52411)) % 154.70/154.56 [5287]P1(f328(x52871,x52872))+~E(x52873,f328(f104(a1),x52872))+~P1(f328(x52871,f328(a108,x52873))) % 154.70/154.56 [5757]~E(x57573,f2(a875))+~P1(f328(x57571,x57572))+P1(f328(x57571,f44(a875,x57572,x57573))) % 154.70/154.56 [5888]~P1(f328(a25,x58883))+~P1(f328(a25,x58882))+P1(f328(a25,f30(x58881,x58882,x58883))) % 154.70/154.56 [5920]~P59(x59203)+~P12(x59203,x59201,x59202)+P1(f328(x59201,f721(x59202,x59201,x59203))) % 154.70/154.56 [6161]~E(x61613,f2(a875))+P1(f328(x61611,x61612))+~P1(f328(x61611,f44(a875,x61612,x61613))) % 154.70/154.56 [6312]~P59(x63121)+P13(x63121,x63122,x63123)+~P1(f328(x63122,f722(x63123,x63122,x63121))) % 154.70/154.56 [6838]E(x68381,f2(a875))+~P1(f328(x68382,f512(x68381,x68383,x68382)))+P1(f328(x68382,f44(a875,x68383,x68381))) % 154.70/154.56 [6945]~P5(x69451)+~P1(f328(f328(f242(x69451),x69452),f343(x69453,x69452,x69451)))+P1(f328(f328(f242(x69451),x69452),f40(x69451,x69453))) % 154.70/154.56 [6947]~P1(f328(x69471,x69472))+~P1(f328(x69471,f512(x69473,x69472,x69471)))+P1(f328(x69471,f44(a875,x69472,x69473))) % 154.70/154.56 [7049]E(x70491,f117(x70492))+E(f328(f328(f148(x70492),f707(x70493,x70491,x70492)),f711(x70493,x70491,x70492)),x70491)+~P1(f328(f328(f330(f876(x70492)),x70491),f158(x70492,x70493))) % 154.70/154.56 [7080]~P135(x70801)+~P1(f328(f328(f330(x70801),x70802),f113(x70801)))+P1(f328(f328(f330(x70801),f328(f328(f253(x70801),x70802),x70803)),f113(x70801))) % 154.70/154.56 [7402]P39(x74021,x74022)+~P1(f328(f328(f330(x74021),x74023),f632(x74022,x74021)))+P1(f328(f328(f330(x74021),f653(x74022,x74021,x74023)),f632(x74022,x74021))) % 154.70/154.56 [7674]E(x76741,f117(x76742))+~P1(f328(f328(f330(f876(x76742)),x76741),f158(x76742,x76743)))+P1(f328(f328(f330(f876(x76742)),f711(x76743,x76741,x76742)),f158(x76742,x76743))) % 154.70/154.56 [7727]E(x77271,f2(a875))+E(f328(f328(f80(a875),f328(f328(f81(a875),x77271),f513(x77271,x77272,x77273))),f512(x77271,x77272,x77273)),x77272)+P1(f328(x77273,f44(a875,x77272,x77271))) % 154.70/154.56 [7772]~P1(f328(x77723,x77722))+E(f328(f328(f80(a875),f328(f328(f81(a875),x77721),f513(x77721,x77722,x77723))),f512(x77721,x77722,x77723)),x77722)+P1(f328(x77723,f44(a875,x77722,x77721))) % 154.70/154.56 [7913]P1(f328(f328(f243(a1),x79131),f503(x79132,x79133,x79131)))+P1(f328(f328(x79133,f328(f328(f38(a1),x79132),x79131)),f44(a1,x79132,x79131)))+~P1(f328(f328(f243(a1),x79131),f2(a1))) % 154.70/154.56 [8187]P1(f328(f328(x81872,f328(f328(f38(a1),x81871),x81873)),f44(a1,x81871,x81873)))+~P1(f328(f328(f243(a1),x81873),f2(a1)))+P1(f328(f328(f242(a1),f503(x81871,x81872,x81873)),f2(a1))) % 154.70/154.56 [8374]E(f328(f328(f80(a1),f328(f328(f81(a1),x83741),f507(x83742,x83743,x83741))),f503(x83742,x83743,x83741)),x83742)+P1(f328(f328(x83743,f328(f328(f38(a1),x83742),x83741)),f44(a1,x83742,x83741)))+~P1(f328(f328(f243(a1),x83741),f2(a1))) % 154.70/154.56 [8618]~P1(f328(f328(x86181,f507(x86182,x86181,x86183)),f503(x86182,x86181,x86183)))+P1(f328(f328(x86181,f328(f328(f38(a1),x86182),x86183)),f44(a1,x86182,x86183)))+~P1(f328(f328(f243(a1),x86183),f2(a1))) % 154.70/154.56 [8846]~P105(x88461)+~P16(x88461,x88463)+P16(x88461,f146(x88461,x88461,f5(x88461),x88462,x88463)) % 154.70/154.56 [9355]~P114(x93552)+E(x93551,f2(x93552))+~P1(f328(f328(f242(x93552),f328(f328(f80(x93552),f328(f328(f81(x93552),x93553),x93553)),f328(f328(f81(x93552),x93551),x93551))),f2(x93552))) % 154.70/154.56 [9356]~P114(x93562)+E(x93561,f2(x93562))+~P1(f328(f328(f242(x93562),f328(f328(f80(x93562),f328(f328(f81(x93562),x93561),x93561)),f328(f328(f81(x93562),x93563),x93563))),f2(x93562))) % 154.70/154.56 [10132]~P121(x101321)+~P1(f328(f328(f243(x101321),x101322),f2(x101321)))+P1(f328(f328(f243(x101321),f328(f328(f253(x101321),x101322),f328(a116,f328(f328(f81(a875),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x101323)))),f2(x101321))) % 154.70/154.56 [10140]~P121(x101402)+E(x101401,f2(x101402))+~P1(f328(f328(f242(x101402),f328(f328(f80(x101402),f328(f328(f253(x101402),x101403),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x101402),x101401),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))),f2(x101402))) % 154.70/154.56 [10141]~P121(x101412)+E(x101411,f2(x101412))+~P1(f328(f328(f242(x101412),f328(f328(f80(x101412),f328(f328(f253(x101412),x101411),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x101412),x101413),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))),f2(x101412))) % 154.70/154.56 [4766]~E(x47662,x47663)+~P65(x47661)+E(f328(f328(f22(x47661),x47662),x47663),f2(x47661)) % 154.70/154.56 [4767]~E(x47672,x47673)+~P72(x47671)+E(f328(f328(f22(x47671),x47672),x47673),f2(x47671)) % 154.70/154.56 [4780]~P141(x47801)+~E(x47803,f2(x47801))+E(f328(f328(f80(x47801),x47802),x47803),x47802) % 154.70/154.56 [4797]~P136(x47971)+~E(x47973,f2(x47971))+E(f328(f328(f81(x47971),x47972),x47973),f2(x47971)) % 154.70/154.56 [4798]~P136(x47981)+~E(x47982,f2(x47981))+E(f328(f328(f81(x47981),x47982),x47983),f2(x47981)) % 154.70/154.56 [4819]~E(x48193,f117(x48191))+~E(x48192,f117(x48191))+E(f328(f328(f125(x48191),x48192),x48193),f117(x48191)) % 154.70/154.56 [4906]~P141(x49062)+E(x49061,f2(x49062))+~E(f328(f328(f80(x49062),x49063),x49061),x49063) % 154.70/154.56 [4907]~P72(x49071)+~E(x49072,f328(f79(x49071),x49073))+E(f328(f328(f80(x49071),x49072),x49073),f2(x49071)) % 154.70/154.56 [4914]E(x49141,f117(x49142))+E(x49143,f2(a875))+~E(f328(f328(f173(x49142),x49143),x49141),f117(x49142)) % 154.70/154.56 [4920]~P65(x49203)+E(x49201,x49202)+~E(f328(f328(f22(x49203),x49201),x49202),f2(x49203)) % 154.70/154.56 [4921]~P72(x49213)+E(x49211,x49212)+~E(f328(f328(f22(x49213),x49211),x49212),f2(x49213)) % 154.70/154.56 [4930]~P137(x49302)+E(x49301,f2(x49302))+~E(f328(f328(f253(x49302),x49301),x49303),f2(x49302)) % 154.70/154.56 [4931]~P3(x49312)+E(x49311,f192(x49312))+~E(f328(f328(f114(x49312),x49313),x49311),f192(x49312)) % 154.70/154.56 [4932]~P3(x49322)+E(x49321,f192(x49322))+~E(f328(f328(f114(x49322),x49321),x49323),f192(x49322)) % 154.70/154.56 [4933]~P97(x49332)+E(x49331,f251(x49332))+~E(f328(f328(f105(x49332),x49333),x49331),f251(x49332)) % 154.70/154.56 [4934]~P97(x49342)+E(x49341,f251(x49342))+~E(f328(f328(f105(x49342),x49341),x49343),f251(x49342)) % 154.70/154.56 [5000]~P72(x50002)+E(x50001,f328(f79(x50002),x50003))+~E(f328(f328(f80(x50002),x50001),x50003),f2(x50002)) % 154.70/154.56 [5001]~P72(x50011)+E(f328(f79(x50011),x50012),x50013)+~E(f328(f328(f80(x50011),x50012),x50013),f2(x50011)) % 154.70/154.56 [5003]~E(x50032,x50033)+~P106(x50031)+P1(f328(f328(f242(x50031),x50032),x50033)) % 154.70/154.56 [5005]~E(x50052,x50053)+~P107(x50051)+P1(f328(f328(f242(x50051),x50052),x50053)) % 154.70/154.56 [5006]~E(x50062,x50063)+~P92(x50061)+P1(f328(f328(f91(x50061),x50062),x50063)) % 154.70/154.56 [5103]~P116(x51031)+~E(x51032,f328(f79(x51031),x51033))+E(f328(f328(f81(x51031),x51032),x51032),f328(f328(f81(x51031),x51033),x51033)) % 154.70/154.56 [5111]~P105(x51111)+~P16(x51111,x51113)+P16(x51111,f328(f328(f173(x51111),x51112),x51113)) % 154.70/154.56 [5112]~P105(x51121)+~P16(x51121,x51123)+P16(x51121,f328(f328(f135(x51121),x51122),x51123)) % 154.70/154.56 [5150]E(x51501,x51502)+E(x51503,f2(a875))+~E(f328(f328(f81(a875),x51503),x51501),f328(f328(f81(a875),x51503),x51502)) % 154.70/154.56 [5151]E(x51511,x51512)+E(x51513,f2(a875))+~E(f328(f328(f81(a875),x51511),x51513),f328(f328(f81(a875),x51512),x51513)) % 154.70/154.56 [5232]~E(x52322,x52323)+~P107(x52321)+E(f299(x52321,x52322,x52323),f328(f328(f306(x52321),x52322),f192(f882(x52321,a870)))) % 154.70/154.56 [5274]E(x52741,x52742)+~P92(x52743)+~P1(f328(f328(f91(x52743),x52741),x52742)) % 154.70/154.56 [5285]~E(x52851,x52852)+~P105(x52853)+~P1(f328(f328(f243(x52853),x52851),x52852)) % 154.70/154.56 [5286]~E(x52861,x52862)+~P107(x52863)+~P1(f328(f328(f243(x52863),x52861),x52862)) % 154.70/154.56 [5296]~P107(x52961)+E(f328(f298(x52961,x52962),x52963),f192(f882(x52961,a870)))+P1(f328(f328(f243(x52961),x52962),x52963)) % 154.70/154.56 [5342]~P107(x53421)+E(f301(x53421,x53422,x53423),f192(f882(x53421,a870)))+P1(f328(f328(f243(x53421),x53422),x53423)) % 154.70/154.56 [5343]~P107(x53431)+E(f299(x53431,x53432,x53433),f192(f882(x53431,a870)))+P1(f328(f328(f242(x53431),x53432),x53433)) % 154.70/154.56 [5344]~P107(x53441)+E(f192(f882(x53441,a870)),f301(x53441,x53442,x53443))+P1(f328(f328(f243(x53441),x53442),x53443)) % 154.70/154.56 [5345]~P107(x53451)+E(f192(f882(x53451,a870)),f299(x53451,x53452,x53453))+P1(f328(f328(f242(x53451),x53452),x53453)) % 154.70/154.56 [5353]~P99(x53531)+~E(f328(f328(f114(x53531),x53532),x53533),x53533)+P1(f328(f328(f242(x53531),x53532),x53533)) % 154.70/154.56 [5354]~P100(x53541)+~E(f328(f328(f105(x53541),x53542),x53543),x53542)+P1(f328(f328(f242(x53541),x53542),x53543)) % 154.70/154.56 [5355]~P105(x53551)+~E(f328(f328(f240(x53551),x53552),x53553),x53552)+P1(f328(f328(f242(x53551),x53552),x53553)) % 154.70/154.56 [5356]~P105(x53561)+~E(f328(f328(f241(x53561),x53562),x53563),x53563)+P1(f328(f328(f242(x53561),x53562),x53563)) % 154.70/154.56 [5376]~P105(x53761)+P16(x53761,x53762)+~P16(x53761,f328(f328(f148(x53761),x53763),x53762)) % 154.70/154.56 [5377]~P105(x53771)+P16(x53771,x53772)+~P16(x53771,f328(f328(f125(x53771),x53773),x53772)) % 154.70/154.56 [5378]~P105(x53781)+P16(x53781,x53782)+~P16(x53781,f328(f328(f125(x53781),x53782),x53783)) % 154.70/154.56 [5446]~P105(x54461)+P1(f328(f328(f242(x54461),x54463),x54462))+P1(f328(f328(f243(x54461),x54462),x54463)) % 154.70/154.56 [5448]~P105(x54481)+P1(f328(f328(f242(x54481),x54483),x54482))+P1(f328(f328(f242(x54481),x54482),x54483)) % 154.70/154.56 [5486]~P99(x54861)+E(f328(f328(f114(x54861),x54862),x54863),x54862)+~P1(f328(f328(f242(x54861),x54863),x54862)) % 154.70/154.56 [5488]~P99(x54881)+E(f328(f328(f114(x54881),x54882),x54883),x54883)+~P1(f328(f328(f242(x54881),x54882),x54883)) % 154.70/154.56 [5489]~P100(x54891)+E(f328(f328(f105(x54891),x54892),x54893),x54893)+~P1(f328(f328(f242(x54891),x54893),x54892)) % 154.70/154.56 [5491]~P100(x54911)+E(f328(f328(f105(x54911),x54912),x54913),x54912)+~P1(f328(f328(f242(x54911),x54912),x54913)) % 154.70/154.56 [5492]~P105(x54921)+E(f328(f328(f240(x54921),x54922),x54923),x54923)+~P1(f328(f328(f242(x54921),x54923),x54922)) % 154.70/154.56 [5494]~P105(x54941)+E(f328(f328(f240(x54941),x54942),x54943),x54942)+~P1(f328(f328(f242(x54941),x54942),x54943)) % 154.70/154.56 [5495]~P105(x54951)+E(f328(f328(f241(x54951),x54952),x54953),x54952)+~P1(f328(f328(f242(x54951),x54953),x54952)) % 154.70/154.56 [5497]~P105(x54971)+E(f328(f328(f241(x54971),x54972),x54973),x54973)+~P1(f328(f328(f242(x54971),x54972),x54973)) % 154.70/154.56 [5504]~P117(x55042)+E(x55041,f2(x55042))+E(f328(f328(f286(x55042),f328(f79(x55042),x55043)),f328(f79(x55042),x55041)),f328(f328(f286(x55042),x55043),x55041)) % 154.70/154.56 [5549]~P107(x55491)+E(f328(f298(x55491,x55492),x55493),f192(f882(x55491,a870)))+~P1(f328(f328(f242(x55491),x55493),x55492)) % 154.70/154.56 [5581]~P107(x55811)+E(f302(x55811,x55812,x55813),f192(f882(x55811,a870)))+~P1(f328(f328(f242(x55811),x55813),x55812)) % 154.70/154.56 [5582]~P107(x55821)+E(f301(x55821,x55822,x55823),f192(f882(x55821,a870)))+~P1(f328(f328(f242(x55821),x55823),x55822)) % 154.70/154.56 [5583]~P107(x55831)+E(f299(x55831,x55832,x55833),f192(f882(x55831,a870)))+~P1(f328(f328(f243(x55831),x55833),x55832)) % 154.70/154.56 [5634]~E(f328(f328(f22(a875),x56341),x56343),x56342)+E(x56341,f328(f328(f80(a875),x56342),x56343))+~P1(f328(f328(f242(a875),x56343),x56341)) % 154.70/154.56 [5635]~E(x56351,f328(f328(f80(a875),x56353),x56352))+E(f328(f328(f22(a875),x56351),x56352),x56353)+~P1(f328(f328(f242(a875),x56352),x56351)) % 154.70/154.56 [5681]~P1(f328(x56811,x56813))+P1(f328(x56811,f368(x56811,x56812)))+~P1(f328(f328(f243(a875),x56813),x56812)) % 154.70/154.56 [5682]~P1(f328(x56821,x56823))+P1(f328(x56821,f373(x56821,x56822)))+~P1(f328(f328(f242(a875),x56823),x56822)) % 154.70/154.56 [5690]~P107(x56901)+~E(f328(f298(x56901,x56902),x56903),f192(f882(x56901,a870)))+~P1(f328(f328(f243(x56901),x56902),x56903)) % 154.70/154.56 [5695]~P106(x56951)+~P1(f328(f328(f243(x56951),x56952),x56953))+P1(f328(f328(f242(x56951),x56952),x56953)) % 154.70/154.56 [5697]~P107(x56971)+~P1(f328(f328(f243(x56971),x56972),x56973))+P1(f328(f328(f242(x56971),x56972),x56973)) % 154.70/154.56 [5805]~P107(x58051)+~E(f301(x58051,x58052,x58053),f192(f882(x58051,a870)))+~P1(f328(f328(f243(x58051),x58052),x58053)) % 154.70/154.56 [5806]~P107(x58061)+~E(f299(x58061,x58062,x58063),f192(f882(x58061,a870)))+~P1(f328(f328(f242(x58061),x58062),x58063)) % 154.70/154.56 [5807]~P107(x58071)+~E(f192(f882(x58071,a870)),f301(x58071,x58072,x58073))+~P1(f328(f328(f243(x58071),x58072),x58073)) % 154.70/154.56 [5808]~P107(x58081)+~E(f192(f882(x58081,a870)),f299(x58081,x58082,x58083))+~P1(f328(f328(f242(x58081),x58082),x58083)) % 154.70/154.56 [5816]P1(f328(x58161,x58162))+~P1(f328(x58161,f369(x58161,x58163)))+~P1(f328(f328(f243(a875),x58162),x58163)) % 154.70/154.56 [5817]P1(f328(x58171,x58172))+~P1(f328(x58171,f374(x58171,x58173)))+~P1(f328(f328(f242(a875),x58172),x58173)) % 154.70/154.56 [5825]~E(x58251,f328(a116,x58253))+P1(f328(f328(f243(a875),x58251),f328(a116,x58252)))+~P1(f328(f328(f243(a875),x58253),x58252)) % 154.70/154.56 [5841]E(x58411,x58412)+~E(f328(f328(f81(a875),x58413),x58411),f328(f328(f81(a875),x58413),x58412))+~P1(f328(f328(f243(a875),f2(a875)),x58413)) % 154.70/154.56 [5899]E(f328(x58991,f809(x58991,x58992,x58993)),f78(a875))+~E(f328(f328(f6(x58993,a875),x58991),x58992),f78(a875))+~P1(f328(f61(x58993),x58992)) % 154.70/154.56 [5911]~P5(x59111)+P1(f328(f328(f242(x59111),x59112),f39(x59111,x59113)))+~P1(f328(f328(f330(x59111),x59112),x59113)) % 154.70/154.56 [5937]~P105(x59371)+~P1(f328(f328(f243(x59371),x59373),x59372))+~P1(f328(f328(f243(x59371),x59372),x59373)) % 154.70/154.56 [5940]~P105(x59401)+~P1(f328(f328(f242(x59401),x59403),x59402))+~P1(f328(f328(f243(x59401),x59402),x59403)) % 154.70/154.56 [5944]~P106(x59441)+~P1(f328(f328(f243(x59441),x59443),x59442))+~P1(f328(f328(f243(x59441),x59442),x59443)) % 154.70/154.56 [5945]~P106(x59451)+~P1(f328(f328(f242(x59451),x59453),x59452))+~P1(f328(f328(f243(x59451),x59452),x59453)) % 154.70/154.56 [5946]~P107(x59461)+~P1(f328(f328(f243(x59461),x59463),x59462))+~P1(f328(f328(f243(x59461),x59462),x59463)) % 154.70/154.56 [5972]~E(f328(x59722,f811(x59722,x59723,x59721)),f2(a875))+E(f328(f328(f6(x59721,a875),x59722),x59723),f2(a875))+~P1(f328(f61(x59721),x59723)) % 154.70/154.56 [5973]~E(f328(x59732,f455(x59732,x59733,x59731)),f78(a875))+E(f328(f328(f9(x59731,a875),x59732),x59733),f78(a875))+~P1(f328(f61(x59731),x59733)) % 154.70/154.56 [5986]~P108(x59861)+~P1(f328(f328(f243(x59861),x59863),x59862))+P1(f328(f328(f330(x59861),x59862),f328(f300(x59861),x59863))) % 154.70/154.56 [5987]~P108(x59871)+~P1(f328(f328(f242(x59871),x59873),x59872))+P1(f328(f328(f330(x59871),x59872),f328(f250(x59871),x59873))) % 154.70/154.56 [5988]~P108(x59881)+~P1(f328(f328(f243(x59881),x59882),x59883))+P1(f328(f328(f330(x59881),x59882),f328(f249(x59881),x59883))) % 154.70/154.56 [5989]~P108(x59891)+~P1(f328(f328(f242(x59891),x59892),x59893))+P1(f328(f328(f330(x59891),x59892),f328(f297(x59891),x59893))) % 154.70/154.56 [6001]E(f328(x60011,f851(x60011,x60012,x60013)),f328(a116,f2(a875)))+~E(f328(f328(f6(x60013,a875),x60011),x60012),f328(a116,f2(a875)))+~P1(f328(f61(x60013),x60012)) % 154.70/154.56 [6084]~P5(x60841)+~P1(f328(f328(f330(x60841),x60843),x60842))+P1(f328(f328(f242(x60841),f40(x60841,x60842)),x60843)) % 154.70/154.56 [6101]~P1(f328(f328(f242(a875),x61011),x61013))+P1(f328(f328(f242(a875),x61011),x61012))+~P1(f328(f328(f242(a875),x61013),x61012)) % 154.70/154.56 [6102]~P1(f328(f328(f242(a1),x61021),x61023))+P1(f328(f328(f242(a1),x61021),x61022))+~P1(f328(f328(f242(a1),x61023),x61022)) % 154.70/154.56 [6119]~P108(x61191)+~P1(f328(f328(f330(x61191),x61193),f328(f300(x61191),x61192)))+P1(f328(f328(f243(x61191),x61192),x61193)) % 154.70/154.56 [6120]~P108(x61201)+~P1(f328(f328(f330(x61201),x61202),f328(f249(x61201),x61203)))+P1(f328(f328(f243(x61201),x61202),x61203)) % 154.70/154.56 [6121]~P108(x61211)+~P1(f328(f328(f330(x61211),x61213),f328(f250(x61211),x61212)))+P1(f328(f328(f242(x61211),x61212),x61213)) % 154.70/154.56 [6122]~P108(x61221)+~P1(f328(f328(f330(x61221),x61222),f328(f297(x61221),x61223)))+P1(f328(f328(f242(x61221),x61222),x61223)) % 154.70/154.56 [6247]P1(f328(x62471,x62472))+~P1(f328(x62471,f593(x62471)))+~P1(f328(f328(f330(x62473),x62472),f251(f882(x62473,a870)))) % 154.70/154.56 [6346]~P62(x63461)+P1(f328(f328(f243(x63461),f2(x63461)),f498(x63463,x63462,x63461)))+P1(f328(f328(f242(x63461),x63462),x63463)) % 154.70/154.56 [6413]~P81(x64131)+~P1(f328(f328(f243(x64131),x64133),f328(f79(x64131),x64132)))+P1(f328(f328(f243(x64131),x64132),f328(f79(x64131),x64133))) % 154.70/154.56 [6415]~P81(x64151)+~P1(f328(f328(f242(x64151),x64153),f328(f79(x64151),x64152)))+P1(f328(f328(f242(x64151),x64152),f328(f79(x64151),x64153))) % 154.70/154.56 [6427]~P1(f328(f328(f243(a875),x64271),x64273))+~P1(f328(f328(f243(a875),x64273),x64272))+P1(f328(f328(f243(a875),f328(a116,x64271)),x64272)) % 154.70/154.56 [6454]~P121(x64541)+P1(f328(f328(f243(x64541),f328(f106(x64541),x64542)),f328(f106(x64541),x64543)))+~P1(f328(f328(f243(a1),x64542),x64543)) % 154.70/154.56 [6455]~P123(x64551)+P1(f328(f328(f243(x64551),f328(f104(x64551),x64552)),f328(f104(x64551),x64553)))+~P1(f328(f328(f243(a875),x64552),x64553)) % 154.70/154.56 [6456]~P123(x64561)+P1(f328(f328(f242(x64561),f328(f104(x64561),x64562)),f328(f104(x64561),x64563)))+~P1(f328(f328(f242(a875),x64562),x64563)) % 154.70/154.56 [6457]~P121(x64571)+P1(f328(f328(f242(x64571),f328(f106(x64571),x64572)),f328(f106(x64571),x64573)))+~P1(f328(f328(f242(a1),x64572),x64573)) % 154.70/154.56 [6463]~P105(x64631)+E(f328(f328(f114(f882(x64631,a870)),f328(f249(x64631),x64632)),f328(f298(x64631,x64632),x64633)),f328(f249(x64631),x64633))+~P1(f328(f328(f242(x64631),x64632),x64633)) % 154.70/154.56 [6492]~P81(x64921)+~P1(f328(f328(f243(x64921),x64923),x64922))+P1(f328(f328(f243(x64921),f328(f79(x64921),x64922)),f328(f79(x64921),x64923))) % 154.70/154.56 [6494]~P81(x64941)+~P1(f328(f328(f242(x64941),x64943),x64942))+P1(f328(f328(f242(x64941),f328(f79(x64941),x64942)),f328(f79(x64941),x64943))) % 154.70/154.56 [6496]~P93(x64961)+~P1(f328(f328(f242(x64961),x64963),x64962))+P1(f328(f328(f242(x64961),f328(f79(x64961),x64962)),f328(f79(x64961),x64963))) % 154.70/154.56 [6528]~P105(x65281)+E(f328(f328(f114(f882(x65281,a870)),f328(f249(x65281),x65282)),f299(x65281,x65282,x65283)),f328(f297(x65281),x65283))+~P1(f328(f328(f242(x65281),x65282),x65283)) % 154.70/154.56 [6529]~P105(x65291)+E(f328(f328(f114(f882(x65291,a870)),f328(f297(x65291),x65292)),f302(x65291,x65292,x65293)),f328(f249(x65291),x65293))+~P1(f328(f328(f243(x65291),x65292),x65293)) % 154.70/154.56 [6530]~P105(x65301)+E(f328(f328(f114(f882(x65301,a870)),f328(f297(x65301),x65302)),f301(x65301,x65302,x65303)),f328(f297(x65301),x65303))+~P1(f328(f328(f242(x65301),x65302),x65303)) % 154.70/154.56 [6564]~P105(x65641)+E(f328(f328(f114(f882(x65641,a870)),f328(f298(x65641,x65642),x65643)),f328(f250(x65641),x65643)),f328(f250(x65641),x65642))+~P1(f328(f328(f242(x65641),x65642),x65643)) % 154.70/154.56 [6720]~P105(x67201)+E(f328(f328(f114(f882(x67201,a870)),f302(x67201,x67202,x67203)),f328(f250(x67201),x67203)),f328(f300(x67201),x67202))+~P1(f328(f328(f243(x67201),x67202),x67203)) % 154.70/154.56 [6721]~P105(x67211)+E(f328(f328(f114(f882(x67211,a870)),f301(x67211,x67212,x67213)),f328(f300(x67211),x67213)),f328(f300(x67211),x67212))+~P1(f328(f328(f242(x67211),x67212),x67213)) % 154.70/154.56 [6722]~P105(x67221)+E(f328(f328(f114(f882(x67221,a870)),f299(x67221,x67222,x67223)),f328(f300(x67221),x67223)),f328(f250(x67221),x67222))+~P1(f328(f328(f242(x67221),x67222),x67223)) % 154.70/154.56 [6740]P1(f328(x67401,x67402))+~P1(f328(f328(f242(a875),x67402),x67403))+P1(f328(f328(f330(a875),f374(x67401,x67403)),f299(a875,f2(a875),x67403))) % 154.70/154.56 [6774]E(x67741,x67742)+~E(f328(f328(f162(x67743),x67741),f666(x67743,x67742,x67741)),f328(f328(f162(x67743),x67742),f666(x67743,x67742,x67741)))+~E(f328(f193(f876(x67743)),x67741),f328(f193(f876(x67743)),x67742)) % 154.70/154.56 [6779]~E(x67793,f328(f328(f38(a875),x67791),x67792))+~P1(f328(f328(f243(a875),f2(a875)),x67792))+P1(f328(f328(f243(a875),x67791),f328(f328(f81(a875),x67792),f328(a116,x67793)))) % 154.70/154.56 [6796]~P1(f328(x67961,x67963))+~P1(f328(f328(f242(a875),x67963),x67962))+P1(f328(f328(f330(a875),f373(x67961,x67962)),f299(a875,f2(a875),x67962))) % 154.70/154.56 [6835]~P1(f328(x68351,x68353))+P1(f328(x68351,f384(x68351,x68352)))+~P1(f328(f328(f330(a875),x68353),f299(a875,f2(a875),x68352))) % 154.70/154.56 [6855]~P123(x68553)+~P1(f328(f328(f243(x68553),f328(f104(x68553),x68551)),f328(f104(x68553),x68552)))+P1(f328(f328(f243(a875),x68551),x68552)) % 154.70/154.56 [6856]~P121(x68563)+~P1(f328(f328(f243(x68563),f328(f106(x68563),x68561)),f328(f106(x68563),x68562)))+P1(f328(f328(f243(a1),x68561),x68562)) % 154.70/154.56 [6857]~P123(x68573)+~P1(f328(f328(f242(x68573),f328(f104(x68573),x68571)),f328(f104(x68573),x68572)))+P1(f328(f328(f242(a875),x68571),x68572)) % 154.70/154.56 [6858]~P121(x68583)+~P1(f328(f328(f242(x68583),f328(f106(x68583),x68581)),f328(f106(x68583),x68582)))+P1(f328(f328(f242(a1),x68581),x68582)) % 154.70/154.56 [6876]~P123(x68761)+~P1(f328(f328(f243(x68761),f78(x68761)),x68762))+P1(f328(f328(f243(x68761),f78(x68761)),f328(f328(f253(x68761),x68762),f328(a116,x68763)))) % 154.70/154.56 [6878]~P81(x68781)+~P1(f328(f328(f243(x68781),f328(f79(x68781),x68783)),f328(f79(x68781),x68782)))+P1(f328(f328(f243(x68781),x68782),x68783)) % 154.70/154.56 [6879]~P81(x68791)+~P1(f328(f328(f242(x68791),f328(f79(x68791),x68793)),f328(f79(x68791),x68792)))+P1(f328(f328(f242(x68791),x68792),x68793)) % 154.70/154.56 [6880]~P93(x68801)+~P1(f328(f328(f242(x68801),f328(f79(x68801),x68803)),f328(f79(x68801),x68802)))+P1(f328(f328(f242(x68801),x68802),x68803)) % 154.70/154.56 [6904]P1(f328(x69041,x69042))+~P1(f328(x69041,f376(x69041,x69043)))+~P1(f328(f328(f330(a875),x69042),f299(a875,f2(a875),x69043))) % 154.70/154.56 [6923]~P62(x69231)+P1(f328(f328(f243(x69231),f498(x69233,x69232,x69231)),f78(x69231)))+P1(f328(f328(f242(x69231),x69232),x69233)) % 154.70/154.56 [6942]~E(f44(a875,x69423,x69422),f44(a875,x69421,x69422))+E(f328(f328(f80(a875),x69421),f328(f328(f81(a875),x69422),f516(x69421,x69422,x69423))),x69423)+~P1(f328(f328(f242(a875),x69421),x69423)) % 154.70/154.56 [6961]E(f328(x69611,f763(x69611,x69612,x69613)),f205(x69612))+~P1(f328(f61(x69613),f182(x69613,x69612,x69611)))+P1(f328(f61(x69613),f251(f882(x69613,a870)))) % 154.70/154.56 [7000]E(f328(f328(f6(x70001,a875),x70002),x70003),f2(a875))+~P1(f328(f61(x70001),x70003))+P1(f328(f328(f330(x70001),f811(x70002,x70003,x70001)),x70003)) % 154.70/154.56 [7001]E(f328(f328(f9(x70011,a875),x70012),x70013),f78(a875))+~P1(f328(f61(x70011),x70013))+P1(f328(f328(f330(x70011),f455(x70012,x70013,x70011)),x70013)) % 154.70/154.56 [7023]~P105(x70231)+~P1(f328(f328(f243(x70231),x70232),x70233))+P1(f328(f328(f243(f882(x70231,a870)),f328(f249(x70231),x70232)),f328(f249(x70231),x70233))) % 154.70/154.56 [7024]~P105(x70241)+~P1(f328(f328(f242(x70241),x70242),x70243))+P1(f328(f328(f242(f882(x70241,a870)),f328(f249(x70241),x70242)),f328(f249(x70241),x70243))) % 154.70/154.56 [7025]~P105(x70251)+~P1(f328(f328(f242(x70251),x70253),x70252))+P1(f328(f328(f242(f882(x70251,a870)),f328(f300(x70251),x70252)),f328(f300(x70251),x70253))) % 154.70/154.56 [7026]~P107(x70261)+~P1(f328(f328(f242(x70261),x70262),x70263))+P1(f328(f328(f242(f882(x70261,a870)),f328(f297(x70261),x70262)),f328(f297(x70261),x70263))) % 154.70/154.56 [7027]~P107(x70271)+~P1(f328(f328(f242(x70271),x70273),x70272))+P1(f328(f328(f242(f882(x70271,a870)),f328(f250(x70271),x70272)),f328(f250(x70271),x70273))) % 154.70/154.56 [7035]~P5(x70351)+P1(f328(f328(f242(x70351),x70352),f40(x70351,x70353)))+P1(f328(f328(f330(x70351),f343(x70353,x70352,x70351)),x70353)) % 154.70/154.56 [7041]~P81(x70411)+P1(f328(f328(f243(x70411),f328(f328(f22(x70411),x70412),x70413)),f2(x70411)))+~P1(f328(f328(f243(x70411),x70412),x70413)) % 154.70/154.56 [7042]~P81(x70421)+P1(f328(f328(f242(x70421),f328(f328(f22(x70421),x70422),x70423)),f2(x70421)))+~P1(f328(f328(f242(x70421),x70422),x70423)) % 154.70/154.56 [7084]P1(f328(x70841,x70842))+P1(f328(f328(f242(a875),f376(x70841,x70843)),x70843))+~P1(f328(f328(f330(a875),x70842),f299(a875,f2(a875),x70843))) % 154.70/154.56 [7124]~E(f328(f328(f6(x71241,a875),x71242),x71243),f78(a875))+~P1(f328(f61(x71241),x71243))+P1(f328(f328(f330(x71241),f809(x71242,x71243,x71241)),x71243)) % 154.70/154.56 [7125]~P1(f328(x71251,x71253))+P1(f328(f328(f242(a875),f384(x71251,x71252)),x71252))+~P1(f328(f328(f330(a875),x71253),f299(a875,f2(a875),x71252))) % 154.70/154.56 [7165]~P5(x71651)+P1(f328(f328(f330(x71651),f862(x71653,x71652,x71651)),x71652))+P1(f328(f328(f242(x71651),f39(x71651,x71652)),x71653)) % 154.70/154.56 [7198]~E(f328(f328(f6(x71981,a875),x71982),x71983),f328(a116,f2(a875)))+~P1(f328(f61(x71981),x71983))+P1(f328(f328(f330(x71981),f851(x71982,x71983,x71981)),x71983)) % 154.70/154.56 [7209]E(x72091,f2(a875))+P1(f328(x72092,f44(a875,x72093,x72091)))+P1(f328(f328(f243(a875),f512(x72091,x72093,x72092)),x72091)) % 154.70/154.56 [7314]~P1(f328(x73141,x73142))+P1(f328(x73141,f44(a875,x73142,x73143)))+P1(f328(f328(f243(a875),f512(x73143,x73142,x73141)),x73143)) % 154.70/154.56 [7436]E(x74361,f117(x74362))+~P1(f328(f328(f330(f876(x74362)),x74361),f158(x74362,x74363)))+P1(f328(f328(f330(x74362),f707(x74363,x74361,x74362)),x74363)) % 154.70/154.56 [7458]~P105(x74581)+E(f328(f328(f114(f882(x74581,a870)),f328(f328(f306(x74581),x74582),f192(f882(x74581,a870)))),f302(x74581,x74582,x74583)),f328(f298(x74581,x74582),x74583))+~P1(f328(f328(f243(x74581),x74582),x74583)) % 154.70/154.56 [7484]~P105(x74841)+E(f328(f328(f114(f882(x74841,a870)),f328(f328(f306(x74841),x74842),f192(f882(x74841,a870)))),f301(x74841,x74842,x74843)),f299(x74841,x74842,x74843))+~P1(f328(f328(f242(x74841),x74842),x74843)) % 154.70/154.56 [7592]~P105(x75921)+P1(f328(f328(f243(x75921),x75922),x75923))+~P1(f328(f328(f243(f882(x75921,a870)),f328(f249(x75921),x75922)),f328(f249(x75921),x75923))) % 154.70/154.56 [7593]~P105(x75931)+P1(f328(f328(f242(x75931),x75932),x75933))+~P1(f328(f328(f242(f882(x75931,a870)),f328(f300(x75931),x75933)),f328(f300(x75931),x75932))) % 154.70/154.56 [7594]~P107(x75941)+P1(f328(f328(f242(x75941),x75942),x75943))+~P1(f328(f328(f242(f882(x75941,a870)),f328(f250(x75941),x75943)),f328(f250(x75941),x75942))) % 154.70/154.56 [7595]~P105(x75951)+P1(f328(f328(f242(x75951),x75952),x75953))+~P1(f328(f328(f242(f882(x75951,a870)),f328(f249(x75951),x75952)),f328(f249(x75951),x75953))) % 154.70/154.56 [7596]~P107(x75961)+P1(f328(f328(f242(x75961),x75962),x75963))+~P1(f328(f328(f242(f882(x75961,a870)),f328(f297(x75961),x75962)),f328(f297(x75961),x75963))) % 154.70/154.56 [7619]~P81(x76191)+~P1(f328(f328(f243(x76191),f328(f328(f22(x76191),x76192),x76193)),f2(x76191)))+P1(f328(f328(f243(x76191),x76192),x76193)) % 154.70/154.56 [7620]~P81(x76201)+~P1(f328(f328(f242(x76201),f328(f328(f22(x76201),x76202),x76203)),f2(x76201)))+P1(f328(f328(f242(x76201),x76202),x76203)) % 154.70/154.56 [7779]E(x77791,f2(a875))+~E(f328(f139(a875,a875,f80(a875),x77792),x77793),f2(a875))+~P1(f328(f328(f330(a875),x77791),f328(f170(a875),x77793))) % 154.70/154.56 [7783]~P5(x77831)+~P1(f328(f328(f242(x77831),f862(x77833,x77832,x77831)),x77833))+P1(f328(f328(f242(x77831),f39(x77831,x77832)),x77833)) % 154.70/154.56 [7939]P1(f328(f328(f242(a1),f2(a1)),f504(x79391,x79392,x79393)))+P1(f328(f328(x79392,f328(f328(f38(a1),x79391),x79393)),f44(a1,x79391,x79393)))+~P1(f328(f328(f243(a1),f2(a1)),x79393)) % 154.70/154.56 [8025]E(x80251,x80252)+~E(f328(f193(f876(x80253)),x80251),f328(f193(f876(x80253)),x80252))+~P1(f328(f328(f267(x80253,x80253,a870),a325),f682(x80253,x80251,x80252))) % 154.70/154.56 [8094]~P39(x80942,x80943)+E(x80941,f192(f882(x80942,a870)))+~P1(f328(f328(f242(f882(x80942,a870)),x80941),f328(f282(x80942,x80942,x80943),x80941))) % 154.70/154.56 [8165]P41(x81651,x81652,x81653)+P1(f328(f328(f330(x81651),f591(x81653,x81652,x81651)),x81652))+P1(f328(f328(f330(f881(x81651,x81651)),f592(x81653,x81652,x81651)),x81653)) % 154.70/154.56 [8191]P1(f328(f328(x81912,f328(f328(f38(a1),x81911),x81913)),f44(a1,x81911,x81913)))+~P1(f328(f328(f243(a1),f2(a1)),x81913))+P1(f328(f328(f243(a1),f504(x81911,x81912,x81913)),x81913)) % 154.70/154.56 [8220]E(f328(f307(a875,a875,f328(f328(f7(a875,a875,a875),f22(a875)),x82201)),f328(f298(a875,x82202),x82203)),f192(f882(a875,a870)))+P1(f328(f328(f243(a875),x82201),x82203))+P1(f328(f328(f243(a875),x82202),x82203)) % 154.70/154.56 [8327]E(f328(f307(a875,a875,f328(f328(f7(a875,a875,a875),f22(a875)),x83271)),f328(f298(a875,x83272),x83273)),f328(f328(f306(a875),f2(a875)),f192(f882(a875,a870))))+P1(f328(f328(f243(a875),x83271),x83273))+~P1(f328(f328(f243(a875),x83272),x83273)) % 154.70/154.56 [8344]~P105(x83441)+E(f146(x83441,x83441,f5(x83441),x83442,x83443),x83443)+~P1(f328(f328(f330(x83441),x83442),f328(f170(x83441),x83443))) % 154.70/154.56 [8358]P27(x83581,x83581,x83582,x83583)+~P1(f328(f61(x83581),x83583))+~P1(f328(f328(f242(f882(x83581,a870)),x83583),f328(f307(x83581,x83581,x83582),x83583))) % 154.70/154.56 [8381]E(f328(f328(f80(a1),f328(f328(f81(a1),x83811),f505(x83812,x83813,x83811))),f504(x83812,x83813,x83811)),x83812)+P1(f328(f328(x83813,f328(f328(f38(a1),x83812),x83811)),f44(a1,x83812,x83811)))+~P1(f328(f328(f243(a1),f2(a1)),x83811)) % 154.70/154.56 [8624]~P1(f328(f328(x86241,f505(x86242,x86241,x86243)),f504(x86242,x86241,x86243)))+P1(f328(f328(x86241,f328(f328(f38(a1),x86242),x86243)),f44(a1,x86242,x86243)))+~P1(f328(f328(f243(a1),f2(a1)),x86243)) % 154.70/154.56 [9493]~P1(f328(f61(x94931),x94932))+~P1(f328(f328(f330(x94931),x94933),x94932))+P1(f328(f328(f243(a875),f328(f37(x94931),f328(f328(f22(f882(x94931,a870)),x94932),f328(f328(f306(x94931),x94933),f192(f882(x94931,a870)))))),f328(f37(x94931),x94932))) % 154.70/154.56 [10092]P41(x100921,x100922,x100923)+~P1(f328(f328(f267(x100921,x100921,a870),f328(f328(f7(x100921,f882(x100921,a870),f882(x100921,a870)),f328(f328(f8(f882(a870,a870),f882(f882(x100921,a870),f882(x100921,a870)),x100921),f8(a870,a870,x100921)),f328(f328(f8(a870,f882(a870,a870),x100921),a326),f328(f328(f7(x100921,f882(x100921,a870),a870),f330(x100921)),x100922)))),f328(f328(f7(x100921,f882(x100921,a870),a870),f330(x100921)),x100922))),f592(x100923,x100922,x100921)))+P1(f328(f328(f330(x100921),f591(x100923,x100922,x100921)),x100922)) % 154.70/154.56 [5465]~P117(x54652)+E(x54651,f2(x54652))+E(f328(f328(f286(x54652),x54653),f328(f79(x54652),x54651)),f328(f79(x54652),f328(f328(f286(x54652),x54653),x54651))) % 154.70/154.56 [5597]~E(x55973,f192(f882(x55971,a870)))+~E(x55972,f192(f882(x55971,a870)))+E(f328(f328(f114(f882(x55971,a870)),x55972),x55973),f192(f882(x55971,a870))) % 154.70/154.56 [5655]~E(x56553,f2(a875))+~P1(f328(x56551,f2(a875)))+P1(f328(x56551,f328(f328(f38(a875),x56552),x56553))) % 154.70/154.56 [5797]~P63(x57972)+E(x57971,f2(x57972))+E(f328(f328(f286(x57972),f328(f75(x57972),x57973)),f328(f75(x57972),x57971)),f328(f75(x57972),f328(f328(f286(x57972),x57973),x57971))) % 154.70/154.56 [5962]~P1(f328(f61(x59621),x59623))+E(f328(f37(x59621),f328(f328(f306(x59621),x59622),x59623)),f328(a116,f328(f37(x59621),x59623)))+P1(f328(f328(f330(x59621),x59622),x59623)) % 154.70/154.56 [6033]~E(x60332,f2(a875))+P1(f328(x60331,f2(a875)))+~P1(f328(x60331,f328(f328(f38(a875),x60333),x60332))) % 154.70/154.56 [6052]~P1(f328(f61(x60521),x60523))+E(f328(f37(x60521),f328(f328(f306(x60521),x60522),x60523)),f328(f37(x60521),x60523))+~P1(f328(f328(f330(x60521),x60522),x60523)) % 154.70/154.56 [6086]~P1(f328(f61(x60861),x60863))+E(f328(f37(x60861),f328(f328(f306(x60861),x60862),x60863)),f328(f328(f80(a875),f78(a875)),f328(f37(x60861),x60863)))+P1(f328(f328(f330(x60861),x60862),x60863)) % 154.70/154.56 [6209]E(f328(f328(f80(a875),x62091),f852(x62091,x62092,x62093)),x62092)+~P1(f328(x62093,f2(a875)))+P1(f328(x62093,f328(f328(f22(a875),x62092),x62091))) % 154.70/154.56 [6210]E(f328(f328(f80(a875),x62101),f857(x62101,x62102,x62103)),x62102)+~P1(f328(x62103,f2(a875)))+P1(f328(x62103,f328(f328(f22(a875),x62102),x62101))) % 154.70/154.56 [6257]~P5(x62571)+~P1(f328(f61(x62571),x62573))+E(f328(f328(f64(x62571,x62571,f114(x62571)),x62572),x62573),f328(f328(f114(x62571),x62572),f39(x62571,x62573))) % 154.70/154.56 [6258]~P5(x62581)+~P1(f328(f61(x62581),x62583))+E(f328(f328(f64(x62581,x62581,f105(x62581)),x62582),x62583),f328(f328(f105(x62581),x62582),f40(x62581,x62583))) % 154.70/154.56 [6264]~P90(x62641)+~E(f328(f107(x62641),x62642),f328(f107(x62641),x62643))+P32(x62641,f328(f107(x62641),f328(f328(f80(a1),x62642),f328(f79(a1),x62643)))) % 154.70/154.56 [6271]~P135(x62711)+E(f328(f328(f22(x62711),f328(f104(x62711),x62712)),f328(f104(x62711),x62713)),f328(f104(x62711),f328(f328(f22(a875),x62712),x62713)))+~P1(f328(f328(f242(a875),x62713),x62712)) % 154.70/154.56 [6356]E(f328(f328(f80(a875),x63561),f852(x63561,x63562,x63563)),x63562)+P1(f328(f328(f243(a875),x63562),x63561))+P1(f328(x63563,f328(f328(f22(a875),x63562),x63561))) % 154.70/154.56 [6357]E(f328(f328(f80(a875),x63571),f857(x63571,x63572,x63573)),x63572)+P1(f328(f328(f243(a875),x63572),x63571))+P1(f328(x63573,f328(f328(f22(a875),x63572),x63571))) % 154.70/154.56 [6372]~P121(x63721)+E(f328(f328(f81(x63721),f328(f75(x63721),x63722)),x63723),f328(f75(x63721),f328(f328(f81(x63721),x63722),x63723)))+~P1(f328(f328(f242(x63721),f2(x63721)),x63723)) % 154.70/154.56 [6373]~P62(x63731)+E(f328(f328(f286(x63731),f328(f75(x63731),x63732)),x63733),f328(f75(x63731),f328(f328(f286(x63731),x63732),x63733)))+~P1(f328(f328(f243(x63731),f2(x63731)),x63733)) % 154.70/154.56 [6381]~P2(x63811)+~P1(f328(f61(x63811),x63813))+E(f328(f328(f64(x63811,x63811,f114(x63811)),x63812),x63813),f10(x63811,f328(f328(f306(x63811),x63812),x63813))) % 154.70/154.56 [6382]~P2(x63821)+~P1(f328(f61(x63821),x63823))+E(f328(f328(f64(x63821,x63821,f105(x63821)),x63822),x63823),f11(x63821,f328(f328(f306(x63821),x63822),x63823))) % 154.70/154.56 [6383]~P105(x63831)+~P1(f328(f61(x63831),x63833))+E(f328(f328(f64(x63831,x63831,f240(x63831)),x63832),x63833),f14(x63831,f328(f328(f306(x63831),x63832),x63833))) % 154.70/154.56 [6384]~P105(x63841)+~P1(f328(f61(x63841),x63843))+E(f328(f328(f64(x63841,x63841,f241(x63841)),x63842),x63843),f15(x63841,f328(f328(f306(x63841),x63842),x63843))) % 154.70/154.56 [6429]E(x64291,f117(x64292))+~E(f178(x64292,x64293),f117(f876(x64292)))+~P1(f328(f328(f330(f876(x64292)),x64291),f328(f170(f876(x64292)),x64293))) % 154.70/154.56 [6471]~P1(f328(f134(x64711),x64713))+P1(f328(f328(f330(x64711),x64712),f328(f170(x64711),x64713)))+P1(f328(f134(x64711),f328(f328(f148(x64711),x64712),x64713))) % 154.70/154.56 [6482]~P94(x64821)+~P1(f328(f61(x64821),x64823))+E(f328(f63(x64821,f81(x64821)),f328(f328(f306(x64821),x64822),x64823)),f328(f328(f64(x64821,x64821,f81(x64821)),x64822),x64823)) % 154.70/154.56 [6504]~P105(x65041)+~P1(f328(f61(x65041),x65043))+E(f12(x65041,f241(x65041),f328(f328(f306(x65041),x65042),x65043)),f328(f328(f64(x65041,x65041,f241(x65041)),x65042),x65043)) % 154.70/154.56 [6505]~P105(x65051)+~P1(f328(f61(x65051),x65053))+E(f13(x65051,f240(x65051),f328(f328(f306(x65051),x65052),x65053)),f328(f328(f64(x65051,x65051,f240(x65051)),x65052),x65053)) % 154.70/154.56 [6507]P1(f328(x65071,f2(a875)))+~P1(f328(f328(f243(a875),x65072),x65073))+~P1(f328(x65071,f328(f328(f22(a875),x65072),x65073))) % 154.70/154.56 [6525]~P121(x65251)+P1(f328(f328(f243(x65251),x65252),x65253))+~P1(f328(f328(f243(x65251),f328(f75(x65251),x65252)),x65253)) % 154.70/154.56 [6527]~P83(x65271)+P1(f328(f328(f242(x65271),x65272),x65273))+~P1(f328(f328(f242(x65271),f328(f75(x65271),x65272)),x65273)) % 154.70/154.56 [6544]E(x65441,f117(x65442))+E(f328(f138(x65442),f328(f328(f135(x65442),x65443),x65441)),f328(f328(f162(x65442),x65441),x65443))+~P1(f328(f328(f243(a875),x65443),f328(f193(f876(x65442)),x65441))) % 154.70/154.56 [6595]~P1(f328(x65951,x65953))+P1(f328(x65951,f375(x65951,x65952)))+~P1(f328(f328(f330(a875),x65953),f328(f298(a875,f2(a875)),x65952))) % 154.70/154.56 [6617]P1(f328(x66171,x66172))+~P1(f328(f328(f243(a875),x66172),x66173))+P1(f328(f328(f330(a875),f369(x66171,x66173)),f328(f298(a875,f2(a875)),x66173))) % 154.70/154.56 [6634]~P123(x66341)+~P1(f328(f328(f243(x66341),f2(x66341)),x66342))+P1(f328(f328(f243(x66341),f2(x66341)),f328(f328(f253(x66341),x66342),x66343))) % 154.70/154.56 [6636]~P123(x66361)+~P1(f328(f328(f242(x66361),f2(x66361)),x66362))+P1(f328(f328(f242(x66361),f2(x66361)),f328(f328(f253(x66361),x66362),x66363))) % 154.70/154.56 [6637]~P123(x66371)+~P1(f328(f328(f242(x66371),f78(x66371)),x66372))+P1(f328(f328(f242(x66371),f78(x66371)),f328(f328(f253(x66371),x66372),x66373))) % 154.70/154.56 [6661]~P1(f328(x66611,x66613))+~P1(f328(f328(f243(a875),x66613),x66612))+P1(f328(f328(f330(a875),f368(x66611,x66612)),f328(f298(a875,f2(a875)),x66612))) % 154.70/154.56 [6668]P1(f328(f61(x66681),x66682))+~P1(f328(f61(x66681),x66683))+~P1(f328(f328(f242(f882(x66681,a870)),x66682),x66683)) % 154.70/154.56 [6676]P1(f328(x66761,x66762))+~P1(f328(x66761,f371(x66761,x66763)))+~P1(f328(f328(f330(a875),x66762),f328(f298(a875,f2(a875)),x66763))) % 154.70/154.56 [6687]E(x66871,f2(a875))+P1(f328(x66872,f467(x66871,x66873,x66872)))+~P1(f328(x66872,f328(f328(f38(a875),x66873),x66871))) % 154.70/154.56 [6695]~P114(x66952)+E(x66951,f2(x66952))+~E(f328(f328(f80(x66952),f328(f328(f81(x66952),x66953),x66953)),f328(f328(f81(x66952),x66951),x66951)),f2(x66952)) % 154.70/154.56 [6696]~P114(x66962)+E(x66961,f2(x66962))+~E(f328(f328(f80(x66962),f328(f328(f81(x66962),x66961),x66961)),f328(f328(f81(x66962),x66963),x66963)),f2(x66962)) % 154.70/154.56 [6741]E(x67411,f2(a875))+~P1(f328(x67412,f468(x67411,x67413,x67412)))+P1(f328(x67412,f328(f328(f38(a875),x67413),x67411))) % 154.70/154.56 [6746]~P105(x67461)+~P16(x67461,x67463)+P16(x67461,f328(f328(f145(x67461,x67461,f5(x67461)),x67462),x67463)) % 154.70/154.56 [6789]P1(f328(x67891,f467(x67892,x67893,x67891)))+P1(f328(x67891,f2(a875)))+~P1(f328(x67891,f328(f328(f38(a875),x67893),x67892))) % 154.70/154.56 [6795]~P90(x67951)+E(f328(f107(x67951),x67952),f328(f107(x67951),x67953))+~P32(x67951,f328(f107(x67951),f328(f328(f80(a1),x67952),f328(f79(a1),x67953)))) % 154.70/154.56 [6861]E(x68611,f2(a1))+E(x68612,f2(a1))+~P1(f328(f48(x68612,x68612),f328(f328(f263(a1,a1),x68613),x68611))) % 154.70/154.56 [6862]E(x68621,f78(a1))+E(x68622,f2(a1))+~P1(f328(f48(x68622,x68622),f328(f328(f263(a1,a1),x68621),x68623))) % 154.70/154.56 [6877]P1(f328(x68771,x68772))+P1(f328(f328(f243(a875),f371(x68771,x68773)),x68773))+~P1(f328(f328(f330(a875),x68772),f328(f298(a875,f2(a875)),x68773))) % 154.70/154.56 [6899]~P1(f328(x68991,f852(x68993,x68992,x68991)))+~P1(f328(x68991,f2(a875)))+P1(f328(x68991,f328(f328(f22(a875),x68992),x68993))) % 154.70/154.56 [6900]~P1(f328(x69001,f857(x69003,x69002,x69001)))+~P1(f328(x69001,f2(a875)))+P1(f328(x69001,f328(f328(f22(a875),x69002),x69003))) % 154.70/154.56 [6901]~P1(f328(x69011,f468(x69013,x69012,x69011)))+~P1(f328(x69011,f2(a875)))+P1(f328(x69011,f328(f328(f38(a875),x69012),x69013))) % 154.70/154.56 [6919]~P1(f328(x69191,x69193))+P1(f328(f328(f243(a875),f375(x69191,x69192)),x69192))+~P1(f328(f328(f330(a875),x69193),f328(f298(a875,f2(a875)),x69192))) % 154.70/154.56 [6920]E(f328(f328(f22(a875),f328(f328(f22(a875),x69201),x69202)),f328(f328(f22(a875),x69203),x69202)),f328(f328(f22(a875),x69201),x69203))+~P1(f328(f328(f242(a875),x69202),x69201))+~P1(f328(f328(f242(a875),x69202),x69203)) % 154.70/154.56 [6955]~P81(x69551)+~P1(f328(f328(f243(x69551),f328(f79(x69551),x69553)),x69552))+P1(f328(f328(f243(x69551),f328(f79(x69551),x69552)),x69553)) % 154.70/154.56 [6956]~P121(x69561)+~P1(f328(f328(f243(x69561),f328(f75(x69561),x69562)),x69563))+P1(f328(f328(f243(x69561),f328(f79(x69561),x69562)),x69563)) % 154.70/154.56 [6958]~P81(x69581)+~P1(f328(f328(f242(x69581),f328(f79(x69581),x69583)),x69582))+P1(f328(f328(f242(x69581),f328(f79(x69581),x69582)),x69583)) % 154.70/154.56 [6960]~P83(x69601)+~P1(f328(f328(f242(x69601),f328(f75(x69601),x69602)),x69603))+P1(f328(f328(f242(x69601),f328(f79(x69601),x69602)),x69603)) % 154.70/154.56 [6994]~P1(f328(x69943,f852(x69942,x69941,x69943)))+P1(f328(f328(f243(a875),x69941),x69942))+P1(f328(x69943,f328(f328(f22(a875),x69941),x69942))) % 154.70/154.56 [6995]~P1(f328(x69953,f857(x69952,x69951,x69953)))+P1(f328(f328(f243(a875),x69951),x69952))+P1(f328(x69953,f328(f328(f22(a875),x69951),x69952))) % 154.70/154.56 [7045]~E(f825(x70453,x70452,x70451),f826(x70453,x70452,x70451))+E(f328(f328(f105(f882(x70451,a870)),x70452),f39(f882(x70451,a870),x70453)),f192(f882(x70451,a870)))+P1(f328(f328(f330(f882(x70451,a870)),x70452),x70453)) % 154.70/154.56 [7054]~P1(f328(f61(x70541),x70543))+P1(f328(f61(x70541),f40(f882(x70541,a870),x70542)))+~P1(f328(f328(f330(f882(x70541,a870)),x70543),x70542)) % 154.70/154.56 [7113]~P105(x71131)+E(f328(f328(f114(f882(x71131,a870)),f328(f298(x71131,x71132),x71133)),f328(f328(f306(x71131),x71133),f192(f882(x71131,a870)))),f299(x71131,x71132,x71133))+~P1(f328(f328(f242(x71131),x71132),x71133)) % 154.70/154.56 [7114]E(x71141,f2(a875))+P1(f328(f328(f243(a875),f495(x71141,x71143,x71142)),x71141))+P1(f328(x71142,f328(f328(f38(a875),x71143),x71141))) % 154.70/154.56 [7149]E(x71491,x71492)+~P1(f328(f328(f242(f882(x71493,a870)),x71491),x71492))+P1(f328(f328(f243(f882(x71493,a870)),x71491),x71492)) % 154.70/154.56 [7162]E(x71621,x71622)+~E(f328(f193(f876(x71623)),x71621),f328(f193(f876(x71623)),x71622))+P1(f328(f328(f243(a875),f666(x71623,x71621,x71622)),f328(f193(f876(x71623)),x71622))) % 154.70/154.56 [7210]P8(x72101,x72102,x72103)+~E(f328(f261(x72101,x72101),x72103),x72102)+~E(f328(f328(f285(x72101,x72101,x72101),f328(f283(x72101,x72101),x72103)),x72103),x72103) % 154.70/154.56 [7282]~P1(f328(x72821,f2(a875)))+P1(f328(f328(f243(a875),f495(x72823,x72822,x72821)),x72823))+P1(f328(x72821,f328(f328(f38(a875),x72822),x72823))) % 154.70/154.56 [7291]~P105(x72911)+E(f328(f328(f114(f882(x72911,a870)),f302(x72911,x72912,x72913)),f328(f328(f306(x72911),x72913),f192(f882(x72911,a870)))),f301(x72911,x72912,x72913))+~P1(f328(f328(f243(x72911),x72912),x72913)) % 154.70/154.56 [7391]~P1(f328(f61(x73911),x73913))+P1(f328(f328(f243(a875),f328(f37(x73911),x73912)),f328(f37(x73911),x73913)))+~P1(f328(f328(f243(f882(x73911,a870)),x73912),x73913)) % 154.70/154.56 [7392]~P1(f328(f61(x73921),x73923))+P1(f328(f328(f242(a875),f328(f37(x73921),x73922)),f328(f37(x73921),x73923)))+~P1(f328(f328(f242(f882(x73921,a870)),x73922),x73923)) % 154.70/154.56 [7528]E(x75281,x75282)+~P1(f328(f328(f242(f882(x75283,a870)),x75282),x75281))+~P1(f328(f328(f242(f882(x75283,a870)),x75281),x75282)) % 154.70/154.56 [7531]~P105(x75311)+P16(x75311,x75312)+~P16(x75311,f328(f328(f145(x75311,x75311,f5(x75311)),x75313),x75312)) % 154.70/154.56 [7599]~P1(f328(f328(f243(a875),x75993),x75992))+~P1(f328(f328(f243(a875),x75993),x75991))+P1(f328(f328(f243(a875),f328(f328(f22(a875),x75991),x75992)),f328(f328(f22(a875),x75991),x75993))) % 154.70/154.56 [7600]~P1(f328(f328(f243(a875),x76001),x76003))+~P1(f328(f328(f242(a875),x76002),x76001))+P1(f328(f328(f243(a875),f328(f328(f22(a875),x76001),x76002)),f328(f328(f22(a875),x76003),x76002))) % 154.70/154.56 [7617]~P1(f328(f328(f243(a1),x76172),f2(a1)))+~P1(f328(f328(f242(a1),x76173),x76171))+P1(f328(f328(f242(a1),f328(f328(f38(a1),x76171),x76172)),f328(f328(f38(a1),x76173),x76172))) % 154.70/154.56 [7637]~P1(f328(f328(f243(a875),f2(a875)),x76372))+~P1(f328(f328(f243(a875),x76371),x76373))+P1(f328(f328(f243(a875),f328(f328(f81(a875),x76371),x76372)),f328(f328(f81(a875),x76373),x76372))) % 154.70/154.56 [7638]~P1(f328(f328(f243(a875),f2(a875)),x76381))+~P1(f328(f328(f243(a875),x76382),x76383))+P1(f328(f328(f243(a875),f328(f328(f81(a875),x76381),x76382)),f328(f328(f81(a875),x76381),x76383))) % 154.70/154.56 [7639]~P1(f328(f328(f243(a1),f2(a1)),x76391))+~P1(f328(f328(f243(a1),x76392),x76393))+P1(f328(f328(f243(a1),f328(f328(f81(a1),x76391),x76392)),f328(f328(f81(a1),x76391),x76393))) % 154.70/154.56 [7641]~P1(f328(f328(f243(a875),f2(a875)),x76413))+~P1(f328(f328(f242(a875),x76413),x76412))+P1(f328(f328(f242(a875),f328(f328(f38(a875),x76411),x76412)),f328(f328(f38(a875),x76411),x76413))) % 154.70/154.56 [7642]~P1(f328(f328(f243(a1),f2(a1)),x76422))+~P1(f328(f328(f242(a1),x76421),x76423))+P1(f328(f328(f242(a1),f328(f328(f38(a1),x76421),x76422)),f328(f328(f38(a1),x76423),x76422))) % 154.70/154.56 [7692]E(x76921,f2(a875))+E(f328(f328(f80(a875),f328(f328(f81(a875),x76921),f468(x76921,x76922,x76923))),f495(x76921,x76922,x76923)),x76922)+P1(f328(x76923,f328(f328(f38(a875),x76922),x76921))) % 154.70/154.56 [7750]E(f328(f328(f80(a875),f328(f328(f81(a875),x77501),f468(x77501,x77502,x77503))),f495(x77501,x77502,x77503)),x77502)+~P1(f328(x77503,f2(a875)))+P1(f328(x77503,f328(f328(f38(a875),x77502),x77501))) % 154.70/154.56 [7759]~P1(f328(x77593,x77592))+P1(f328(f328(f328(a198,x77591),x77592),f412(x77592,x77591,x77593)))+~P1(f328(f328(f328(a198,f32(x77593,x77591)),x77592),x77592)) % 154.70/154.56 [7770]~P1(f328(f61(x77701),x77703))+P1(f328(f328(f330(x77701),f471(x77702,x77703,x77701)),x77703))+P1(f328(f328(f243(a875),f2(a875)),f328(f328(f9(x77701,a875),x77702),x77703))) % 154.70/154.56 [7771]~P1(f328(f61(x77711),x77713))+P1(f328(f328(f330(x77711),f508(x77712,x77713,x77711)),x77713))+P1(f328(f328(f243(a875),f2(a875)),f328(f328(f9(x77711,a875),x77712),x77713))) % 154.70/154.56 [8058]E(x80581,f192(f882(x80582,a870)))+E(x80581,f328(f328(f306(x80582),x80583),f192(f882(x80582,a870))))+~P1(f328(f328(f242(f882(x80582,a870)),x80581),f328(f328(f306(x80582),x80583),f192(f882(x80582,a870))))) % 154.70/154.56 [8076]~P59(x80761)+P13(x80761,x80762,x80763)+P1(f328(f328(f330(f876(x80761)),f722(x80763,x80762,x80761)),f328(f170(f876(x80761)),f54(x80761,x80763,f55(x80761))))) % 154.70/154.56 [8096]~P1(f328(f328(f243(a875),f2(a875)),x80963))+P1(f328(f328(f243(a875),x80961),x80962))+~P1(f328(f328(f243(a875),f328(f328(f253(a875),x80963),x80961)),f328(f328(f253(a875),x80963),x80962))) % 154.70/154.56 [8098]~P1(f328(f328(f243(a875),f2(a875)),x80983))+P1(f328(f328(f242(a875),x80981),x80982))+~P1(f328(f328(f242(a875),f328(f328(f81(a875),x80983),x80981)),f328(f328(f81(a875),x80983),x80982))) % 154.70/154.56 [8099]~P1(f328(f328(f243(a875),f2(a875)),x80993))+P1(f328(f328(f242(a875),x80991),x80992))+~P1(f328(f328(f242(a875),f328(f328(f81(a875),x80991),x80993)),f328(f328(f81(a875),x80992),x80993))) % 154.70/154.56 [8125]~P59(x81251)+~P12(x81251,x81253,x81252)+P1(f328(f328(f330(f876(x81251)),f721(x81252,x81253,x81251)),f328(f170(f876(x81251)),f54(x81251,x81252,f55(x81251))))) % 154.70/154.56 [8143]~E(f328(f328(f105(f882(x81431,a870)),f826(x81433,x81432,x81431)),f825(x81433,x81432,x81431)),f192(f882(x81431,a870)))+E(f328(f328(f105(f882(x81431,a870)),x81432),f39(f882(x81431,a870),x81433)),f192(f882(x81431,a870)))+P1(f328(f328(f330(f882(x81431,a870)),x81432),x81433)) % 154.70/154.56 [8160]E(x81601,f117(x81602))+~E(f328(f139(f876(x81602),f876(x81602),f125(x81602),f117(x81602)),x81603),f117(x81602))+~P1(f328(f328(f330(f876(x81602)),x81601),f328(f170(f876(x81602)),x81603))) % 154.70/154.56 [8225]E(x82251,f192(f882(f882(x82252,a870),a870)))+P1(f328(f328(f330(f882(x82252,a870)),f441(x82253,x82251,x82252)),x82251))+P1(f328(f328(f242(f882(x82252,a870)),f40(f882(x82252,a870),x82251)),x82253)) % 154.70/154.56 [8233]~P66(x82331)+~P73(x82331)+E(f328(f328(f6(a1,x82331),f328(f328(f8(a875,x82331,a1),x82332),a108)),f328(f307(a875,a1,f104(a1)),x82333)),f328(f328(f6(a875,x82331),x82332),x82333)) % 154.70/154.56 [8234]~P66(x82341)+~P73(x82341)+E(f328(f328(f9(a1,x82341),f328(f328(f8(a875,x82341,a1),x82342),a108)),f328(f307(a875,a1,f104(a1)),x82343)),f328(f328(f9(a875,x82341),x82342),x82343)) % 154.70/154.56 [8274]~P1(f328(f61(x82741),x82743))+~P1(f328(f328(f243(a875),f2(a875)),f328(x82742,f471(x82742,x82743,x82741))))+P1(f328(f328(f243(a875),f2(a875)),f328(f328(f9(x82741,a875),x82742),x82743))) % 154.70/154.56 [8275]~P1(f328(f61(x82751),x82753))+~P1(f328(f328(f243(a875),f2(a875)),f328(x82752,f508(x82752,x82753,x82751))))+P1(f328(f328(f243(a875),f2(a875)),f328(f328(f9(x82751,a875),x82752),x82753))) % 154.70/154.56 [8305]~P1(f328(x83051,x83053))+P1(f328(f328(f328(a198,f32(x83051,x83052)),f412(x83053,x83052,x83051)),x83053))+~P1(f328(f328(f328(a198,f32(x83051,x83052)),x83053),x83053)) % 154.70/154.56 [8309]~P61(x83092)+E(x83091,f78(x83092))+E(f328(f328(f286(x83092),f328(f328(f22(x83092),f328(f328(f253(x83092),x83091),x83093)),f78(x83092))),f328(f328(f22(x83092),x83091),f78(x83092))),f328(f328(f6(a875,x83092),f328(f253(x83092),x83091)),f328(f298(a875,f2(a875)),x83093))) % 154.70/154.56 [8367]E(x83671,f2(a875))+~P1(f328(x83673,f328(f328(f38(a875),x83672),x83671)))+P1(f328(f328(f243(a875),x83672),f328(f328(f81(a875),x83671),f328(a116,f467(x83671,x83672,x83673))))) % 154.70/154.56 [8384]P1(f328(x83841,f2(a875)))+~P1(f328(x83841,f328(f328(f38(a875),x83842),x83843)))+P1(f328(f328(f243(a875),x83842),f328(f328(f81(a875),x83843),f328(a116,f467(x83843,x83842,x83841))))) % 154.70/154.56 [8426]E(x84261,f2(a875))+~P1(f328(x84263,f328(f328(f38(a875),x84262),x84261)))+P1(f328(f328(f242(a875),f328(f328(f81(a875),x84261),f467(x84261,x84262,x84263))),x84262)) % 154.70/154.56 [8460]P1(f328(x84601,f2(a875)))+~P1(f328(x84601,f328(f328(f38(a875),x84603),x84602)))+P1(f328(f328(f242(a875),f328(f328(f81(a875),x84602),f467(x84602,x84603,x84601))),x84603)) % 154.70/154.56 [8463]~P105(x84631)+E(f328(f328(f145(x84631,x84631,f5(x84631)),x84632),x84633),f146(x84631,x84631,f5(x84631),x84632,x84633))+P1(f328(f328(f330(x84631),x84632),f328(f170(x84631),x84633))) % 154.70/154.56 [8499]~E(f328(x84993,f601(x84992,x84993,x84991)),f328(x84993,f604(x84992,x84993,x84991)))+~P56(x84991,f328(x84993,f602(x84992,x84993,x84991)))+P56(x84991,f328(f328(f41(x84992,f882(x84991,f882(x84991,a870))),f251(f882(x84992,a870))),x84993)) % 154.70/154.56 [8510]E(x85101,f192(f882(f882(x85102,a870),a870)))+~P1(f328(f328(f242(f882(x85102,a870)),f441(x85103,x85101,x85102)),x85103))+P1(f328(f328(f242(f882(x85102,a870)),f40(f882(x85102,a870),x85101)),x85103)) % 154.70/154.56 [8575]~P63(x85751)+~P1(f328(f328(f243(x85751),x85752),x85753))+P1(f328(f328(f243(x85751),x85752),f328(f328(f286(x85751),f328(f328(f80(x85751),x85752),x85753)),f328(f328(f80(x85751),f78(x85751)),f78(x85751))))) % 154.70/154.56 [8630]~P1(f328(f328(x86301,f530(x86301,x86303,x86302)),f534(x86301,x86303,x86302)))+P1(f328(f328(x86301,x86302),x86303))+~P1(f328(f316(f881(a1,a1),a51),f328(f328(f263(a1,a1),x86302),x86303))) % 154.70/154.56 [8631]~P1(f328(f328(x86311,f536(x86311,x86313,x86312)),f537(x86311,x86313,x86312)))+P1(f328(f328(x86311,x86312),x86313))+~P1(f328(f316(f881(a1,a1),a56),f328(f328(f263(a1,a1),x86312),x86313))) % 154.70/154.56 [8632]~P1(f328(f328(x86321,f540(x86321,x86323,x86322)),f541(x86321,x86323,x86322)))+P1(f328(f328(x86321,x86322),x86323))+~P1(f328(f316(f881(a1,a1),a231),f328(f328(f263(a1,a1),x86322),x86323))) % 154.70/154.56 [8633]~P1(f328(f328(x86331,f542(x86331,x86333,x86332)),f543(x86331,x86333,x86332)))+P1(f328(f328(x86331,x86332),x86333))+~P1(f328(f316(f881(a875,a875),a226),f328(f328(f263(a875,a875),x86332),x86333))) % 154.70/154.56 [8634]~P1(f328(f328(x86341,f692(x86341,x86343,x86342)),f694(x86341,x86343,x86342)))+P1(f328(f328(x86341,x86342),x86343))+~P1(f328(f316(f881(a1,a1),a181),f328(f328(f263(a1,a1),x86342),x86343))) % 154.70/154.56 [8887]P1(f328(f328(x88871,x88872),x88873))+P1(f328(f316(f881(a875,a875),a226),f328(f328(f263(a875,a875),f542(x88871,x88873,x88872)),f543(x88871,x88873,x88872))))+~P1(f328(f316(f881(a875,a875),a226),f328(f328(f263(a875,a875),x88872),x88873))) % 154.70/154.56 [8888]P1(f328(f328(x88881,x88882),x88883))+P1(f328(f316(f881(a1,a1),a51),f328(f328(f263(a1,a1),f530(x88881,x88883,x88882)),f534(x88881,x88883,x88882))))+~P1(f328(f316(f881(a1,a1),a51),f328(f328(f263(a1,a1),x88882),x88883))) % 154.70/154.56 [8889]P1(f328(f328(x88891,x88892),x88893))+P1(f328(f316(f881(a1,a1),a56),f328(f328(f263(a1,a1),f536(x88891,x88893,x88892)),f537(x88891,x88893,x88892))))+~P1(f328(f316(f881(a1,a1),a56),f328(f328(f263(a1,a1),x88892),x88893))) % 154.70/154.56 [8890]P1(f328(f328(x88901,x88902),x88903))+P1(f328(f316(f881(a1,a1),a231),f328(f328(f263(a1,a1),f540(x88901,x88903,x88902)),f541(x88901,x88903,x88902))))+~P1(f328(f316(f881(a1,a1),a231),f328(f328(f263(a1,a1),x88902),x88903))) % 154.70/154.56 [8891]P1(f328(f328(x88911,x88912),x88913))+P1(f328(f316(f881(a1,a1),a181),f328(f328(f263(a1,a1),f692(x88911,x88913,x88912)),f694(x88911,x88913,x88912))))+~P1(f328(f316(f881(a1,a1),a181),f328(f328(f263(a1,a1),x88912),x88913))) % 154.70/154.56 [9240]~P1(f328(f61(x92401),x92403))+P1(f328(f328(f330(f881(f882(x92401,a870),f882(x92401,a870))),f328(f328(f263(f882(x92401,a870),f882(x92401,a870)),x92402),x92403)),f303(x92401)))+~P1(f328(f328(f243(f882(x92401,a870)),x92402),x92403)) % 154.70/154.56 [9311]~P56(x93111,f328(x93113,f602(x93112,x93113,x93111)))+P56(x93111,f328(f328(f41(x93112,f882(x93111,f882(x93111,a870))),f251(f882(x93112,a870))),x93113))+~E(f328(f328(f105(f882(x93111,a870)),f257(x93111,x93111,f328(x93113,f601(x93112,x93113,x93111)))),f258(x93111,x93111,f328(x93113,f604(x93112,x93113,x93111)))),f192(f882(x93111,a870))) % 154.70/154.56 [9400]~P30(a872,f192(f882(f874(a872),a870)),f328(f328(f306(f874(a872)),f328(f328(f328(f92(a872),x94001),x94002),x94003)),f192(f882(f874(a872),a870))))+P26(a872,f192(f882(f874(a872),a870)),f328(f328(f306(f874(a872)),f328(f328(f328(f92(a872),x94001),x94002),x94003)),f192(f882(f874(a872),a870))))+~P26(a872,f192(f882(f874(a872),a870)),f328(f328(f306(f874(a872)),f328(f328(f328(f92(a872),a325),x94002),f328(a198,x94002))),f192(f882(f874(a872),a870)))) % 154.70/154.56 [9508]P41(x95081,x95082,x95083)+P1(f328(f328(f330(f881(x95081,x95081)),f592(x95083,x95082,x95081)),x95083))+~P1(f328(f328(f330(f881(x95081,x95081)),f328(f328(f263(x95081,x95081),f591(x95083,x95082,x95081)),f591(x95083,x95082,x95081))),x95083)) % 154.70/154.56 [10093]P41(x100931,x100932,x100933)+~P1(f328(f328(f267(x100931,x100931,a870),f328(f328(f7(x100931,f882(x100931,a870),f882(x100931,a870)),f328(f328(f8(f882(a870,a870),f882(f882(x100931,a870),f882(x100931,a870)),x100931),f8(a870,a870,x100931)),f328(f328(f8(a870,f882(a870,a870),x100931),a326),f328(f328(f7(x100931,f882(x100931,a870),a870),f330(x100931)),x100932)))),f328(f328(f7(x100931,f882(x100931,a870),a870),f330(x100931)),x100932))),f592(x100933,x100932,x100931)))+~P1(f328(f328(f330(f881(x100931,x100931)),f328(f328(f263(x100931,x100931),f591(x100933,x100932,x100931)),f591(x100933,x100932,x100931))),x100933)) % 154.70/154.56 [5636]~P57(x56362)+E(x56361,f2(x56362))+E(f328(f328(f38(x56362),f328(f328(f81(x56362),x56363),x56361)),x56361),x56363) % 154.70/154.56 [5637]~P57(x56372)+E(x56371,f2(x56372))+E(f328(f328(f38(x56372),f328(f328(f81(x56372),x56371),x56373)),x56371),x56373) % 154.70/154.56 [6428]~P66(x64281)+~E(f328(x64282,f2(a875)),f2(x64281))+E(f328(f328(f6(a875,x64281),x64282),f328(f298(a875,f328(a116,f2(a875))),x64283)),f328(f328(f6(a875,x64281),x64282),f328(f298(a875,f2(a875)),x64283))) % 154.70/154.56 [6556]~P57(x65562)+E(x65561,f2(x65562))+E(f328(f328(f38(x65562),f328(f328(f80(x65562),x65563),x65561)),x65561),f328(f328(f80(x65562),f328(f328(f38(x65562),x65563),x65561)),f78(x65562))) % 154.70/154.56 [6557]~P57(x65572)+E(x65571,f2(x65572))+E(f328(f328(f38(x65572),f328(f328(f80(x65572),x65571),x65573)),x65571),f328(f328(f80(x65572),f328(f328(f38(x65572),x65573),x65571)),f78(x65572))) % 154.70/154.56 [6777]~P1(f328(x67773,f2(a1)))+P1(f328(f328(f242(a875),x67771),x67772))+P1(f328(x67773,f328(f104(a1),f328(f328(f22(a875),x67772),x67771)))) % 154.70/154.56 [6883]P1(f328(f328(f242(a875),x68832),x68831))+P1(f328(f328(f243(a875),x68831),x68832))+P1(f328(x68833,f328(f104(a1),f328(f328(f22(a875),x68831),x68832)))) % 154.70/154.56 [6953]E(f328(f328(f80(a875),f328(f107(a875),x69531)),f328(f328(f80(a875),f328(f107(a875),x69532)),x69533)),f328(f328(f80(a875),f328(f107(a875),x69531)),x69533))+P1(f328(a197,f328(f107(a1),x69531)))+~P1(f328(a197,f328(f107(a1),x69532))) % 154.70/154.56 [7032]~E(x70322,f328(f328(f38(a875),x70323),x70321))+~P1(f328(f328(f243(a875),f2(a875)),x70321))+P1(f328(f328(f242(a875),f328(f328(f81(a875),x70321),x70322)),x70323)) % 154.70/154.56 [7146]~P1(f328(f61(x71461),x71463))+~P1(f328(f61(x71461),x71462))+P1(f328(f61(x71461),f328(f328(f114(f882(x71461,a870)),x71462),x71463))) % 154.70/154.56 [7442]~P105(x74421)+~P1(f328(f61(x74421),x74422))+E(f136(x74421,f328(f328(f22(f882(x74421,a870)),x74422),f328(f328(f306(x74421),x74423),f192(f882(x74421,a870))))),f167(x74421,x74423,f136(x74421,x74422))) % 154.70/154.56 [7508]P1(f328(x75081,f2(a1)))+~P1(f328(f328(f243(a875),x75082),x75083))+~P1(f328(x75081,f328(f104(a1),f328(f328(f22(a875),x75082),x75083)))) % 154.70/154.56 [7525]~P1(f328(f61(x75251),x75252))+E(f328(f37(x75251),f328(f328(f22(f882(x75251,a870)),x75252),f328(f328(f306(x75251),x75253),f192(f882(x75251,a870))))),f328(f37(x75251),x75252))+P1(f328(f328(f330(x75251),x75253),x75252)) % 154.70/154.56 [7657]~P123(x76571)+~P1(f328(f328(f243(x76571),f78(x76571)),x76572))+P1(f328(f328(f243(x76571),f78(x76571)),f328(f328(f81(x76571),x76572),f328(f328(f253(x76571),x76572),x76573)))) % 154.70/154.56 [7702]~P1(f328(f61(x77021),x77023))+E(f328(f328(f22(a875),f328(f37(x77021),x77022)),f328(f37(x77021),x77023)),f328(f37(x77021),f328(f328(f22(f882(x77021,a870)),x77022),x77023)))+~P1(f328(f328(f242(f882(x77021,a870)),x77023),x77022)) % 154.70/154.56 [7760]~P1(f328(f328(f242(a875),x77602),x77603))+~P1(f328(f328(f242(a875),x77601),f328(f328(f22(a875),x77603),x77602)))+P1(f328(f328(f242(a875),f328(f328(f80(a875),x77601),x77602)),x77603)) % 154.70/154.56 [7815]P1(f328(f61(x78151),x78152))+~P1(f328(f61(x78151),x78153))+~P1(f328(f61(x78151),f328(f328(f22(f882(x78151,a870)),x78152),x78153))) % 154.70/154.56 [7821]~P1(f328(f61(x78211),x78212))+E(f328(f37(x78211),f328(f328(f22(f882(x78211,a870)),x78212),f328(f328(f306(x78211),x78213),f192(f882(x78211,a870))))),f328(f328(f22(a875),f328(f37(x78211),x78212)),f78(a875)))+~P1(f328(f328(f330(x78211),x78213),x78212)) % 154.70/154.56 [7897]P56(x78971,x78972)+~P56(x78971,x78973)+~P1(f328(f328(f242(f882(x78971,f882(x78971,a870))),x78972),x78973)) % 154.70/154.56 [7938]~P1(f328(f328(f242(a875),x79383),x79382))+P1(f328(f328(f242(a875),x79381),f328(f328(f22(a875),x79382),x79383)))+~P1(f328(f328(f242(a875),f328(f328(f80(a875),x79381),x79383)),x79382)) % 154.70/154.56 [7956]P39(x79561,x79562)+~P39(x79561,x79563)+~P1(f328(f328(f242(f882(f881(x79561,x79561),a870)),x79562),x79563)) % 154.70/154.56 [7957]P54(x79571,x79572)+~P54(x79571,x79573)+~P1(f328(f328(f242(f882(f881(x79571,x79571),a870)),x79572),x79573)) % 154.70/154.56 [8198]~P123(x81981)+~P1(f328(f328(f243(x81981),f78(x81981)),x81982))+P1(f328(f328(f243(x81981),f328(f328(f253(x81981),x81982),x81983)),f328(f328(f81(x81981),x81982),f328(f328(f253(x81981),x81982),x81983)))) % 154.70/154.56 [8292]~P1(f328(x82921,f2(a1)))+~P1(f328(x82921,f328(f328(f22(a1),f328(f104(a1),x82922)),f328(f104(a1),x82923))))+P1(f328(x82921,f328(f104(a1),f328(f328(f22(a875),x82922),x82923)))) % 154.70/154.56 [8306]~P1(f328(f328(f242(a875),x83063),x83062))+P1(f328(x83061,f328(f328(f22(a1),f328(f104(a1),x83062)),f328(f104(a1),x83063))))+~P1(f328(x83061,f328(f104(a1),f328(f328(f22(a875),x83062),x83063)))) % 154.70/154.56 [8324]P1(f328(f328(f243(a875),x83241),x83242))+~P1(f328(x83243,f328(f328(f22(a1),f328(f104(a1),x83241)),f328(f104(a1),x83242))))+P1(f328(x83243,f328(f104(a1),f328(f328(f22(a875),x83241),x83242)))) % 154.70/154.56 [8378]~P114(x83782)+E(x83781,f2(x83782))+P1(f328(f328(f243(x83782),f2(x83782)),f328(f328(f80(x83782),f328(f328(f81(x83782),x83783),x83783)),f328(f328(f81(x83782),x83781),x83781)))) % 154.70/154.56 [8379]~P114(x83792)+E(x83791,f2(x83792))+P1(f328(f328(f243(x83792),f2(x83792)),f328(f328(f80(x83792),f328(f328(f81(x83792),x83791),x83791)),f328(f328(f81(x83792),x83793),x83793)))) % 154.70/154.56 [8482]~P1(f328(f328(f243(a875),f2(a875)),x84821))+~P1(f328(f328(f243(a1),x84822),x84823))+P1(f328(f328(f243(a1),f328(f328(f81(a1),f328(f104(a1),x84821)),x84822)),f328(f328(f81(a1),f328(f104(a1),x84821)),x84823))) % 154.70/154.56 [8539]E(f328(f328(f105(f882(x85391,a870)),x85392),f39(f882(x85391,a870),x85393)),f192(f882(x85391,a870)))+P1(f328(f328(f330(f882(x85391,a870)),x85392),x85393))+P1(f328(f328(f330(f882(x85391,a870)),f826(x85393,x85392,x85391)),f328(f328(f306(f882(x85391,a870)),x85392),x85393))) % 154.70/154.56 [8540]E(f328(f328(f105(f882(x85401,a870)),x85402),f39(f882(x85401,a870),x85403)),f192(f882(x85401,a870)))+P1(f328(f328(f330(f882(x85401,a870)),x85402),x85403))+P1(f328(f328(f330(f882(x85401,a870)),f825(x85403,x85402,x85401)),f328(f328(f306(f882(x85401,a870)),x85402),x85403))) % 154.70/154.56 [8574]E(x85741,x85742)+~E(f328(f193(f876(x85743)),x85741),f328(f193(f876(x85743)),x85742))+P1(f328(f328(f330(f881(x85743,x85743)),f682(x85743,x85741,x85742)),f328(f170(f881(x85743,x85743)),f328(f328(f180(x85743,x85743),x85742),x85741)))) % 154.70/154.56 [8807]E(f304(x88071,x88072),f304(x88071,x88073))+~P1(f328(f328(f242(f882(f881(x88071,x88071),a870)),x88073),f304(x88071,x88072)))+~P1(f328(f328(f242(f882(f881(x88071,x88071),a870)),x88072),x88073)) % 154.70/154.56 [8867]~P41(x88671,f251(f882(x88671,a870)),x88673)+P1(f328(f328(f242(f882(f881(f876(x88671),f876(x88671)),a870)),f154(x88671,x88672)),f155(x88671,x88673)))+~P1(f328(f328(f242(f882(f881(x88671,x88671),a870)),x88672),x88673)) % 154.70/154.56 [9076]P39(x90761,x90762)+~P1(f328(f328(f330(x90761),x90763),f632(x90762,x90761)))+P1(f328(f328(f330(f881(x90761,x90761)),f328(f328(f263(x90761,x90761),f653(x90762,x90761,x90763)),x90763)),x90762)) % 154.70/154.56 [9110]~P1(f328(f61(x91101),x91102))+P1(f328(f61(f882(x91101,a870)),f328(f328(f60(x91101),x91102),x91103)))+~P1(f328(f328(f242(f882(f881(x91101,x91101),a870)),x91103),f328(f328(f265(x91101,x91101),x91102),f328(f16(f882(x91101,a870),x91101),x91102)))) % 154.70/154.56 [9145]P41(x91451,x91452,x91453)+P1(f328(f328(f330(x91451),f586(x91453,x91452,x91451)),x91452))+~P1(f328(f328(f242(f882(f881(x91451,x91451),a870)),x91453),f328(f328(f265(x91451,x91451),x91452),f328(f16(f882(x91451,a870),x91451),x91452)))) % 154.70/154.56 [9146]P41(x91461,x91462,x91463)+P1(f328(f328(f330(x91461),f589(x91462,x91463,x91461)),x91462))+~P1(f328(f328(f242(f882(f881(x91461,x91461),a870)),x91463),f328(f328(f265(x91461,x91461),x91462),f328(f16(f882(x91461,a870),x91461),x91462)))) % 154.70/154.56 [9181]~P63(x91811)+~P1(f328(f328(f243(x91811),x91812),x91813))+P1(f328(f328(f243(x91811),f328(f328(f286(x91811),f328(f328(f80(x91811),x91812),x91813)),f328(f328(f80(x91811),f78(x91811)),f78(x91811)))),x91813)) % 154.70/154.56 [9210]~P62(x92101)+P1(f328(f328(f242(x92101),x92102),x92103))+~P1(f328(f328(f242(x92101),f328(f328(f81(x92101),f498(x92103,x92102,x92101)),x92102)),x92103)) % 154.70/154.56 [9346]E(f328(f193(f876(f876(x93461))),f328(f133(f876(x93461),f328(f328(f8(a875,a870,f876(x93461)),f328(f243(a875),x93462)),f193(f876(x93461)))),f178(x93461,x93463))),f328(f193(f876(x93461)),f328(f328(f162(f876(x93461)),x93463),x93462)))+~P16(a875,f328(f166(a875),f328(f328(f151(f876(x93461),a875),f193(f876(x93461))),x93463)))+~P1(f328(f328(f243(a875),x93462),f328(f193(f876(f876(x93461))),x93463))) % 154.70/154.56 [9454]~P39(x94541,x94542)+P28(x94541,f328(f328(f263(f882(f881(x94541,x94541),a870),f882(f881(x94541,x94541),a870)),x94542),x94543))+~P1(f328(f328(f242(f882(f881(x94541,x94541),a870)),f328(f328(f285(x94541,x94541,x94541),x94542),x94543)),x94542)) % 154.70/154.56 [9461]E(f328(f328(f151(f876(x94611),x94611),f328(f328(f7(f876(x94611),a875,x94611),f162(x94611)),x94612)),f328(f133(f876(x94611),f328(f328(f8(a875,a870,f876(x94611)),f328(f243(a875),x94612)),f193(f876(x94611)))),f178(x94611,x94613))),f328(f328(f162(f876(x94611)),x94613),x94612))+~P16(a875,f328(f166(a875),f328(f328(f151(f876(x94611),a875),f193(f876(x94611))),x94613)))+~P1(f328(f328(f243(a875),x94612),f328(f193(f876(f876(x94611))),x94613))) % 154.70/154.56 [9596]P41(x95961,x95962,x95963)+~P1(f328(f328(f330(f881(x95961,x95961)),f328(f328(f263(x95961,x95961),f586(x95963,x95962,x95961)),f586(x95963,x95962,x95961))),x95963))+~P1(f328(f328(f242(f882(f881(x95961,x95961),a870)),x95963),f328(f328(f265(x95961,x95961),x95962),f328(f16(f882(x95961,a870),x95961),x95962)))) % 154.70/154.56 [9597]P41(x95971,x95972,x95973)+~P1(f328(f328(f330(f881(x95971,x95971)),f328(f328(f263(x95971,x95971),f589(x95972,x95973,x95971)),f589(x95972,x95973,x95971))),x95973))+~P1(f328(f328(f242(f882(f881(x95971,x95971),a870)),x95973),f328(f328(f265(x95971,x95971),x95972),f328(f16(f882(x95971,a870),x95971),x95972)))) % 154.70/154.56 [9772]~P135(x97721)+~P119(x97721)+E(f328(f328(f286(x97721),f328(f106(x97721),f328(f328(f73(f881(a1,a1),a1,x97722,f262(a1,a1)),f219(x97722)),x97723))),f328(f106(x97721),f328(f328(f73(f881(a1,a1),a1,x97722,f266(a1,a1)),f219(x97722)),x97723))),f232(x97722,x97721,x97723)) % 154.70/154.56 [9973]~E(x99733,f2(a875))+~E(f328(f193(f876(x99731)),f328(f328(f162(f876(x99731)),x99732),f748(x99733,x99731,x99732))),x99733)+E(f328(f328(f151(a875,f876(x99731)),f328(f328(f7(a875,f876(a875),f876(x99731)),f328(f328(f8(f882(a875,x99731),f882(f876(a875),f876(x99731)),a875),f151(a875,x99731)),f328(f7(a875,a875,x99731),f328(f328(f8(f876(x99731),f882(a875,x99731),a875),f162(x99731)),f328(f162(f876(x99731)),x99732))))),f136(a875,f328(f298(a875,f2(a875)),f328(f193(f876(f876(x99731))),x99732))))),f136(a875,f328(f298(a875,f2(a875)),x99733))),f178(x99731,x99732)) % 154.70/154.56 [9974]E(x99741,f117(f876(x99742)))+~E(f328(f193(f876(x99742)),f328(f328(f162(f876(x99742)),x99741),f748(x99743,x99742,x99741))),x99743)+E(f328(f328(f151(a875,f876(x99742)),f328(f328(f7(a875,f876(a875),f876(x99742)),f328(f328(f8(f882(a875,x99742),f882(f876(a875),f876(x99742)),a875),f151(a875,x99742)),f328(f7(a875,a875,x99742),f328(f328(f8(f876(x99742),f882(a875,x99742),a875),f162(x99742)),f328(f162(f876(x99742)),x99741))))),f136(a875,f328(f298(a875,f2(a875)),f328(f193(f876(f876(x99742))),x99741))))),f136(a875,f328(f298(a875,f2(a875)),x99743))),f178(x99742,x99741)) % 154.70/154.56 [9975]~E(x99753,f2(a875))+E(f328(f328(f151(a875,f876(x99751)),f328(f328(f7(a875,f876(a875),f876(x99751)),f328(f328(f8(f882(a875,x99751),f882(f876(a875),f876(x99751)),a875),f151(a875,x99751)),f328(f7(a875,a875,x99751),f328(f328(f8(f876(x99751),f882(a875,x99751),a875),f162(x99751)),f328(f162(f876(x99751)),x99752))))),f136(a875,f328(f298(a875,f2(a875)),f328(f193(f876(f876(x99751))),x99752))))),f136(a875,f328(f298(a875,f2(a875)),x99753))),f178(x99751,x99752))+P1(f328(f328(f243(a875),f748(x99753,x99751,x99752)),f328(f193(f876(f876(x99751))),x99752))) % 154.70/154.56 [9976]E(x99761,f117(f876(x99762)))+E(f328(f328(f151(a875,f876(x99762)),f328(f328(f7(a875,f876(a875),f876(x99762)),f328(f328(f8(f882(a875,x99762),f882(f876(a875),f876(x99762)),a875),f151(a875,x99762)),f328(f7(a875,a875,x99762),f328(f328(f8(f876(x99762),f882(a875,x99762),a875),f162(x99762)),f328(f162(f876(x99762)),x99761))))),f136(a875,f328(f298(a875,f2(a875)),f328(f193(f876(f876(x99762))),x99761))))),f136(a875,f328(f298(a875,f2(a875)),x99763))),f178(x99762,x99761))+P1(f328(f328(f243(a875),f748(x99763,x99762,x99761)),f328(f193(f876(f876(x99762))),x99761))) % 154.70/154.56 [7699]E(f328(f328(f80(a875),f328(f107(a875),x76991)),f328(f328(f80(a875),f328(f107(a875),x76992)),x76993)),f328(f328(f80(a875),f328(f107(a875),f328(f328(f80(a1),x76991),x76992))),x76993))+P1(f328(a197,f328(f107(a1),x76991)))+P1(f328(a197,f328(f107(a1),x76992))) % 154.70/154.56 [8472]~P1(f328(f61(x84721),x84722))+~P1(f328(f328(f330(x84721),x84723),x84722))+E(f328(a116,f328(f37(x84721),f328(f328(f22(f882(x84721,a870)),x84722),f328(f328(f306(x84721),x84723),f192(f882(x84721,a870)))))),f328(f37(x84721),x84722)) % 154.70/154.56 [8489]~P1(f328(f61(x84891),x84892))+~P1(f328(f328(f330(x84891),x84893),x84892))+E(f328(f328(f80(a875),f78(a875)),f328(f37(x84891),f328(f328(f22(f882(x84891,a870)),x84892),f328(f328(f306(x84891),x84893),f192(f882(x84891,a870)))))),f328(f37(x84891),x84892)) % 154.70/154.56 [8583]~P105(x85831)+~P1(f328(f61(x85831),x85833))+E(f328(f328(f145(x85831,x85831,f5(x85831)),x85832),f136(x85831,f328(f328(f22(f882(x85831,a870)),x85833),f328(f328(f306(x85831),x85832),f192(f882(x85831,a870)))))),f136(x85831,f328(f328(f306(x85831),x85832),x85833))) % 154.70/154.56 [8737]~P1(f328(f61(x87371),x87373))+~P1(f328(f61(x87371),x87372))+E(f328(f328(f80(a875),f328(f37(x87371),f328(f328(f114(f882(x87371,a870)),x87372),x87373))),f328(f37(x87371),f328(f328(f105(f882(x87371,a870)),x87372),x87373))),f328(f328(f80(a875),f328(f37(x87371),x87372)),f328(f37(x87371),x87373))) % 154.70/154.56 [9921]~P27(x99211,f882(f882(x99211,a870),a870),f328(f328(f7(x99211,f882(f881(x99211,x99211),a870),f882(f882(x99211,a870),a870)),f328(f328(f8(f882(x99211,a870),f882(f882(f881(x99211,x99211),a870),f882(f882(x99211,a870),a870)),x99211),f60(x99211)),f328(f328(f7(x99211,f882(x99211,a870),f882(x99211,a870)),f306(x99211)),f192(f882(x99211,a870))))),x99213),x99212)+~P1(f328(f61(x99211),x99212))+E(f328(f37(f882(x99211,a870)),f328(f328(f60(x99211),x99212),x99213)),f328(f37(x99211),x99212)) % 154.70/154.56 [7969]~P90(x79691)+P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x79693)))+E(f328(f328(f253(x79691),x79692),f328(f107(a875),f328(f328(f22(a1),f328(f328(f80(a1),x79693),x79693)),a101))),f78(x79691)) % 154.70/154.56 [9437]~P90(x94371)+~P1(f328(f328(f242(a1),f2(a1)),f328(f107(a1),x94373)))+E(f328(f328(f253(x94371),x94372),f328(f107(a875),f328(f328(f22(a1),f328(f328(f80(a1),x94373),x94373)),a101))),f328(f328(f86(x94371,x94371),f328(f328(f253(x94371),x94372),f328(f107(a875),x94373))),f328(f328(f18(x94371,x94371,x94371),f328(f328(f8(x94371,f882(x94371,x94371),x94371),f81(x94371)),f328(f81(x94371),x94372))),f5(x94371)))) % 154.70/154.56 [9831]~P1(f328(f134(x98311),x98313))+~P1(f328(f328(f330(x98311),x98312),f328(f170(x98311),x98313)))+E(f328(f328(f135(x98311),f328(f193(f876(x98311)),f175(x98311,f328(f328(f8(a870,a870,x98311),a323),f328(f328(f7(x98311,x98311,a870),a325),x98312)),f328(f166(x98311),x98313)))),f328(f166(x98311),x98313)),f328(f328(f148(x98311),x98312),f328(f166(x98311),f175(x98311,f328(f328(f8(a870,a870,x98311),a323),f328(f328(f7(x98311,x98311,a870),a325),x98312)),x98313)))) % 154.70/154.56 [9902]P1(f328(f328(f242(f882(f881(x99021,x99021),a870)),f304(x99021,x99022)),x99023))+~P1(f328(f328(f242(f882(f881(x99021,x99021),a870)),f304(x99021,f192(f882(f881(x99021,x99021),a870)))),x99023))+~P1(f328(f328(f242(f882(f881(x99021,x99021),a870)),f328(f328(f285(x99021,x99021,x99021),f328(f328(f105(f882(f881(x99021,x99021),a870)),f304(x99021,x99022)),x99023)),x99022)),x99023)) % 154.70/154.56 [9743]~P1(f328(f61(x97431),f328(f248(x97431),x97433)))+~P1(f328(f61(x97431),f328(f248(x97431),x97432)))+P1(f328(f61(x97431),f328(f248(x97431),f328(f328(f18(x97431,a870,a870),f328(f328(f8(a870,f882(a870,a870),x97431),a327),x97432)),x97433)))) % 154.70/154.56 [10035]P1(f328(f328(f242(f882(f881(x100351,x100351),a870)),f328(f328(f285(x100351,x100351,x100351),x100352),f304(x100351,x100352))),x100353))+~P1(f328(f328(f242(f882(f881(x100351,x100351),a870)),x100352),x100353))+~P1(f328(f328(f242(f882(f881(x100351,x100351),a870)),f328(f328(f285(x100351,x100351,x100351),f328(f328(f105(f882(f881(x100351,x100351),a870)),f328(f328(f285(x100351,x100351,x100351),x100352),f304(x100351,x100352))),x100353)),x100352)),x100353)) % 154.70/154.56 [9989]~P121(x99892)+E(x99891,f2(x99892))+~E(f328(f328(f80(x99892),f328(f328(f253(x99892),x99893),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x99892),x99891),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f2(x99892)) % 154.70/154.56 [9990]~P121(x99902)+E(x99901,f2(x99902))+~E(f328(f328(f80(x99902),f328(f328(f253(x99902),x99901),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x99902),x99903),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f2(x99902)) % 154.70/154.56 [9995]~P1(f328(f134(x99951),x99953))+~P1(f328(f328(f330(x99951),x99952),f328(f170(x99951),x99953)))+E(f328(f166(x99951),f328(f169(x99951),f328(f328(f135(x99951),f328(f193(f876(x99951)),f175(x99951,f328(f328(f8(a870,a870,x99951),a323),f328(f328(f7(x99951,x99951,a870),a325),x99952)),x99953))),x99953))),f175(x99951,f328(f328(f8(a870,a870,x99951),a323),f328(f328(f7(x99951,x99951,a870),a325),x99952)),f328(f166(x99951),x99953))) % 154.70/154.56 [10080]~P121(x100802)+E(x100801,f2(x100802))+P1(f328(f328(f243(x100802),f2(x100802)),f328(f328(f80(x100802),f328(f328(f253(x100802),x100803),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x100802),x100801),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))))) % 154.70/154.56 [10081]~P121(x100812)+E(x100811,f2(x100812))+P1(f328(f328(f243(x100812),f2(x100812)),f328(f328(f80(x100812),f328(f328(f253(x100812),x100811),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x100812),x100813),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))))) % 154.70/154.56 [10124]~P121(x101241)+P1(f328(f328(f242(x101241),f2(x101241)),x101242))+~P1(f328(f328(f242(x101241),f2(x101241)),f328(f328(f253(x101241),x101242),f328(a116,f328(f328(f81(a875),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),x101243))))) % 154.70/154.56 [5478]~P26(x54781,x54784,x54783)+P26(x54781,x54782,x54783)+~P26(x54781,x54782,x54784) % 154.70/154.56 [4940]~E(x49402,f90(x49403,x49401))+P1(f328(x49401,x49402))+~P1(f328(x49401,x49404)) % 154.70/154.56 [6688]~P39(x66882,x66884)+~P39(x66881,x66883)+P39(f881(x66881,x66882),f320(x66881,x66882,x66883,x66884)) % 154.70/154.56 [5122]~P7(x51224,x51221)+~E(f328(x51221,x51222),f328(x51221,x51223))+P1(f328(f328(x51221,x51222),x51223)) % 154.70/154.56 [5294]~P7(x52944,x52941)+E(f328(x52941,x52942),f328(x52941,x52943))+~P1(f328(f328(x52941,x52942),x52943)) % 154.70/154.56 [5385]~P20(x53853,x53854,x53851)+E(f328(x53851,x53852),f328(f63(x53853,x53854),x53852))+~P1(f328(f61(x53853),x53852)) % 154.70/154.56 [5386]~P10(x53863,x53864,x53861)+E(f328(x53861,x53862),f328(f63(x53863,x53864),x53862))+~P1(f328(f61(x53863),x53862)) % 154.70/154.56 [5511]~P7(x55114,x55111)+~P1(f328(f328(x55111,x55113),x55112))+P1(f328(f328(x55111,x55112),x55113)) % 154.70/154.56 [5578]E(x55781,x55782)+~E(f328(f262(x55783,x55784),x55781),f328(f262(x55783,x55784),x55782))+~E(f328(f266(x55783,x55784),x55781),f328(f266(x55783,x55784),x55782)) % 154.70/154.56 [5604]E(x56041,x56042)+~P1(f328(f47(x56043,x56044),x56042))+~P1(f328(f47(x56043,x56044),x56041)) % 154.70/154.56 [5796]~P66(x57962)+E(f233(x57961,x57962,x57963,x57964),f2(x57962))+P1(f328(f61(x57961),x57964)) % 154.70/154.56 [5932]~P1(f328(f316(x59321,x59322),x59324))+P1(f328(f316(x59321,x59322),x59323))+~P1(f328(f328(x59322,x59323),x59324)) % 154.70/154.56 [7809]E(x78091,f2(a875))+~P1(f328(x78092,x78093))+P1(f328(x78092,f816(x78092,x78093,x78091,x78094))) % 154.70/154.56 [7892]~P105(x78922)+~P1(f328(f134(x78921),x78924))+P1(f328(f134(x78921),f147(x78921,x78922,x78923,x78924))) % 154.70/154.56 [8113]~P1(f328(f61(x81132),x81134))+~P1(f328(f61(x81131),x81133))+P1(f328(f61(f880(x81131,x81132)),f315(x81131,x81132,x81133,x81134))) % 154.70/154.56 [8114]~P1(f328(f134(x81142),x81144))+~P1(f328(f134(x81141),x81143))+P1(f328(f134(f881(x81141,x81142)),f59(x81141,x81142,x81143,x81144))) % 154.70/154.56 [8118]P1(f328(f328(f330(f876(x81181)),f328(f328(f125(x81181),x81182),x81183)),f158(x81181,x81184)))+~P1(f328(f328(f330(f876(x81181)),x81183),f158(x81181,x81184)))+~P1(f328(f328(f330(f876(x81181)),x81182),f158(x81181,x81184))) % 154.70/154.56 [8411]E(x84111,f2(a875))+P1(f328(x84112,x84113))+~P1(f328(x84112,f817(x84112,x84113,x84111,x84114))) % 154.70/154.56 [8451]~P105(x84513)+~P1(f328(f134(x84511),f147(x84511,x84513,x84514,x84512)))+P1(f328(f134(x84511),x84512)) % 154.70/154.56 [8728]~P1(f328(f328(f330(f881(x87281,x87281)),f328(f328(f263(x87281,x87281),x87282),x87284)),f304(x87281,x87283)))+P1(f328(f328(f330(x87281),x87282),f317(x87281,x87283)))+~P1(f328(f328(f330(x87281),x87284),f317(x87281,x87283))) % 154.70/154.56 [5106]~P66(x51062)+E(f328(f328(f6(x51061,x51062),x51063),x51064),f2(x51062))+P1(f328(f61(x51061),x51064)) % 154.70/154.56 [5109]~P73(x51092)+E(f328(f328(f9(x51091,x51092),x51093),x51094),f78(x51092))+P1(f328(f61(x51091),x51094)) % 154.70/154.56 [5257]~P68(x52573)+E(x52571,x52572)+~E(f328(f328(f80(x52573),x52574),x52571),f328(f328(f80(x52573),x52574),x52572)) % 154.70/154.56 [5258]~P69(x52583)+E(x52581,x52582)+~E(f328(f328(f80(x52583),x52584),x52581),f328(f328(f80(x52583),x52584),x52582)) % 154.70/154.56 [5260]~P68(x52603)+E(x52601,x52602)+~E(f328(f328(f80(x52603),x52601),x52604),f328(f328(f80(x52603),x52602),x52604)) % 154.70/154.56 [5381]~P5(x53813)+E(x53811,f192(f882(x53812,a870)))+E(f328(f328(f41(x53812,x53813),x53811),f328(f16(x53813,x53812),x53814)),x53814) % 154.70/154.56 [5382]~P5(x53823)+E(x53821,f192(f882(x53822,a870)))+E(f328(f328(f42(x53822,x53823),x53821),f328(f16(x53823,x53822),x53824)),x53824) % 154.70/154.56 [5592]~P107(x55923)+E(x55921,x55922)+~E(f299(x55923,x55924,x55921),f328(f328(f306(x55923),x55922),f192(f882(x55923,a870)))) % 154.70/154.56 [5593]~P107(x55933)+E(x55931,x55932)+~E(f299(x55933,x55931,x55932),f328(f328(f306(x55933),x55934),f192(f882(x55933,a870)))) % 154.70/154.56 [5653]~P37(x56533,x56531,x56534)+P37(x56533,x56531,f328(f328(f148(x56533),x56532),x56534))+P1(f328(x56531,x56532)) % 154.70/154.56 [5756]~P33(x57561,x57562,x57564)+~P1(f328(x57562,x57563))+P33(x57561,x57562,f328(f328(f148(x57561),x57563),x57564)) % 154.70/154.56 [5889]P1(f328(x58891,x58892))+~P1(f328(f256(x58893,x58891),x58894))+~P1(f328(f328(f330(x58893),x58892),x58894)) % 154.70/154.56 [5898]~P33(x58981,x58982,x58984)+~P33(x58981,x58982,x58983)+P33(x58981,x58982,f328(f328(f125(x58981),x58983),x58984)) % 154.70/154.56 [5908]P35(x59081,x59082,x59083)+~P35(x59081,x59082,f328(f328(f148(x59081),x59084),x59083))+P1(f328(x59082,x59084)) % 154.70/154.56 [5909]P37(x59091,x59092,x59093)+~P37(x59091,x59092,f328(f328(f148(x59091),x59094),x59093))+P1(f328(x59092,x59094)) % 154.70/154.56 [5983]P35(x59831,x59832,x59833)+P35(x59831,x59832,x59834)+~P35(x59831,x59832,f328(f328(f125(x59831),x59834),x59833)) % 154.70/154.56 [6002]~P66(x60021)+E(f328(f328(f6(a875,x60021),x60022),f328(f298(a875,x60023),f328(a116,x60024))),f2(x60021))+~P1(f328(f328(f243(a875),x60024),x60023)) % 154.70/154.56 [6007]~P58(x60071)+~E(f44(x60071,x60072,x60073),f44(x60071,x60074,x60073))+E(f44(x60071,f328(f79(x60071),x60072),x60073),f44(x60071,f328(f79(x60071),x60074),x60073)) % 154.70/154.56 [6075]P1(f328(x60751,x60752))+~E(f328(f133(x60753,x60751),x60754),x60754)+~P1(f328(f328(f330(x60753),x60752),f328(f170(x60753),x60754))) % 154.70/154.56 [6094]~E(f328(f328(f80(a875),x60943),x60942),f328(f328(f80(a875),x60941),x60944))+~P1(f328(f328(f243(a875),x60943),x60944))+P1(f328(f328(f243(a875),x60941),x60942)) % 154.70/154.56 [6098]P35(x60981,x60982,x60983)+~P1(f328(x60982,x60984))+~P1(f328(f328(f330(x60981),x60984),f328(f170(x60981),x60983))) % 154.70/154.56 [6134]~P33(x61343,x61341,x61344)+P1(f328(x61341,x61342))+~P1(f328(f328(f330(x61343),x61342),f328(f170(x61343),x61344))) % 154.70/154.56 [6136]~E(f328(f133(x61361,x61362),x61363),f117(x61361))+~P1(f328(x61362,x61364))+~P1(f328(f328(f330(x61361),x61364),f328(f170(x61361),x61363))) % 154.70/154.56 [6137]~E(f175(x61373,x61371,x61374),x61374)+P1(f328(x61371,x61372))+~P1(f328(f328(f330(x61373),x61372),f328(f170(x61373),x61374))) % 154.70/154.56 [6173]~E(x61734,f192(f882(x61732,a870)))+~E(x61733,f192(f882(x61731,a870)))+E(f315(x61731,x61732,x61733,x61734),f192(f882(f880(x61731,x61732),a870))) % 154.70/154.56 [6319]P1(f328(x63191,x63192))+~P1(f328(f157(x63193,x63191),x63194))+~P1(f328(f328(f330(x63193),x63192),f328(f170(x63193),x63194))) % 154.70/154.56 [6585]~P66(x65851)+E(f328(f328(f6(a875,x65851),x65852),f299(a875,x65853,f328(a116,x65854))),f2(x65851))+~P1(f328(f328(f243(a875),f328(a116,x65854)),x65853)) % 154.70/154.56 [6632]E(x66321,x66322)+~P1(f328(f328(f328(a198,x66323),x66324),x66321))+~P1(f328(f328(f328(a198,x66323),x66324),x66322)) % 154.70/154.56 [6727]~P105(x67271)+E(f328(f328(f22(f882(x67271,a870)),f328(f298(x67271,x67272),x67273)),f328(f298(x67271,x67272),x67274)),f328(f298(x67271,x67274),x67273))+~P1(f328(f328(f242(x67271),x67272),x67274)) % 154.70/154.56 [6799]~E(x67993,x67994)+E(x67991,f2(a875))+P1(f328(f328(f330(x67992),x67993),f328(f170(x67992),f168(x67992,x67991,x67994)))) % 154.70/154.56 [7078]~P1(f328(f328(f330(f876(x70781)),x70784),f158(x70781,x70783)))+P1(f328(f328(f330(x70781),x70782),x70783))+~P1(f328(f328(f330(x70781),x70782),f328(f170(x70781),x70784))) % 154.70/154.56 [7085]~P39(x70851,x70852)+P1(f328(f328(f330(x70851),f633(x70852,x70851,x70853)),x70853))+~P1(f328(f328(f330(x70851),x70854),x70853)) % 154.70/154.56 [7141]~P66(x71411)+E(f328(f328(f328(f65(x71411,x71412,f80(x71411)),x71413),f2(x71411)),x71414),f328(f328(f6(x71412,x71411),x71413),x71414))+~P1(f328(f61(x71412),x71414)) % 154.70/154.56 [7143]~P73(x71431)+E(f328(f328(f328(f65(x71431,x71432,f81(x71431)),x71433),f78(x71431)),x71434),f328(f328(f9(x71432,x71431),x71433),x71434))+~P1(f328(f61(x71432),x71434)) % 154.70/154.56 [7173]P27(x71731,x71732,x71733,x71734)+~E(f328(f37(x71732),f328(f307(x71731,x71732,x71733),x71734)),f328(f37(x71731),x71734))+~P1(f328(f61(x71731),x71734)) % 154.70/154.56 [7359]~P66(x73591)+E(f328(f328(f80(x73591),f328(x73592,x73593)),f328(f328(f6(a875,x73591),x73592),f301(a875,x73593,x73594))),f328(f328(f6(a875,x73591),x73592),f299(a875,x73593,x73594)))+~P1(f328(f328(f242(a875),x73593),x73594)) % 154.70/154.56 [7369]~P66(x73691)+~P27(x73692,x73691,x73693,x73694)+E(f328(f328(f6(x73691,x73691),f34(x73691)),f328(f307(x73692,x73691,x73693),x73694)),f328(f328(f6(x73692,x73691),x73693),x73694)) % 154.70/154.56 [7370]~P73(x73701)+~P27(x73702,x73701,x73703,x73704)+E(f328(f328(f9(x73701,x73701),f34(x73701)),f328(f307(x73702,x73701,x73703),x73704)),f328(f328(f9(x73702,x73701),x73703),x73704)) % 154.70/154.56 [7423]E(f328(f37(f880(x74231,x74232)),f315(x74231,x74232,x74233,x74234)),f328(f328(f80(a875),f328(f37(x74231),x74233)),f328(f37(x74232),x74234)))+~P1(f328(f61(x74232),x74234))+~P1(f328(f61(x74231),x74233)) % 154.70/154.56 [7509]E(x75091,x75092)+P1(f328(f328(f330(x75093),x75091),f328(f170(x75093),f167(x75093,x75092,x75094))))+~P1(f328(f328(f330(x75093),x75091),f328(f170(x75093),x75094))) % 154.70/154.56 [7736]~P66(x77361)+E(f328(f328(f80(x77361),f328(f328(f6(a875,x77361),x77362),f328(f298(a875,x77363),x77364))),f328(x77362,x77364)),f328(f328(f6(a875,x77361),x77362),f328(f298(a875,x77363),f328(a116,x77364))))+P1(f328(f328(f243(a875),x77364),x77363)) % 154.70/154.56 [7791]~P27(x77911,x77912,x77913,f251(f882(x77911,a870)))+~P1(f328(f61(x77912),x77914))+P1(f328(f61(x77911),f328(f308(x77911,x77912,x77913),x77914))) % 154.70/154.56 [7905]P1(f328(f328(f330(f876(x79051)),f328(f328(f148(x79051),x79052),x79053)),f158(x79051,x79054)))+~P1(f328(f328(f330(f876(x79051)),x79053),f158(x79051,x79054)))+~P1(f328(f328(f330(x79051),x79052),x79054)) % 154.70/154.56 [7993]~E(f328(f307(x79933,x79931,x79934),f251(f882(x79933,a870))),f251(f882(x79931,a870)))+P1(f328(f61(x79931),x79932))+~P1(f328(f61(x79933),f328(f308(x79933,x79931,x79934),x79932))) % 154.70/154.56 [8084]~P27(x80841,x80843,x80844,x80842)+P1(f328(f61(x80841),x80842))+~P1(f328(f61(x80843),f328(f307(x80841,x80843,x80844),x80842))) % 154.70/154.56 [8106]~E(x81062,x81063)+P1(f328(f328(f330(f881(x81061,x81061)),f328(f328(f263(x81061,x81061),x81062),x81063)),f260(x81061,x81064)))+~P1(f328(f328(f330(x81061),x81062),x81064)) % 154.70/154.56 [8145]~P66(x81451)+E(f328(f328(f80(x81451),f328(f328(f6(a875,x81451),x81452),f299(a875,x81453,x81454))),f328(x81452,f328(a116,x81454))),f328(f328(f6(a875,x81451),x81452),f299(a875,x81453,f328(a116,x81454))))+P1(f328(f328(f243(a875),f328(a116,x81454)),x81453)) % 154.70/154.56 [8217]P1(f328(x82171,x82172))+~P1(f328(x82171,f328(f328(f162(x82173),x82174),f680(x82171,x82174,x82173))))+~P1(f328(f328(f330(x82173),x82172),f328(f170(x82173),x82174))) % 154.70/154.56 [8357]~P1(f328(f328(f330(x83571),x83572),f317(x83571,x83574)))+P1(f328(f328(f330(f876(x83571)),f328(f328(f148(x83571),x83572),x83573)),f317(f876(x83571),f154(x83571,x83574))))+~P1(f328(f328(f330(f876(x83571)),x83573),f317(f876(x83571),f154(x83571,x83574)))) % 154.70/154.56 [8370]~P27(x83702,x83703,x83704,f443(x83704,x83703,x83702,x83701))+P27(x83702,x83703,x83704,f40(f882(x83702,a870),x83701))+E(x83701,f192(f882(f882(x83702,a870),a870))) % 154.70/154.56 [8647]E(x86471,x86472)+~P1(f328(f328(f330(f881(x86473,x86473)),f328(f328(f263(x86473,x86473),x86471),x86472)),f304(x86473,x86474)))+P1(f328(f328(f330(x86473),x86471),f328(f261(x86473,x86473),x86474))) % 154.70/154.56 [8909]E(x89091,f2(a875))+P1(f328(x89092,x89093))+P1(f328(f328(f330(x89094),f817(x89092,x89093,x89091,x89094)),f328(f170(x89094),f168(x89094,x89091,x89093)))) % 154.70/154.56 [8919]E(x89191,f2(a875))+~P1(f328(x89193,x89194))+P1(f328(f328(f330(x89192),f816(x89193,x89194,x89191,x89192)),f328(f170(x89192),f168(x89192,x89191,x89194)))) % 154.70/154.56 [8927]P27(x89272,x89273,x89274,f40(f882(x89272,a870),x89271))+E(x89271,f192(f882(f882(x89272,a870),a870)))+P1(f328(f328(f330(f882(x89272,a870)),f443(x89274,x89273,x89272,x89271)),x89271)) % 154.70/154.56 [9064]P1(f328(f61(x90641),x90642))+~P1(f328(f61(x90644),f328(f307(x90641,x90644,x90643),x90642)))+P1(f328(f328(f330(x90641),f466(x90643,x90644,x90642,x90641)),x90642)) % 154.70/154.56 [9159]~P5(x91592)+E(f328(f328(f64(x91591,x91592,f328(f328(f8(x91592,f882(x91592,x91592),x91591),f114(x91592)),x91593)),f192(x91592)),x91594),f328(f328(f41(x91591,x91592),x91594),x91593))+~P1(f328(f61(x91591),x91594)) % 154.70/154.56 [9160]~P5(x91602)+E(f328(f328(f64(x91601,x91602,f328(f328(f8(x91602,f882(x91602,x91602),x91601),f105(x91602)),x91603)),f251(x91602)),x91604),f328(f328(f42(x91601,x91602),x91604),x91603))+~P1(f328(f61(x91601),x91604)) % 154.70/154.56 [9243]P1(f328(x92431,x92432))+~P1(f328(x92431,f328(f328(f162(x92433),x92434),f736(x92432,x92431,x92434,x92433))))+~P1(f328(f328(f330(x92433),x92432),f328(f170(x92433),x92434))) % 154.70/154.56 [9263]E(x92631,x92632)+~P1(f328(f328(f330(f881(x92633,x92633)),f328(f328(f263(x92633,x92633),x92631),x92632)),f304(x92633,x92634)))+P1(f328(f328(f330(f881(x92633,x92633)),f328(f328(f263(x92633,x92633),x92631),x92632)),f328(f328(f285(x92633,x92633,x92633),x92634),f304(x92633,x92634)))) % 154.70/154.56 [9312]~E(f328(f193(f876(x93121)),x93122),f328(f193(f876(x93121)),x93123))+~P1(f328(f328(f330(f881(f876(x93121),f876(x93121))),f328(f328(f263(f876(x93121),f876(x93121)),x93122),x93123)),f144(x93121,x93124)))+P1(f328(f328(f330(f881(f876(x93121),f876(x93121))),f328(f328(f263(f876(x93121),f876(x93121)),x93122),x93123)),f142(x93121,x93124))) % 154.70/154.56 [9543]P33(x95431,f328(f328(f18(x95431,a870,a870),f328(f328(f8(a870,f882(a870,a870),x95431),a327),f328(f328(f8(a870,a870,x95431),a323),x95432))),f328(a325,x95433)),x95434)+~P1(f328(x95432,x95433))+~P37(x95431,x95432,f328(f328(f148(x95431),x95433),x95434)) % 154.70/154.56 [9705]~P33(x97051,f328(f328(f18(x97051,a870,a870),f328(f328(f8(a870,f882(a870,a870),x97051),a327),f328(f328(f8(a870,a870,x97051),a323),x97052))),f328(a325,x97053)),x97054)+~P1(f328(x97052,x97053))+P37(x97051,x97052,f328(f328(f148(x97051),x97053),x97054)) % 154.70/154.56 [9709]~P37(x97091,x97092,x97094)+~P33(x97091,f328(f328(f18(x97091,a870,a870),f328(f328(f8(a870,f882(a870,a870),x97091),a327),f328(f328(f8(a870,a870,x97091),a323),x97092))),f328(a325,x97093)),x97094)+P37(x97091,x97092,f328(f328(f148(x97091),x97093),x97094)) % 154.70/154.56 [9746]~P65(x97461)+E(f328(f328(f6(a875,x97461),f328(f328(f18(a875,x97461,x97461),f328(f328(f8(x97461,f882(x97461,x97461),a875),f22(x97461)),x97462)),f328(f328(f8(a875,x97461,a875),x97462),f328(f328(f7(a875,a875,a875),f80(a875)),f78(a875))))),f299(a875,x97463,x97464)),f2(x97461))+P1(f328(f328(f242(a875),x97463),x97464)) % 154.70/154.56 [9988]~P39(x99882,x99884)+~P27(x99882,x99881,x99883,f251(f882(x99882,a870)))+P39(x99881,f328(f307(f881(x99882,x99882),f881(x99881,x99881),f268(x99882,x99881,x99882,x99881,x99883,x99883)),x99884)) % 154.70/154.56 [10151]~E(f328(f193(f876(x101511)),x101513),f328(f193(f876(x101511)),x101512))+P1(f328(f328(f330(f881(f876(x101511),f876(x101511))),f328(f328(f263(f876(x101511),f876(x101511)),x101512),x101513)),f155(x101511,x101514)))+~P1(f328(f328(f267(x101511,x101511,a870),f328(f328(f7(x101511,f882(f881(x101511,x101511),a870),f882(x101511,a870)),f328(f328(f8(f882(x101511,f882(f882(f881(x101511,x101511),a870),a870)),f882(f882(f881(x101511,x101511),a870),f882(x101511,a870)),x101511),f7(x101511,f882(f881(x101511,x101511),a870),a870)),f328(f328(f8(f882(x101511,f881(x101511,x101511)),f882(x101511,f882(f882(f881(x101511,x101511),a870),a870)),x101511),f328(f8(f881(x101511,x101511),f882(f882(f881(x101511,x101511),a870),a870),x101511),f330(f881(x101511,x101511)))),f263(x101511,x101511)))),x101514)),f683(x101514,x101513,x101512,x101511))) % 154.70/154.56 [6059]~P57(x60591)+~E(x60592,f2(x60591))+E(f328(f328(f38(x60591),f328(f328(f81(x60591),x60592),x60593)),f328(f328(f81(x60591),x60592),x60594)),f2(x60591)) % 154.70/154.56 [6097]E(x60971,f117(x60972))+E(x60973,f328(f328(f22(a875),f328(f193(f876(x60972)),x60971)),f78(a875)))+E(f141(x60972,f328(f328(f156(x60972,x60971),x60973),x60974)),f141(x60972,x60971)) % 154.70/154.56 [6125]E(x61251,x61252)+P1(f328(x61253,x61252))+~P1(f328(f328(f328(f306(x61254),x61251),x61253),x61252)) % 154.70/154.56 [6141]~P66(x61411)+~P1(f328(f134(x61412),x61414))+E(f328(f163(x61411),f328(f328(f151(x61412,x61411),x61413),x61414)),f328(f328(f6(x61412,x61411),x61413),f328(f170(x61412),x61414))) % 154.70/154.56 [6166]~P73(x61662)+~P1(f328(f61(x61661),x61664))+E(f328(f328(f9(x61661,x61662),f328(f16(x61662,x61661),x61663)),x61664),f328(f328(f253(x61662),x61663),f328(f37(x61661),x61664))) % 154.70/154.56 [6174]~E(x61744,x61742)+P1(f328(x61741,x61742))+P1(f328(f328(f328(a198,f32(x61741,x61743)),x61742),x61744)) % 154.70/154.56 [6222]~P60(x62222)+E(x62221,f2(x62222))+E(f328(f328(f286(x62222),f328(f328(f81(x62222),x62223),x62221)),f328(f328(f81(x62222),x62224),x62221)),f328(f328(f286(x62222),x62223),x62224)) % 154.70/154.56 [6223]~P60(x62232)+E(x62231,f2(x62232))+E(f328(f328(f286(x62232),f328(f328(f81(x62232),x62231),x62233)),f328(f328(f81(x62232),x62231),x62234)),f328(f328(f286(x62232),x62233),x62234)) % 154.70/154.56 [6224]~P57(x62242)+E(x62241,f2(x62242))+E(f328(f328(f38(x62242),f328(f328(f81(x62242),x62243),x62241)),f328(f328(f81(x62242),x62244),x62241)),f328(f328(f38(x62242),x62243),x62244)) % 154.70/154.56 [6226]~P57(x62262)+E(x62261,f2(x62262))+E(f328(f328(f38(x62262),f328(f328(f81(x62262),x62261),x62263)),f328(f328(f81(x62262),x62261),x62264)),f328(f328(f38(x62262),x62263),x62264)) % 154.70/154.56 [6289]P1(f328(x62891,x62892))+~E(x62893,f328(f328(f80(a875),x62894),x62892))+~P1(f328(x62891,f328(f328(f22(a875),x62893),x62894))) % 154.70/154.56 [6369]P30(x63691,x63692,x63693)+P29(x63691,f599(x63693,x63692,x63691),x63694)+~P1(f328(f328(f330(f874(x63691)),x63694),x63692)) % 154.70/154.56 [6371]~P1(f328(x63712,x63713))+~P1(f328(f157(x63711,x63712),x63714))+P1(f328(f157(x63711,x63712),f328(f328(f148(x63711),x63713),x63714))) % 154.70/154.56 [6411]E(x64111,f117(x64112))+~E(x64113,f328(f328(f22(a875),f328(f193(f876(x64112)),x64111)),f78(a875)))+E(f141(x64112,f328(f328(f156(x64112,x64111),x64113),x64114)),x64114) % 154.70/154.56 [6434]~P99(x64341)+~P1(f328(f328(f243(x64341),x64342),x64344))+P1(f328(f328(f243(x64341),x64342),f328(f328(f114(x64341),x64343),x64344))) % 154.70/154.56 [6435]~P99(x64351)+~P1(f328(f328(f243(x64351),x64352),x64353))+P1(f328(f328(f243(x64351),x64352),f328(f328(f114(x64351),x64353),x64354))) % 154.70/154.56 [6437]~P105(x64371)+~P1(f328(f328(f243(x64371),x64372),x64374))+P1(f328(f328(f243(x64371),x64372),f328(f328(f241(x64371),x64373),x64374))) % 154.70/154.56 [6439]~P105(x64391)+~P1(f328(f328(f243(x64391),x64392),x64393))+P1(f328(f328(f243(x64391),x64392),f328(f328(f241(x64391),x64393),x64394))) % 154.70/154.56 [6440]~P99(x64401)+~P1(f328(f328(f242(x64401),x64402),x64404))+P1(f328(f328(f242(x64401),x64402),f328(f328(f114(x64401),x64403),x64404))) % 154.70/154.56 [6441]~P99(x64411)+~P1(f328(f328(f242(x64411),x64412),x64413))+P1(f328(f328(f242(x64411),x64412),f328(f328(f114(x64411),x64413),x64414))) % 154.70/154.56 [6443]~P105(x64431)+~P1(f328(f328(f242(x64431),x64432),x64434))+P1(f328(f328(f242(x64431),x64432),f328(f328(f241(x64431),x64433),x64434))) % 154.70/154.56 [6445]~P105(x64451)+~P1(f328(f328(f242(x64451),x64452),x64453))+P1(f328(f328(f242(x64451),x64452),f328(f328(f241(x64451),x64453),x64454))) % 154.70/154.56 [6531]~E(f328(f328(f162(x65311),x65312),x65313),x65314)+E(f328(f328(f156(x65311,x65312),x65313),x65314),x65312)+~P1(f328(f328(f243(a875),x65313),f328(f193(f876(x65311)),x65312))) % 154.70/154.56 [6571]P1(f328(x65711,x65712))+~P1(f328(x65713,x65712))+~P1(f328(f328(f242(f882(x65714,a870)),x65713),x65711)) % 154.70/154.56 [6603]~E(f328(f328(f156(x66031,x66032),x66033),x66034),x66032)+E(f328(f328(f162(x66031),x66032),x66033),x66034)+~P1(f328(f328(f243(a875),x66033),f328(f193(f876(x66031)),x66032))) % 154.70/154.56 [6618]~P1(f328(f157(x66181,x66182),x66184))+~P1(f328(f157(x66181,x66182),x66183))+P1(f328(f157(x66181,x66182),f328(f328(f125(x66181),x66183),x66184))) % 154.70/154.56 [6715]P29(x67151,x67152,x67153)+~P29(x67151,f328(a116,x67152),f600(x67152,x67154,x67151))+~P1(f328(f328(f330(f874(x67151)),x67153),x67154)) % 154.70/154.56 [6724]E(x67241,f192(f882(x67242,a870)))+E(x67243,f192(f882(x67244,a870)))+~E(f328(f328(f265(x67244,x67242),x67243),f328(f16(f882(x67242,a870),x67244),x67241)),f192(f882(f881(x67244,x67242),a870))) % 154.70/154.56 [6743]E(x67431,x67432)+P1(f328(f328(f330(x67433),x67431),x67434))+~P1(f328(f328(f330(x67433),x67431),f328(f328(f306(x67433),x67432),x67434))) % 154.70/154.56 [6759]~P105(x67591)+P1(f328(f328(f243(x67591),x67592),x67593))+~P1(f328(f328(f243(x67591),x67592),f328(f328(f240(x67591),x67594),x67593))) % 154.70/154.56 [6760]~P105(x67601)+P1(f328(f328(f243(x67601),x67602),x67603))+~P1(f328(f328(f243(x67601),x67602),f328(f328(f240(x67601),x67603),x67604))) % 154.70/154.56 [6762]~P100(x67621)+P1(f328(f328(f242(x67621),x67622),x67623))+~P1(f328(f328(f242(x67621),x67622),f328(f328(f105(x67621),x67624),x67623))) % 154.70/154.56 [6764]~P100(x67641)+P1(f328(f328(f242(x67641),x67642),x67643))+~P1(f328(f328(f242(x67641),x67642),f328(f328(f105(x67641),x67643),x67644))) % 154.70/154.56 [6766]~P105(x67661)+P1(f328(f328(f242(x67661),x67662),x67663))+~P1(f328(f328(f242(x67661),x67662),f328(f328(f240(x67661),x67664),x67663))) % 154.70/154.56 [6768]~P105(x67681)+P1(f328(f328(f242(x67681),x67682),x67683))+~P1(f328(f328(f242(x67681),x67682),f328(f328(f240(x67681),x67683),x67684))) % 154.70/154.56 [6790]~E(f328(f328(f162(x67901),x67903),x67904),x67902)+P1(f328(f328(f330(x67901),x67902),f328(f170(x67901),x67903)))+~P1(f328(f328(f243(a875),x67904),f328(f193(f876(x67901)),x67903))) % 154.70/154.56 [6802]~P105(x68021)+~P16(x68021,f328(f328(f148(x68021),x68022),f328(f328(f148(x68021),x68023),x68024)))+P1(f328(f328(f242(x68021),x68022),x68023)) % 154.70/154.56 [6863]E(x68631,x68632)+P1(f328(x68633,x68631))+~P1(f328(f328(f328(a198,f32(x68633,x68634)),x68631),x68632)) % 154.70/154.56 [6943]~P33(x69432,x69431,x69433)+P1(f328(x69431,f328(f328(f162(x69432),x69433),x69434)))+~P1(f328(f328(f243(a875),x69434),f328(f193(f876(x69432)),x69433))) % 154.70/154.56 [6962]E(x69621,f2(a1))+E(f328(f328(f38(a1),x69622),x69621),x69623)+~P1(f328(f48(x69622,x69621),f328(f328(f263(a1,a1),x69623),x69624))) % 154.70/154.56 [6983]E(f44(a1,x69832,x69831),x69833)+E(x69831,f2(a1))+~P1(f328(f48(x69832,x69831),f328(f328(f263(a1,a1),x69834),x69833))) % 154.70/154.56 [7099]P1(f328(f328(f330(x70991),x70992),x70993))+~P1(f328(f328(f330(x70991),x70992),x70994))+~P1(f328(f328(f243(f882(x70991,a870)),x70994),x70993)) % 154.70/154.56 [7103]P1(f328(f328(f330(x71031),x71032),x71033))+~P1(f328(f328(f330(x71031),x71032),x71034))+~P1(f328(f328(f242(f882(x71031,a870)),x71034),x71033)) % 154.70/154.56 [7213]P35(x72131,x72132,x72133)+~P1(f328(x72132,f328(f328(f162(x72131),x72133),x72134)))+~P1(f328(f328(f243(a875),x72134),f328(f193(f876(x72131)),x72133))) % 154.70/154.56 [7324]~P108(x73242)+~P1(f328(f328(f243(f882(x73241,x73242)),x73243),x73244))+P1(f328(f328(f242(f882(x73241,x73242)),x73243),x73244)) % 154.70/154.56 [7411]~P26(x74111,x74112,x74114)+P26(x74111,x74112,f328(f328(f306(f874(x74111)),x74113),x74114))+~P26(x74111,x74112,f328(f328(f306(f874(x74111)),x74113),f192(f882(f874(x74111),a870)))) % 154.70/154.56 [7455]~P1(f328(f328(f330(x74551),x74552),x74554))+P1(f328(f328(f330(x74551),x74552),f39(f882(x74551,a870),x74553)))+~P1(f328(f328(f330(f882(x74551,a870)),x74554),x74553)) % 154.70/154.56 [7467]P29(x74671,x74672,x74673)+P1(f328(f328(f330(f874(x74671)),f600(x74672,x74674,x74671)),x74674))+~P1(f328(f328(f330(f874(x74671)),x74673),x74674)) % 154.70/154.56 [7487]~P80(x74871)+~P1(f328(f328(f243(x74871),x74873),x74874))+P1(f328(f328(f243(x74871),f328(f328(f80(x74871),x74872),x74873)),f328(f328(f80(x74871),x74872),x74874))) % 154.70/154.56 [7488]~P84(x74881)+~P1(f328(f328(f243(x74881),x74883),x74884))+P1(f328(f328(f243(x74881),f328(f328(f80(x74881),x74882),x74883)),f328(f328(f80(x74881),x74882),x74884))) % 154.70/154.56 [7489]~P80(x74891)+~P1(f328(f328(f243(x74891),x74892),x74894))+P1(f328(f328(f243(x74891),f328(f328(f80(x74891),x74892),x74893)),f328(f328(f80(x74891),x74894),x74893))) % 154.70/154.56 [7490]~P84(x74901)+~P1(f328(f328(f243(x74901),x74902),x74904))+P1(f328(f328(f243(x74901),f328(f328(f80(x74901),x74902),x74903)),f328(f328(f80(x74901),x74904),x74903))) % 154.70/154.56 [7491]~P80(x74911)+~P1(f328(f328(f242(x74911),x74913),x74914))+P1(f328(f328(f242(x74911),f328(f328(f80(x74911),x74912),x74913)),f328(f328(f80(x74911),x74912),x74914))) % 154.70/154.56 [7492]~P82(x74921)+~P1(f328(f328(f242(x74921),x74923),x74924))+P1(f328(f328(f242(x74921),f328(f328(f80(x74921),x74922),x74923)),f328(f328(f80(x74921),x74922),x74924))) % 154.70/154.56 [7493]~P80(x74931)+~P1(f328(f328(f242(x74931),x74932),x74934))+P1(f328(f328(f242(x74931),f328(f328(f80(x74931),x74932),x74933)),f328(f328(f80(x74931),x74934),x74933))) % 154.70/154.56 [7494]~P82(x74941)+~P1(f328(f328(f242(x74941),x74942),x74944))+P1(f328(f328(f242(x74941),f328(f328(f80(x74941),x74942),x74943)),f328(f328(f80(x74941),x74944),x74943))) % 154.70/154.56 [7503]~P103(x75031)+~P91(x75031)+E(f328(f328(f22(x75031),f328(f328(f81(x75031),x75032),f328(f107(x75031),x75033))),f328(f328(f81(x75031),x75034),f328(f107(x75031),x75033))),f328(f328(f81(x75031),f328(f328(f22(x75031),x75032),x75034)),f328(f107(x75031),x75033))) % 154.70/154.56 [7504]~P138(x75041)+~P91(x75041)+E(f328(f328(f80(x75041),f328(f328(f81(x75041),x75042),f328(f107(x75041),x75043))),f328(f328(f81(x75041),x75044),f328(f107(x75041),x75043))),f328(f328(f81(x75041),f328(f328(f80(x75041),x75042),x75044)),f328(f107(x75041),x75043))) % 154.70/154.56 [7539]~P66(x75391)+E(f328(f328(f80(x75391),f328(x75392,x75393)),f328(f328(f6(a875,x75391),x75392),f299(a875,f328(a116,x75393),x75394))),f328(f328(f6(a875,x75391),x75392),f299(a875,x75393,x75394)))+~P1(f328(f328(f242(a875),x75393),x75394)) % 154.70/154.56 [7550]~P27(x75502,x75501,x75503,f328(f170(x75502),x75504))+~P1(f328(f134(x75502),x75504))+P1(f328(f134(x75501),f328(f328(f151(x75502,x75501),x75503),x75504))) % 154.70/154.56 [7601]~P1(f328(f328(f243(a875),x76012),x76014))+~P1(f328(f328(f243(a875),x76011),x76013))+P1(f328(f328(f243(a875),f328(f328(f80(a875),x76011),x76012)),f328(f328(f80(a875),x76013),x76014))) % 154.70/154.56 [7602]~P1(f328(f328(f243(a1),x76021),x76023))+~P1(f328(f328(f242(a1),x76022),x76024))+P1(f328(f328(f243(a1),f328(f328(f80(a1),x76021),x76022)),f328(f328(f80(a1),x76023),x76024))) % 154.70/154.56 [7603]~P1(f328(f328(f242(a875),x76032),x76034))+~P1(f328(f328(f242(a875),x76031),x76033))+P1(f328(f328(f242(a875),f328(f328(f80(a875),x76031),x76032)),f328(f328(f80(a875),x76033),x76034))) % 154.70/154.56 [7604]~P1(f328(f328(f242(a875),x76042),x76044))+~P1(f328(f328(f242(a875),x76041),x76043))+P1(f328(f328(f242(a875),f328(f328(f81(a875),x76041),x76042)),f328(f328(f81(a875),x76043),x76044))) % 154.70/154.56 [7652]P1(f328(f328(f330(x76521),x76522),x76523))+~P1(f328(f328(f330(x76521),x76522),f40(f882(x76521,a870),x76524)))+~P1(f328(f328(f330(f882(x76521,a870)),x76523),x76524)) % 154.70/154.56 [7668]~P1(f328(x76681,f677(x76681,x76683,x76682)))+P1(f328(x76681,f328(f328(f162(x76682),x76683),x76684)))+~P1(f328(f328(f243(a875),x76684),f328(f193(f876(x76682)),x76683))) % 154.70/154.56 [7673]P1(f328(x76731,x76732))+~P1(f328(f328(f330(x76734),x76732),f328(f170(x76734),x76733)))+P1(f328(f328(f243(a875),f680(x76731,x76733,x76734)),f328(f193(f876(x76734)),x76733))) % 154.70/154.56 [7721]~P108(x77211)+~P1(f328(f328(f242(f882(x77212,x77211)),x77214),x77213))+~P1(f328(f328(f243(f882(x77212,x77211)),x77213),x77214)) % 154.70/154.56 [7768]~P1(f328(x77684,x77682))+~P1(f328(f328(f330(x77681),x77682),x77683))+P1(f328(f328(f330(x77681),x77682),f328(f328(f105(f882(x77681,a870)),x77683),f328(f248(x77681),x77684)))) % 154.70/154.56 [7914]~P1(f328(f328(f330(x79141),x79143),x79144))+~P1(f328(f328(f243(f882(x79141,a870)),x79142),x79144))+P1(f328(f328(f243(f882(x79141,a870)),x79142),f328(f328(f306(x79141),x79143),x79144))) % 154.70/154.56 [7916]E(f328(f328(f105(f882(x79161,a870)),x79162),x79163),f192(f882(x79161,a870)))+~E(f328(f328(f105(f882(x79161,a870)),f39(f882(x79161,a870),x79164)),x79163),f192(f882(x79161,a870)))+~P1(f328(f328(f330(f882(x79161,a870)),x79162),x79164)) % 154.70/154.56 [7989]P1(f328(f328(f330(x79891),x79892),x79893))+~P1(f328(f328(f242(f882(x79891,a870)),x79893),f328(f328(f306(x79891),x79892),x79894)))+P1(f328(f328(f242(f882(x79891,a870)),x79893),x79894)) % 154.70/154.56 [8006]P1(f328(f328(f330(x80062),f677(x80061,x80063,x80062)),f328(f170(x80062),x80063)))+P1(f328(x80061,f328(f328(f162(x80062),x80063),x80064)))+~P1(f328(f328(f243(a875),x80064),f328(f193(f876(x80062)),x80063))) % 154.70/154.56 [8014]~P1(f328(f328(f243(f882(x80141,a870)),x80142),x80144))+P1(f328(f328(f243(f882(x80141,a870)),x80142),x80143))+~P1(f328(f328(f243(f882(x80141,a870)),x80144),x80143)) % 154.70/154.56 [8015]~P1(f328(f328(f242(f882(x80151,a870)),x80152),x80154))+P1(f328(f328(f243(f882(x80151,a870)),x80152),x80153))+~P1(f328(f328(f243(f882(x80151,a870)),x80154),x80153)) % 154.70/154.56 [8016]~P1(f328(f328(f242(f882(x80161,a870)),x80164),x80163))+~P1(f328(f328(f243(f882(x80161,a870)),x80162),x80164))+P1(f328(f328(f243(f882(x80161,a870)),x80162),x80163)) % 154.70/154.56 [8017]~P1(f328(f328(f242(f882(x80171,a870)),x80172),x80174))+P1(f328(f328(f242(f882(x80171,a870)),x80172),x80173))+~P1(f328(f328(f242(f882(x80171,a870)),x80174),x80173)) % 154.70/154.56 [8057]~P1(f328(f328(f330(x80571),x80574),x80573))+~P1(f328(f328(f243(f882(x80571,a870)),x80572),f328(f328(f306(x80571),x80574),x80573)))+P1(f328(f328(f243(f882(x80571,a870)),x80572),x80573)) % 154.70/154.56 [8069]~P80(x80691)+P1(f328(f328(f243(x80691),x80692),x80693))+~P1(f328(f328(f243(x80691),f328(f328(f80(x80691),x80694),x80692)),f328(f328(f80(x80691),x80694),x80693))) % 154.70/154.56 [8071]~P80(x80711)+P1(f328(f328(f243(x80711),x80712),x80713))+~P1(f328(f328(f243(x80711),f328(f328(f80(x80711),x80712),x80714)),f328(f328(f80(x80711),x80713),x80714))) % 154.70/154.56 [8073]~P80(x80731)+P1(f328(f328(f242(x80731),x80732),x80733))+~P1(f328(f328(f242(x80731),f328(f328(f80(x80731),x80734),x80732)),f328(f328(f80(x80731),x80734),x80733))) % 154.70/154.56 [8075]~P80(x80751)+P1(f328(f328(f242(x80751),x80752),x80753))+~P1(f328(f328(f242(x80751),f328(f328(f80(x80751),x80752),x80754)),f328(f328(f80(x80751),x80753),x80754))) % 154.70/154.56 [8089]~P1(f328(f328(f328(a198,x80892),x80893),x80894))+~P1(f328(f328(f328(a198,f32(x80891,x80892)),x80894),x80893))+P1(f328(f328(f328(a198,f32(x80891,x80892)),x80893),x80893)) % 154.70/154.56 [8124]P1(f328(x81241,x81242))+~E(f328(f328(f135(x81243),f328(f193(f876(x81243)),f175(x81243,x81241,x81244))),x81244),f117(x81243))+~P1(f328(f328(f330(x81243),x81242),f328(f170(x81243),x81244))) % 154.70/154.56 [8260]P1(f328(x82601,x82602))+~P1(f328(f328(f330(x82603),x82602),f328(f170(x82603),x82604)))+P1(f328(f328(f243(a875),f328(f193(f876(x82603)),f328(f133(x82603,x82601),x82604))),f328(f193(f876(x82603)),x82604))) % 154.70/154.56 [8503]E(x85031,x85032)+P1(f328(f328(f328(a198,x85033),x85031),f436(x85032,x85031,x85033,x85034)))+~P1(f328(f328(f328(a198,f32(x85034,x85033)),x85031),x85032)) % 154.70/154.56 [8532]~P1(f328(x85324,x85322))+P1(f328(f328(f328(a198,x85321),x85322),f436(x85323,x85322,x85321,x85324)))+~P1(f328(f328(f328(a198,f32(x85324,x85321)),x85322),x85323)) % 154.70/154.56 [8739]~P1(f328(x87391,f791(x87391,x87393,x87392,x87394)))+P1(f328(x87391,f328(f328(f162(x87392),x87393),x87394)))+~P1(f328(f328(f243(a875),x87394),f328(f193(f876(x87392)),x87393))) % 154.70/154.56 [8762]~P27(x87624,x87623,x87621,f251(f882(x87624,a870)))+E(f328(x87621,f437(x87622,x87621,x87623,x87624)),x87622)+~P1(f328(f328(f330(x87623),x87622),f328(f307(x87624,x87623,x87621),f251(f882(x87624,a870))))) % 154.70/154.56 [8827]E(f175(x88271,x88272,x88273),f328(f328(f173(x88271),x88274),x88273))+P1(f328(f328(f243(a875),f759(x88272,x88273,x88271,x88274)),x88274))+P1(f328(f328(f243(a875),x88274),f328(f193(f876(x88271)),x88273))) % 154.70/154.56 [8830]E(f175(x88301,x88302,x88303),f328(f328(f173(x88301),x88304),x88303))+P1(f328(f328(f243(a875),f759(x88302,x88303,x88301,x88304)),x88304))+P1(f328(x88302,f328(f328(f162(x88301),x88303),x88304))) % 154.70/154.56 [8859]P1(f328(x88591,x88592))+~P1(f328(f328(f330(x88594),x88592),f328(f170(x88594),x88593)))+P1(f328(f328(f243(a875),f736(x88592,x88591,x88593,x88594)),f328(f193(f876(x88594)),x88593))) % 154.70/154.56 [8862]E(f175(x88621,x88622,x88623),f328(f328(f173(x88621),x88624),x88623))+P1(f328(f328(f243(a875),x88624),f328(f193(f876(x88621)),x88623)))+P1(f328(f328(f243(a875),f759(x88622,x88623,x88621,x88624)),f328(f193(f876(x88621)),x88623))) % 154.70/154.56 [8869]E(f175(x88691,x88692,x88693),f328(f328(f173(x88691),x88694),x88693))+P1(f328(x88692,f328(f328(f162(x88691),x88693),x88694)))+P1(f328(f328(f243(a875),f759(x88692,x88693,x88691,x88694)),f328(f193(f876(x88691)),x88693))) % 154.70/154.56 [8894]~P123(x88944)+P1(f328(f328(f330(x88941),f662(x88942,x88943,x88941,x88944)),x88943))+P1(f328(f328(f243(x88944),f2(x88944)),f328(f328(f9(x88941,x88944),x88942),x88943))) % 154.70/154.56 [8895]~P123(x88954)+P1(f328(f328(f330(x88951),f663(x88952,x88953,x88951,x88954)),x88953))+P1(f328(f328(f242(x88954),f2(x88954)),f328(f328(f9(x88951,x88954),x88952),x88953))) % 154.70/154.56 [8929]~P1(f328(f61(x89291),x89294))+P1(f328(f328(f330(x89291),f573(x89292,x89293,x89294,x89291)),x89294))+P1(f328(f61(f881(x89291,x89293)),f328(f328(f265(x89291,x89293),x89294),x89292))) % 154.70/154.56 [8963]P1(f328(f328(f330(x89632),f791(x89631,x89633,x89632,x89634)),f328(f170(x89632),x89633)))+P1(f328(x89631,f328(f328(f162(x89632),x89633),x89634)))+~P1(f328(f328(f243(a875),x89634),f328(f193(f876(x89632)),x89633))) % 154.70/154.56 [9069]E(x90691,x90692)+P1(f328(f328(f328(a198,f32(x90693,x90694)),f436(x90691,x90692,x90694,x90693)),x90691))+~P1(f328(f328(f328(a198,f32(x90693,x90694)),x90692),x90691)) % 154.70/154.56 [9074]~P1(f328(x90741,x90744))+P1(f328(f328(f328(a198,f32(x90741,x90742)),f436(x90743,x90744,x90742,x90741)),x90743))+~P1(f328(f328(f328(a198,f32(x90741,x90742)),x90744),x90743)) % 154.70/154.56 [9096]P1(f328(f328(f242(a875),x90964),f328(f193(f876(x90962)),f175(x90962,x90963,x90961))))+P1(f328(f328(f243(a875),f760(x90961,x90962,x90963,x90964)),x90964))+~P1(f328(f328(f242(a875),x90964),f328(f193(f876(x90962)),x90961))) % 154.70/154.56 [9200]~E(f328(f328(f176(x92001,x92002),x92003),f772(x92004,x92003,x92002,x92001)),f328(f328(f176(x92001,x92002),x92004),f772(x92004,x92003,x92002,x92001)))+E(f328(f176(x92001,x92002),x92003),f328(f176(x92001,x92002),x92004))+~E(f328(f170(x92001),f328(f328(f151(f881(x92001,x92002),x92001),f262(x92001,x92002)),x92003)),f328(f170(x92001),f328(f328(f151(f881(x92001,x92002),x92001),f262(x92001,x92002)),x92004))) % 154.70/154.56 [9246]E(f175(x92461,x92462,x92463),f328(f328(f173(x92461),x92464),x92463))+~P1(f328(x92462,f328(f328(f162(x92461),x92463),f759(x92462,x92463,x92461,x92464))))+P1(f328(f328(f243(a875),x92464),f328(f193(f876(x92461)),x92463))) % 154.70/154.56 [9250]E(f175(x92501,x92502,x92503),f328(f328(f173(x92501),x92504),x92503))+~P1(f328(x92502,f328(f328(f162(x92501),x92503),f759(x92502,x92503,x92501,x92504))))+P1(f328(x92502,f328(f328(f162(x92501),x92503),x92504))) % 154.70/154.56 [9257]~P1(f328(f61(x92571),x92573))+~P1(f328(f61(x92572),f328(x92574,f573(x92574,x92572,x92573,x92571))))+P1(f328(f61(f881(x92571,x92572)),f328(f328(f265(x92571,x92572),x92573),x92574))) % 154.70/154.56 [9265]~P123(x92651)+~P1(f328(f328(f243(x92651),f2(x92651)),f328(x92653,f662(x92653,x92654,x92652,x92651))))+P1(f328(f328(f243(x92651),f2(x92651)),f328(f328(f9(x92652,x92651),x92653),x92654))) % 154.70/154.56 [9266]~P123(x92661)+~P1(f328(f328(f242(x92661),f2(x92661)),f328(x92663,f663(x92663,x92664,x92662,x92661))))+P1(f328(f328(f242(x92661),f2(x92661)),f328(f328(f9(x92662,x92661),x92663),x92664))) % 154.70/154.56 [9272]~E(f328(f193(f876(x92724)),x92722),f328(f193(f876(x92724)),x92723))+P1(f328(f328(f330(f881(f876(x92724),f876(x92724))),f328(f328(f263(f876(x92724),f876(x92724)),x92723),x92722)),f155(x92724,x92721)))+P1(f328(f328(f243(a875),f667(x92721,x92722,x92723,x92724)),f328(f193(f876(x92724)),x92723))) % 154.70/154.56 [9326]~P1(f328(x93263,f328(f328(f162(x93262),x93264),f760(x93264,x93262,x93263,x93261))))+P1(f328(f328(f242(a875),x93261),f328(f193(f876(x93262)),f175(x93262,x93263,x93264))))+~P1(f328(f328(f242(a875),x93261),f328(f193(f876(x93262)),x93264))) % 154.70/154.56 [9403]E(f328(f328(f173(x94031),f679(x94032,x94033,x94034,x94031)),x94033),f328(f328(f173(x94031),f679(x94032,x94033,x94034,x94031)),x94034))+~P1(f328(f328(f330(f881(f876(x94031),f876(x94031))),f328(f328(f263(f876(x94031),f876(x94031)),x94034),x94033)),f144(x94031,x94032)))+P1(f328(f328(f243(a875),f328(f193(f876(x94031)),x94034)),f328(f193(f876(x94031)),x94033))) % 154.70/154.56 [9457]~P1(f328(f328(f243(a875),f2(a875)),x94573))+~P1(f328(f328(f243(a875),x94574),x94571))+P1(f328(f328(f243(a875),f328(f328(f80(a875),f328(f328(f81(a875),x94571),f44(a875,x94572,x94573))),x94574)),f328(f328(f81(a875),x94571),x94573))) % 154.70/154.56 [9649]~P108(x96492)+~P1(f328(f328(f242(x96492),f328(x96493,f868(x96494,x96493,x96491,x96492))),f328(x96494,f868(x96494,x96493,x96491,x96492))))+P1(f328(f328(f242(f882(x96491,x96492)),x96493),x96494)) % 154.70/154.56 [9753]~P65(x97531)+E(f328(f328(f6(a875,x97531),f328(f328(f18(a875,x97531,x97531),f328(f328(f8(x97531,f882(x97531,x97531),a875),f22(x97531)),x97532)),f328(f328(f8(a875,x97531,a875),x97532),f328(f328(f7(a875,a875,a875),f80(a875)),f78(a875))))),f299(a875,x97533,x97534)),f328(f328(f22(x97531),f328(x97532,x97533)),f328(x97532,f328(f328(f80(a875),x97534),f78(a875)))))+~P1(f328(f328(f242(a875),x97533),x97534)) % 154.70/154.56 [6794]E(f328(f328(f125(x67941),x67942),x67943),x67944)+~E(x67943,f328(f328(f135(x67941),f328(f193(f876(x67941)),x67942)),x67944))+~E(f328(f328(f173(x67941),f328(f193(f876(x67941)),x67942)),x67944),x67942) % 154.70/154.56 [6850]~P61(x68502)+E(x68501,f2(x68502))+E(f328(f328(f286(x68502),f328(f328(f253(x68502),x68503),x68504)),f328(f328(f253(x68502),x68501),x68504)),f328(f328(f253(x68502),f328(f328(f286(x68502),x68503),x68501)),x68504)) % 154.70/154.56 [6985]~E(f328(f193(f876(x69851)),x69853),f328(f193(f876(x69852)),x69854))+~P1(f328(f134(x69851),x69853))+E(f182(x69851,x69852,f328(f176(x69851,x69852),f328(f328(f180(x69851,x69852),x69853),x69854))),f328(f170(x69851),x69853)) % 154.70/154.56 [7002]~P100(x70021)+~P1(f328(f328(f243(x70021),x70023),x70024))+P1(f328(f328(f243(x70021),f328(f328(f105(x70021),x70022),x70023)),x70024)) % 154.70/154.56 [7003]~P100(x70031)+~P1(f328(f328(f243(x70031),x70032),x70034))+P1(f328(f328(f243(x70031),f328(f328(f105(x70031),x70032),x70033)),x70034)) % 154.70/154.56 [7005]~P105(x70051)+~P1(f328(f328(f243(x70051),x70053),x70054))+P1(f328(f328(f243(x70051),f328(f328(f240(x70051),x70052),x70053)),x70054)) % 154.70/154.56 [7007]~P105(x70071)+~P1(f328(f328(f243(x70071),x70072),x70074))+P1(f328(f328(f243(x70071),f328(f328(f240(x70071),x70072),x70073)),x70074)) % 154.70/154.56 [7008]~P100(x70081)+~P1(f328(f328(f242(x70081),x70083),x70084))+P1(f328(f328(f242(x70081),f328(f328(f105(x70081),x70082),x70083)),x70084)) % 154.70/154.56 [7009]~P100(x70091)+~P1(f328(f328(f242(x70091),x70092),x70094))+P1(f328(f328(f242(x70091),f328(f328(f105(x70091),x70092),x70093)),x70094)) % 154.70/154.56 [7011]~P105(x70111)+~P1(f328(f328(f242(x70111),x70113),x70114))+P1(f328(f328(f242(x70111),f328(f328(f240(x70111),x70112),x70113)),x70114)) % 154.70/154.56 [7013]~P105(x70131)+~P1(f328(f328(f242(x70131),x70132),x70134))+P1(f328(f328(f242(x70131),f328(f328(f240(x70131),x70132),x70133)),x70134)) % 154.70/154.56 [7033]~P1(f328(x70333,x70334))+~P1(f328(x70332,x70334))+P1(f328(f328(f328(f105(f882(x70331,a870)),x70332),x70333),x70334)) % 154.70/154.56 [7157]P26(x71571,x71572,x71573)+~P26(x71571,x71574,x71573)+~P1(f328(f328(f242(f882(f874(x71571),a870)),x71574),x71572)) % 154.70/154.56 [7158]P26(x71581,x71582,x71583)+~P26(x71581,x71582,x71584)+~P1(f328(f328(f242(f882(f874(x71581),a870)),x71583),x71584)) % 154.70/154.56 [7529]~P66(x75291)+E(f328(f328(f80(x75291),f328(x75292,x75293)),f328(f328(f6(a875,x75291),x75292),f328(f298(a875,f328(a116,x75293)),x75294))),f328(f328(f6(a875,x75291),x75292),f328(f298(a875,x75293),x75294)))+~P1(f328(f328(f243(a875),x75293),x75294)) % 154.70/154.56 [7557]~P105(x75571)+P1(f328(f328(f243(x75571),x75572),x75573))+~P1(f328(f328(f243(x75571),f328(f328(f241(x75571),x75574),x75572)),x75573)) % 154.70/154.56 [7558]~P105(x75581)+P1(f328(f328(f243(x75581),x75582),x75583))+~P1(f328(f328(f243(x75581),f328(f328(f241(x75581),x75582),x75584)),x75583)) % 154.70/154.56 [7560]~P99(x75601)+P1(f328(f328(f242(x75601),x75602),x75603))+~P1(f328(f328(f242(x75601),f328(f328(f114(x75601),x75604),x75602)),x75603)) % 154.70/154.56 [7562]~P99(x75621)+P1(f328(f328(f242(x75621),x75622),x75623))+~P1(f328(f328(f242(x75621),f328(f328(f114(x75621),x75622),x75624)),x75623)) % 154.70/154.56 [7564]~P105(x75641)+P1(f328(f328(f242(x75641),x75642),x75643))+~P1(f328(f328(f242(x75641),f328(f328(f241(x75641),x75644),x75642)),x75643)) % 154.70/154.56 [7566]~P105(x75661)+P1(f328(f328(f242(x75661),x75662),x75663))+~P1(f328(f328(f242(x75661),f328(f328(f241(x75661),x75662),x75664)),x75663)) % 154.70/154.56 [7644]~P1(f328(f328(f330(x76441),x76442),x76444))+P1(f328(f328(f330(x76441),x76442),x76443))+P1(f328(f328(f330(x76441),x76442),f328(f328(f22(f882(x76441,a870)),x76444),x76443))) % 154.70/154.56 [7728]P1(f328(x77281,x77282))+P1(f328(x77283,x77282))+~P1(f328(f328(f328(f114(f882(x77284,a870)),x77283),x77281),x77282)) % 154.70/154.56 [7739]~P1(f328(f328(f330(x77391),x77392),x77394))+~P1(f328(f328(f330(x77391),x77392),x77393))+P1(f328(f328(f330(x77391),x77392),f328(f328(f105(f882(x77391,a870)),x77393),x77394))) % 154.70/154.56 [7792]~P99(x77921)+~P1(f328(f61(x77921),x77924))+E(f328(f328(f64(x77921,x77921,f114(x77921)),x77922),f328(f328(f306(x77921),x77923),x77924)),f328(f328(f114(x77921),x77923),f328(f328(f64(x77921,x77921,f114(x77921)),x77922),x77924))) % 154.70/154.56 [7793]~P100(x77931)+~P1(f328(f61(x77931),x77934))+E(f328(f328(f64(x77931,x77931,f105(x77931)),x77932),f328(f328(f306(x77931),x77933),x77934)),f328(f328(f105(x77931),x77933),f328(f328(f64(x77931,x77931,f105(x77931)),x77932),x77934))) % 154.70/154.56 [7794]~P105(x77941)+~P1(f328(f61(x77941),x77944))+E(f328(f328(f64(x77941,x77941,f240(x77941)),x77942),f328(f328(f306(x77941),x77943),x77944)),f328(f328(f240(x77941),x77943),f328(f328(f64(x77941,x77941,f240(x77941)),x77942),x77944))) % 154.70/154.56 [7795]~P105(x77951)+~P1(f328(f61(x77951),x77954))+E(f328(f328(f64(x77951,x77951,f241(x77951)),x77952),f328(f328(f306(x77951),x77953),x77954)),f328(f328(f241(x77951),x77953),f328(f328(f64(x77951,x77951,f241(x77951)),x77952),x77954))) % 154.70/154.56 [7796]~P103(x77961)+~P91(x77961)+E(f328(f328(f22(x77961),f328(f328(f81(x77961),f328(f107(x77961),x77962)),x77963)),f328(f328(f81(x77961),f328(f107(x77961),x77962)),x77964)),f328(f328(f81(x77961),f328(f107(x77961),x77962)),f328(f328(f22(x77961),x77963),x77964))) % 154.70/154.56 [7797]~P138(x77971)+~P91(x77971)+E(f328(f328(f80(x77971),f328(f328(f81(x77971),f328(f107(x77971),x77972)),x77973)),f328(f328(f81(x77971),f328(f107(x77971),x77972)),x77974)),f328(f328(f81(x77971),f328(f107(x77971),x77972)),f328(f328(f80(x77971),x77973),x77974))) % 154.70/154.56 [7912]E(x79121,x79122)+P1(f328(f328(f330(x79123),x79121),f328(f170(x79123),x79124)))+~P1(f328(f328(f330(x79123),x79121),f328(f170(x79123),f328(f328(f148(x79123),x79122),x79124)))) % 154.70/154.56 [7937]~P59(x79371)+~E(f328(f193(f876(x79372)),x79373),f328(f193(f876(x79371)),f55(x79371)))+E(f328(f328(f176(x79371,x79372),f328(f328(f180(x79371,x79372),f55(x79371)),x79373)),x79374),f328(f235(x79372),f735(x79374,x79373,x79372,x79371))) % 154.70/154.56 [8082]P51(x80821,x80822,x80823)+~P51(x80821,x80822,x80824)+~P1(f328(f328(f242(f882(f881(x80821,x80822),a870)),x80823),x80824)) % 154.70/154.56 [8127]P1(f328(f328(f330(x81271),x81272),x81273))+P1(f328(f328(f330(x81271),x81272),x81274))+~P1(f328(f328(f330(x81271),x81272),f328(f328(f114(f882(x81271,a870)),x81274),x81273))) % 154.70/154.56 [8137]~P41(x81371,x81374,x81373)+~P1(f328(f328(f330(x81371),x81372),x81374))+P1(f328(f328(f330(f881(x81371,x81371)),f328(f328(f263(x81371,x81371),x81372),x81372)),x81373)) % 154.70/154.56 [8154]~P1(f328(f61(x81542),x81544))+~P1(f328(f61(x81541),x81543))+P1(f328(f61(f881(x81541,x81542)),f328(f328(f265(x81541,x81542),x81543),f328(f16(f882(x81542,a870),x81541),x81544)))) % 154.70/154.56 [8155]~P1(f328(f328(f330(x81551),x81552),x81554))+~P1(f328(f328(f242(f882(x81551,a870)),x81553),x81554))+P1(f328(f328(f242(f882(x81551,a870)),f328(f328(f306(x81551),x81552),x81553)),x81554)) % 154.70/154.56 [8163]~P73(x81632)+~P140(x81632)+E(f328(f328(f9(x81631,x81632),f328(f328(f8(a875,x81632,x81631),f104(x81632)),x81633)),x81634),f328(f104(x81632),f328(f328(f9(x81631,a875),x81633),x81634))) % 154.70/154.56 [8164]~P73(x81642)+~P135(x81642)+E(f328(f328(f9(x81641,x81642),f328(f328(f8(a1,x81642,x81641),f106(x81642)),x81643)),x81644),f328(f106(x81642),f328(f328(f9(x81641,a1),x81643),x81644))) % 154.70/154.56 [8193]E(f328(f328(f22(f882(x81931,a870)),x81932),f328(f328(f22(f882(x81931,a870)),x81933),x81934)),x81934)+~P1(f328(f328(f242(f882(x81931,a870)),x81932),x81933))+~P1(f328(f328(f242(f882(x81931,a870)),x81934),x81932)) % 154.70/154.56 [8293]~P1(f328(f61(x82931),x82934))+E(f328(f328(f22(a875),f328(f328(f6(x82931,a875),x82932),x82933)),f328(f328(f6(x82931,a875),x82932),x82934)),f328(f328(f6(x82931,a875),x82932),f328(f328(f22(f882(x82931,a870)),x82933),x82934)))+~P1(f328(f328(f242(f882(x82931,a870)),x82934),x82933)) % 154.70/154.56 [8447]~P8(x84471,x84474,x84473)+~P1(f328(f328(f330(x84471),x84472),x84474))+P1(f328(f328(f330(x84471),x84472),f328(f282(x84471,x84471,x84473),f328(f328(f306(x84471),x84472),f192(f882(x84471,a870)))))) % 154.70/154.56 [8508]~P1(f328(f328(f242(f882(x85081,a870)),x85082),x85083))+~P1(f328(f328(f242(f882(x85081,a870)),x85082),x85084))+P1(f328(f328(f242(f882(x85081,a870)),x85082),f328(f328(f105(f882(x85081,a870)),x85083),x85084))) % 154.70/154.56 [8612]E(x86121,f192(f882(x86122,a870)))+P1(f328(f61(x86123),x86124))+~P1(f328(f61(f881(x86123,x86122)),f328(f328(f265(x86123,x86122),x86124),f328(f16(f882(x86122,a870),x86123),x86121)))) % 154.70/154.56 [8613]E(x86131,f192(f882(x86132,a870)))+P1(f328(f61(x86133),x86134))+~P1(f328(f61(f881(x86132,x86133)),f328(f328(f265(x86132,x86133),x86131),f328(f16(f882(x86133,a870),x86132),x86134)))) % 154.70/154.56 [8682]P1(f328(f328(f330(x86821),x86822),f317(x86821,x86823)))+~P1(f328(f328(f330(x86821),x86824),f317(x86821,x86823)))+~P1(f328(f328(f330(f881(x86821,x86821)),f328(f328(f263(x86821,x86821),x86822),x86824)),x86823)) % 154.70/154.56 [8734]~P39(x87341,x87344)+P1(f328(f328(f330(f881(x87341,x87341)),f328(f328(f263(x87341,x87341),x87343),x87342)),f304(x87341,x87344)))+P39(x87341,f328(f328(f306(f881(x87341,x87341)),f328(f328(f263(x87341,x87341),x87342),x87343)),x87344)) % 154.70/154.56 [8735]~P54(x87351,x87354)+P1(f328(f328(f330(f881(x87351,x87351)),f328(f328(f263(x87351,x87351),x87353),x87352)),f304(x87351,x87354)))+P54(x87351,f328(f328(f306(f881(x87351,x87351)),f328(f328(f263(x87351,x87351),x87352),x87353)),x87354)) % 154.70/154.56 [8812]~E(x88122,x88123)+~P1(f328(f328(f330(x88121),x88122),f328(f170(x88121),x88124)))+P1(f328(f328(f330(f881(x88121,x88121)),f328(f328(f263(x88121,x88121),x88122),x88123)),f328(f170(f881(x88121,x88121)),f328(f328(f180(x88121,x88121),x88124),x88124)))) % 154.70/154.56 [8892]~E(x88923,x88924)+P1(f328(f328(f267(x88921,x88921,a870),a325),x88922))+~P1(f328(f328(f330(f881(x88921,x88921)),x88922),f328(f170(f881(x88921,x88921)),f328(f328(f180(x88921,x88921),x88923),x88924)))) % 154.70/154.56 [8920]~P1(f328(x89204,x89202))+P1(f328(f328(f328(f328(a200,x89201),x89202),x89203),f344(x89203,x89202,x89201,x89204)))+~P1(f328(f328(f328(f328(a200,f32(x89204,x89201)),x89202),x89203),x89202)) % 154.70/154.56 [8947]P1(f328(f328(f330(f881(f876(x89471),f876(x89471))),f328(f328(f263(f876(x89471),f876(x89471)),x89472),x89473)),f144(x89471,x89474)))+~E(f328(f328(f173(x89471),f328(f193(f876(x89471)),x89472)),x89473),x89472)+~P1(f328(f328(f243(a875),f328(f193(f876(x89471)),x89472)),f328(f193(f876(x89471)),x89473))) % 154.70/154.56 [9045]~P1(f328(f61(x90451),x90454))+P1(f328(f328(f330(x90451),f687(x90452,x90453,x90454,x90451)),x90454))+P1(f328(f61(x90453),f328(f328(f41(x90451,f882(x90453,a870)),x90454),x90452))) % 154.70/154.56 [9046]~P1(f328(f61(x90461),x90464))+P1(f328(f328(f330(x90461),f818(x90462,x90463,x90464,x90461)),x90464))+P1(f328(f61(x90463),f328(f328(f41(x90461,f882(x90463,a870)),x90464),x90462))) % 154.70/154.56 [9130]P1(f328(f328(f330(f881(x91301,x91301)),x91302),f328(f328(f285(x91301,x91301,x91301),x91303),f304(x91301,x91303))))+~P1(f328(f328(f243(a875),f2(a875)),x91304))+~P1(f328(f328(f330(f881(x91301,x91301)),x91302),f328(f328(f187(f881(x91301,x91301),a870),x91304),x91303))) % 154.70/154.56 [9138]~P39(x91381,x91382)+~P1(f328(f328(f330(f881(x91381,x91381)),f328(f328(f263(x91381,x91381),x91384),x91383)),x91382))+~P1(f328(f328(f330(f881(x91381,x91381)),f328(f328(f263(x91381,x91381),x91383),x91384)),x91382)) % 154.70/154.56 [9264]~P1(f328(f61(x92641),x92644))+E(f328(f328(f6(x92641,a875),f328(f328(f8(f882(x92642,a870),a875,x92641),f37(x92642)),x92643)),x92644),f328(f37(f881(x92641,x92642)),f328(f328(f265(x92641,x92642),x92644),x92643)))+P1(f328(f328(f330(x92641),f574(x92643,x92642,x92644,x92641)),x92644)) % 154.70/154.56 [9268]~P1(f328(f134(x92681),x92682))+P1(f328(f134(x92681),f328(f328(f156(x92681,x92682),x92683),x92684)))+P1(f328(f328(f330(x92681),x92684),f328(f328(f22(f882(x92681,a870)),f328(f170(x92681),x92682)),f328(f328(f306(x92681),f328(f328(f162(x92681),x92682),x92683)),f192(f882(x92681,a870)))))) % 154.70/154.56 [9284]~P1(f328(f61(x92842),x92843))+~P1(f328(f61(x92841),f328(x92844,f687(x92844,x92841,x92843,x92842))))+P1(f328(f61(x92841),f328(f328(f41(x92842,f882(x92841,a870)),x92843),x92844))) % 154.70/154.56 [9285]~P1(f328(f61(x92852),x92853))+~P1(f328(f61(x92851),f328(x92854,f818(x92854,x92851,x92853,x92852))))+P1(f328(f61(x92851),f328(f328(f41(x92852,f882(x92851,a870)),x92853),x92854))) % 154.70/154.56 [9364]~P1(f328(f328(f330(f881(x93641,x93641)),x93642),f328(f328(f285(x93641,x93641,x93641),x93644),f304(x93641,x93644))))+P1(f328(f328(f330(f881(x93641,x93641)),x93642),f328(f328(f285(x93641,x93641,x93641),x93643),f304(x93641,x93643))))+~P1(f328(f328(f242(f882(f881(x93641,x93641),a870)),x93644),x93643)) % 154.70/154.56 [9371]E(f328(f328(f173(x93711),f679(x93714,x93713,x93712,x93711)),x93713),f328(f328(f173(x93711),f679(x93714,x93713,x93712,x93711)),x93712))+~P1(f328(f328(f330(f881(f876(x93711),f876(x93711))),f328(f328(f263(f876(x93711),f876(x93711)),x93712),x93713)),f144(x93711,x93714)))+E(f328(f328(f173(x93711),f328(f193(f876(x93711)),x93712)),x93713),x93712) % 154.70/154.56 [9387]~P1(f328(f61(x93871),x93874))+E(f328(f328(f6(x93871,a875),f328(f328(f8(f882(x93872,a870),a875,x93871),f37(x93872)),x93873)),x93874),f328(f37(f881(x93871,x93872)),f328(f328(f265(x93871,x93872),x93874),x93873)))+~P1(f328(f61(x93872),f328(x93873,f574(x93873,x93872,x93874,x93871)))) % 154.70/154.56 [9391]~E(f328(f193(f876(x93911)),x93913),f328(f193(f876(x93911)),x93912))+P1(f328(f328(f330(f881(f876(x93911),f876(x93911))),f328(f328(f263(f876(x93911),f876(x93911)),x93912),x93913)),f155(x93911,x93914)))+P1(f328(f328(f330(f881(x93911,x93911)),f683(x93914,x93913,x93912,x93911)),f328(f170(f881(x93911,x93911)),f328(f328(f180(x93911,x93911),x93912),x93913)))) % 154.70/154.56 [9469]~P1(f328(f328(f330(f881(f876(x94691),f876(x94691))),f328(f328(f263(f876(x94691),f876(x94691)),x94692),x94693)),f144(x94691,x94694)))+E(f328(f328(f173(x94691),f328(f193(f876(x94691)),x94692)),x94693),x94692)+P1(f328(f328(f243(a875),f679(x94694,x94693,x94692,x94691)),f328(f328(f240(a875),f328(f193(f876(x94691)),x94692)),f328(f193(f876(x94691)),x94693)))) % 154.70/154.56 [9470]E(f328(f176(x94701,x94702),x94703),f328(f176(x94701,x94702),x94704))+~E(f328(f170(x94701),f328(f328(f151(f881(x94701,x94702),x94701),f262(x94701,x94702)),x94703)),f328(f170(x94701),f328(f328(f151(f881(x94701,x94702),x94701),f262(x94701,x94702)),x94704)))+P1(f328(f328(f330(x94701),f772(x94703,x94704,x94702,x94701)),f328(f170(x94701),f328(f328(f151(f881(x94701,x94702),x94701),f262(x94701,x94702)),x94704)))) % 154.70/154.56 [9486]~P1(f328(x94861,x94864))+P1(f328(f328(f328(f328(a200,f32(x94861,x94862)),f344(x94863,x94864,x94862,x94861)),x94863),x94864))+~P1(f328(f328(f328(f328(a200,f32(x94861,x94862)),x94864),x94863),x94864)) % 154.70/154.56 [9491]~P1(f328(f328(f330(f881(f876(x94911),f876(x94911))),f328(f328(f263(f876(x94911),f876(x94911)),x94912),x94913)),f144(x94911,x94914)))+P1(f328(f328(f243(a875),f328(f193(f876(x94911)),x94912)),f328(f193(f876(x94911)),x94913)))+P1(f328(f328(f243(a875),f679(x94914,x94913,x94912,x94911)),f328(f328(f240(a875),f328(f193(f876(x94911)),x94912)),f328(f193(f876(x94911)),x94913)))) % 154.70/154.56 [9790]~P1(f328(f328(f328(x97901,f726(x97901,x97904,x97903,x97902)),f727(x97901,x97904,x97903,x97902)),f728(x97901,x97904,x97903,x97902)))+P1(f328(f328(f328(x97901,x97902),x97903),x97904))+~P1(f328(f316(f881(f882(a1,f879(f876(a324))),f881(a1,a1)),a314),f328(f328(f263(f882(a1,f879(f876(a324))),f881(a1,a1)),x97902),f328(f328(f263(a1,a1),x97903),x97904)))) % 154.70/154.56 [9869]P1(f328(f328(f328(x98691,x98692),x98693),x98694))+P1(f328(f316(f881(f882(a1,f879(f876(a324))),f881(a1,a1)),a314),f328(f328(f263(f882(a1,f879(f876(a324))),f881(a1,a1)),f726(x98691,x98694,x98693,x98692)),f328(f328(f263(a1,a1),f727(x98691,x98694,x98693,x98692)),f728(x98691,x98694,x98693,x98692)))))+~P1(f328(f316(f881(f882(a1,f879(f876(a324))),f881(a1,a1)),a314),f328(f328(f263(f882(a1,f879(f876(a324))),f881(a1,a1)),x98692),f328(f328(f263(a1,a1),x98693),x98694)))) % 154.70/154.56 [9908]~P1(f328(f328(f330(f881(f876(x99081),f876(x99081))),f328(f328(f263(f876(x99081),f876(x99081)),x99082),x99083)),f144(x99081,x99084)))+E(f328(f328(f173(x99081),f328(f193(f876(x99081)),x99082)),x99083),x99082)+P1(f328(f328(f330(f881(x99081,x99081)),f328(f328(f263(x99081,x99081),f328(f328(f162(x99081),x99082),f679(x99084,x99083,x99082,x99081))),f328(f328(f162(x99081),x99083),f679(x99084,x99083,x99082,x99081)))),x99084)) % 154.70/154.56 [9909]~P1(f328(f328(f330(f881(f876(x99091),f876(x99091))),f328(f328(f263(f876(x99091),f876(x99091)),x99092),x99093)),f144(x99091,x99094)))+P1(f328(f328(f243(a875),f328(f193(f876(x99091)),x99092)),f328(f193(f876(x99091)),x99093)))+P1(f328(f328(f330(f881(x99091,x99091)),f328(f328(f263(x99091,x99091),f328(f328(f162(x99091),x99092),f679(x99094,x99093,x99092,x99091))),f328(f328(f162(x99091),x99093),f679(x99094,x99093,x99092,x99091)))),x99094)) % 154.70/154.56 [9966]~E(f328(f193(f876(x99661)),x99662),f328(f193(f876(x99661)),x99663))+P1(f328(f328(f330(f881(f876(x99661),f876(x99661))),f328(f328(f263(f876(x99661),f876(x99661)),x99662),x99663)),f155(x99661,x99664)))+~P1(f328(f328(f330(f881(x99661,x99661)),f328(f328(f263(x99661,x99661),f328(f328(f162(x99661),x99662),f667(x99664,x99663,x99662,x99661))),f328(f328(f162(x99661),x99663),f667(x99664,x99663,x99662,x99661)))),x99664)) % 154.70/154.56 [10101]~P66(x101011)+~P1(f328(f61(x101012),x101014))+E(f328(f163(x101011),f328(f328(f151(x101012,x101011),x101013),f90(f876(x101012),f328(f328(f18(f876(x101012),a870,a870),f328(f328(f8(a870,f882(a870,a870),f876(x101012)),a326),f328(f328(f7(f876(x101012),f882(x101012,a870),a870),f328(f328(f8(f882(x101012,a870),f882(f882(x101012,a870),a870),f876(x101012)),a325),f170(x101012))),x101014))),f134(x101012))))),f233(x101012,x101011,x101013,x101014)) % 154.70/154.56 [7371]~P60(x73712)+E(x73711,f2(x73712))+E(f328(f328(f286(x73712),f328(f328(f80(x73712),x73713),f328(f328(f81(x73712),x73714),x73711))),x73711),f328(f328(f80(x73712),x73714),f328(f328(f286(x73712),x73713),x73711))) % 154.70/154.56 [7372]~P57(x73722)+E(x73721,f2(x73722))+E(f328(f328(f38(x73722),f328(f328(f80(x73722),x73723),f328(f328(f81(x73722),x73724),x73721))),x73721),f328(f328(f80(x73722),x73724),f328(f328(f38(x73722),x73723),x73721))) % 154.70/154.56 [7373]~P57(x73732)+E(x73731,f2(x73732))+E(f328(f328(f38(x73732),f328(f328(f80(x73732),x73733),f328(f328(f81(x73732),x73731),x73734))),x73731),f328(f328(f80(x73732),x73734),f328(f328(f38(x73732),x73733),x73731))) % 154.70/154.56 [7607]~P61(x76072)+E(x76071,f2(x76072))+E(f328(f328(f286(x76072),f328(f328(f22(x76072),x76073),f328(f328(f81(x76072),x76071),x76074))),x76071),f328(f328(f22(x76072),f328(f328(f286(x76072),x76073),x76071)),x76074)) % 154.70/154.56 [7608]~P60(x76082)+E(x76081,f2(x76082))+E(f328(f328(f286(x76082),f328(f328(f80(x76082),x76083),f328(f328(f81(x76082),x76084),x76081))),x76081),f328(f328(f80(x76082),f328(f328(f286(x76082),x76083),x76081)),x76084)) % 154.70/154.56 [7609]~P61(x76092)+E(x76091,f2(x76092))+E(f328(f328(f286(x76092),f328(f328(f80(x76092),x76093),f328(f328(f81(x76092),x76091),x76094))),x76091),f328(f328(f80(x76092),f328(f328(f286(x76092),x76093),x76091)),x76094)) % 154.70/154.56 [8322]~P1(f328(f157(x83221,x83223),x83224))+~P1(f328(f157(x83221,x83222),x83224))+P1(f328(f157(x83221,f328(f328(f105(f882(x83221,a870)),x83222),x83223)),x83224)) % 154.70/154.56 [8696]~E(f328(f328(f285(x86961,x86961,x86961),x86962),x86964),f192(f882(f881(x86961,x86961),a870)))+~E(f328(f328(f285(x86961,x86961,x86961),x86962),x86963),f192(f882(f881(x86961,x86961),a870)))+E(f328(f328(f285(x86961,x86961,x86961),x86962),f328(f328(f114(f882(f881(x86961,x86961),a870)),x86963),x86964)),f192(f882(f881(x86961,x86961),a870))) % 154.70/154.56 [8813]~P1(f328(f328(f242(f882(x88131,a870)),x88133),x88134))+~P1(f328(f328(f242(f882(x88131,a870)),x88132),x88134))+P1(f328(f328(f242(f882(x88131,a870)),f328(f328(f114(f882(x88131,a870)),x88132),x88133)),x88134)) % 154.70/154.56 [9194]~P1(f328(f61(x91941),x91944))+~P1(f328(f61(x91941),x91943))+E(f328(f328(f22(a875),f328(f328(f80(a875),f328(f328(f6(x91941,a875),x91942),x91943)),f328(f328(f6(x91941,a875),x91942),x91944))),f328(f328(f6(x91941,a875),x91942),f328(f328(f105(f882(x91941,a870)),x91943),x91944))),f328(f328(f6(x91941,a875),x91942),f328(f328(f114(f882(x91941,a870)),x91943),x91944))) % 154.70/154.56 [9281]~P1(f328(f328(f330(x92811),x92813),x92812))+~P1(f328(f328(f242(f882(x92811,a870)),x92812),f328(f328(f306(x92811),x92813),x92814)))+P1(f328(f328(f242(f882(x92811,a870)),f328(f328(f22(f882(x92811,a870)),x92812),f328(f328(f306(x92811),x92813),f192(f882(x92811,a870))))),x92814)) % 154.70/154.56 [9441]~P1(f328(f328(f330(x94411),x94413),x94412))+P1(f328(f328(f242(f882(x94411,a870)),x94412),f328(f328(f306(x94411),x94413),x94414)))+~P1(f328(f328(f242(f882(x94411,a870)),f328(f328(f22(f882(x94411,a870)),x94412),f328(f328(f306(x94411),x94413),f192(f882(x94411,a870))))),x94414)) % 154.70/154.56 [9531]~P1(f328(f328(f243(a875),x95312),x95314))+~P1(f328(f328(f242(a875),x95311),x95313))+P1(f328(f328(f330(f881(f881(a875,a875),f881(a875,a875))),f328(f328(f263(f881(a875,a875),f881(a875,a875)),f328(f328(f263(a875,a875),x95311),x95312)),f328(f328(f263(a875,a875),x95313),x95314))),a35)) % 154.70/154.56 [9532]~P1(f328(f328(f242(a875),x95322),x95324))+~P1(f328(f328(f242(a875),x95321),x95323))+P1(f328(f328(f330(f881(f881(a875,a875),f881(a875,a875))),f328(f328(f263(f881(a875,a875),f881(a875,a875)),f328(f328(f263(a875,a875),x95321),x95322)),f328(f328(f263(a875,a875),x95323),x95324))),a70)) % 154.70/154.56 [9829]~P1(f328(f328(f330(f876(x98291)),x98294),f158(x98291,x98293)))+~P1(f328(f328(f330(f876(x98291)),x98294),f158(x98291,x98292)))+P1(f328(f157(x98291,f328(f328(f105(f882(x98291,a870)),f328(f328(f7(x98291,f882(x98291,a870),a870),f330(x98291)),x98292)),f328(f328(f7(x98291,f882(x98291,a870),a870),f330(x98291)),x98293))),x98294)) % 154.70/154.56 [9931]~P27(x99311,f882(f882(x99311,a870),a870),f328(f328(f7(x99311,f882(f881(x99311,x99311),a870),f882(f882(x99311,a870),a870)),f328(f328(f8(f882(x99311,a870),f882(f882(f881(x99311,x99311),a870),f882(f882(x99311,a870),a870)),x99311),f60(x99311)),f328(f328(f7(x99311,f882(x99311,a870),f882(x99311,a870)),f306(x99311)),f192(f882(x99311,a870))))),x99313),x99312)+~P1(f328(f328(f330(x99311),x99314),x99312))+E(f328(f328(f22(f882(f882(x99311,a870),a870)),f328(f328(f60(x99311),x99312),x99313)),f328(f328(f60(x99311),f328(f328(f306(x99311),x99314),f192(f882(x99311,a870)))),x99313)),f328(f328(f60(x99311),f328(f328(f22(f882(x99311,a870)),x99312),f328(f328(f306(x99311),x99314),f192(f882(x99311,a870))))),x99313)) % 154.70/154.56 [10065]~P41(x100651,x100652,x100654)+~P1(f328(f328(f330(f881(x100651,x100651)),x100653),x100654))+P1(f328(f328(f267(x100651,x100651,a870),f328(f328(f7(x100651,f882(x100651,a870),f882(x100651,a870)),f328(f328(f8(f882(a870,a870),f882(f882(x100651,a870),f882(x100651,a870)),x100651),f8(a870,a870,x100651)),f328(f328(f8(a870,f882(a870,a870),x100651),a326),f328(f328(f7(x100651,f882(x100651,a870),a870),f330(x100651)),x100652)))),f328(f328(f7(x100651,f882(x100651,a870),a870),f330(x100651)),x100652))),x100653)) % 154.70/154.56 [10077]P1(f328(f61(x100771),x100772))+~P1(f328(f61(x100773),f328(f307(x100771,x100773,x100774),x100772)))+~P1(f328(f61(x100771),f328(f248(x100771),f328(f328(f18(x100771,a870,a870),f328(f328(f8(a870,f882(a870,a870),x100771),a326),f328(f328(f7(x100771,f882(x100771,a870),a870),f330(x100771)),x100772))),f328(f328(f7(x100771,x100773,a870),f328(f328(f8(x100773,f882(x100773,a870),x100771),a325),x100774)),f328(x100774,f466(x100774,x100773,x100772,x100771))))))) % 154.70/154.56 [8064]~P61(x80642)+E(x80641,f2(x80642))+E(f328(f328(f286(x80642),f328(f328(f22(x80642),f328(f328(f81(x80642),x80641),x80643)),x80644)),x80641),f328(f328(f22(x80642),x80643),f328(f328(f286(x80642),x80644),x80641))) % 154.70/154.56 [8065]~P61(x80652)+E(x80651,f2(x80652))+E(f328(f328(f286(x80652),f328(f328(f80(x80652),f328(f328(f81(x80652),x80651),x80653)),x80654)),x80651),f328(f328(f80(x80652),x80653),f328(f328(f286(x80652),x80654),x80651))) % 154.70/154.56 [8979]~E(f328(f328(f285(x89791,x89791,x89791),x89793),x89794),f192(f882(f881(x89791,x89791),a870)))+~E(f328(f328(f285(x89791,x89791,x89791),x89792),x89794),f192(f882(f881(x89791,x89791),a870)))+E(f328(f328(f285(x89791,x89791,x89791),f328(f328(f114(f882(f881(x89791,x89791),a870)),x89792),x89793)),x89794),f192(f882(f881(x89791,x89791),a870))) % 154.70/154.56 [10008]~P142(x100081)+~P142(x100082)+E(f328(f328(f313(x100081),f328(f328(f7(x100081,a103,f879(f876(a324))),f328(f328(f8(f882(x100082,f879(f876(a324))),f882(a103,f879(f876(a324))),x100081),f313(x100082)),f328(f328(f8(f882(x100082,f881(x100081,x100082)),f882(x100082,f879(f876(a324))),x100081),f328(f8(f881(x100081,x100082),f879(f876(a324)),x100082),x100083)),f263(x100081,x100082)))),x100084)),x100084),f328(f328(f313(f881(x100081,x100082)),x100083),x100084)) % 154.70/154.56 [9738]~P1(f328(f157(x97381,x97383),x97384))+~P1(f328(f157(x97381,x97382),x97384))+P1(f328(f157(x97381,f328(f328(f18(x97381,a870,a870),f328(f328(f8(a870,f882(a870,a870),x97381),a326),x97382)),x97383)),x97384)) % 154.70/154.56 [10000]P1(f328(x100001,f463(x100002,x100003,x100001,x100004)))+~P1(f328(f61(x100004),f328(f248(x100004),x100001)))+P1(f328(f61(x100003),f328(f248(x100003),f328(f328(f8(f882(x100004,a870),a870,x100003),f87(x100004)),f328(f328(f8(f882(x100004,a870),f882(x100004,a870),x100003),f328(f18(x100004,a870,a870),f328(f328(f8(a870,f882(a870,a870),x100004),a326),x100001))),x100002))))) % 154.70/154.56 [10021]~P1(f328(f61(x100212),f328(f248(x100212),x100213)))+~P1(f328(f61(x100211),f328(f248(x100211),f328(f328(f7(x100211,x100212,a870),x100214),f463(x100214,x100211,x100213,x100212)))))+P1(f328(f61(x100211),f328(f248(x100211),f328(f328(f8(f882(x100212,a870),a870,x100211),f87(x100212)),f328(f328(f8(f882(x100212,a870),f882(x100212,a870),x100211),f328(f18(x100212,a870,a870),f328(f328(f8(a870,f882(a870,a870),x100212),a326),x100213))),x100214))))) % 154.70/154.56 [5015]~E(x50152,x50154)+E(f168(x50151,x50152,x50153),f168(x50151,x50154,x50155))+~E(x50152,f2(a875)) % 154.70/154.56 [5277]E(x52771,x52772)+~E(f168(x52774,x52773,x52771),f168(x52774,x52775,x52772))+E(x52773,f2(a875)) % 154.70/154.56 [6512]E(x65121,x65122)+~E(f328(x65123,x65121),f328(x65123,x65122))+~P27(x65124,x65125,x65123,f251(f882(x65124,a870))) % 154.70/154.56 [6672]~E(f328(x66723,x66725),f205(x66722))+~E(f328(x66724,x66725),f205(x66722))+E(f328(f183(x66721,x66722,x66723,x66724),x66725),f205(x66722)) % 154.70/154.56 [7406]E(x74061,x74062)+~P27(x74063,x74064,x74065,f251(f882(x74063,a870)))+~E(f328(f307(x74063,x74064,x74065),x74061),f328(f307(x74063,x74064,x74065),x74062)) % 154.70/154.56 [7661]P27(x76612,x76613,f429(x76614,x76613,x76612,x76611),x76611)+~E(f328(f307(x76613,x76612,x76615),x76614),x76611)+E(x76611,f192(f882(x76612,a870))) % 154.70/154.56 [8207]~P1(f328(f328(x82073,x82072),x82075))+~P1(f328(f328(x82073,x82074),x82072))+P1(f328(f328(f330(x82071),x82072),f295(x82071,x82073,x82074,x82075))) % 154.70/154.56 [8208]~P1(f328(f328(x82083,x82082),x82085))+~P1(f328(f328(x82083,x82084),x82082))+P1(f328(f328(f330(x82081),x82082),f292(x82081,x82083,x82084,x82085))) % 154.70/154.56 [8771]~P27(x87711,x87713,x87715,f251(f882(x87711,a870)))+~P27(x87713,x87712,x87714,f251(f882(x87713,a870)))+P27(x87711,x87712,f328(f73(x87713,x87712,x87711,x87714),x87715),f251(f882(x87711,a870))) % 154.70/154.56 [9340]P1(f328(f328(f330(f881(x93401,x93401)),f328(f328(f263(x93401,x93401),x93402),x93403)),f304(x93401,x93404)))+~P1(f328(f328(f330(f881(x93401,x93401)),f328(f328(f263(x93401,x93401),x93402),x93405)),f304(x93401,x93404)))+~P1(f328(f328(f330(f881(x93401,x93401)),f328(f328(f263(x93401,x93401),x93405),x93403)),f304(x93401,x93404))) % 154.70/154.56 [9378]~P105(x93782)+~P1(f328(f134(x93781),x93785))+P1(f328(f134(x93781),f146(x93781,x93782,x93783,x93784,x93785))) % 154.70/154.56 [5347]~E(x53472,f117(x53471))+E(f328(f328(f125(x53471),x53472),x53473),f328(f328(f148(x53471),x53474),x53475))+~E(x53473,f328(f328(f148(x53471),x53474),x53475)) % 154.70/154.56 [5348]~E(x53482,f117(x53481))+E(f328(f328(f125(x53481),x53482),x53483),f328(f328(f148(x53481),x53484),x53485))+~E(f328(f328(f148(x53481),x53484),x53485),x53483) % 154.70/154.56 [6469]~E(f328(f193(f876(x64691)),x64695),f328(f193(f876(x64692)),x64694))+E(f328(f328(f151(f881(x64691,x64692),x64692),f266(x64691,x64692)),x64693),x64694)+~E(f328(f328(f180(x64691,x64692),x64695),x64694),x64693) % 154.70/154.56 [6470]~E(f328(f193(f876(x64701)),x64704),f328(f193(f876(x64702)),x64705))+E(f328(f328(f151(f881(x64701,x64702),x64701),f262(x64701,x64702)),x64703),x64704)+~E(f328(f328(f180(x64701,x64702),x64704),x64705),x64703) % 154.70/154.56 [6944]~P105(x69441)+~P16(x69441,f328(f328(f151(x69442,x69441),x69443),x69445))+P16(x69441,f328(f328(f151(x69442,x69441),x69443),f328(f133(x69442,x69444),x69445))) % 154.70/154.56 [6989]~P1(f328(x69893,x69895))+~P1(f328(f328(x69892,x69894),x69895))+P1(f328(f328(f95(x69891,x69892,x69893),x69894),x69895)) % 154.70/154.56 [7086]~P105(x70861)+P16(x70861,f328(f328(f151(x70862,x70861),x70863),f167(x70862,x70864,x70865)))+~P16(x70861,f328(f328(f151(x70862,x70861),x70863),x70865)) % 154.70/154.56 [7109]~P51(x71093,x71092,x71095)+~P51(x71091,x71093,x71094)+P51(x71091,x71092,f328(f328(f285(x71091,x71093,x71092),x71094),x71095)) % 154.70/154.56 [7203]E(x72031,x72032)+~P27(x72033,x72034,x72035,f251(f882(x72033,a870)))+~E(f328(f328(f151(x72033,x72034),x72035),x72031),f328(f328(f151(x72033,x72034),x72035),x72032)) % 154.70/154.56 [7357]~P1(f328(f328(f243(a875),x73571),f328(x73573,x73575)))+P1(f328(f328(f243(a875),x73571),f152(x73572,x73573,x73574)))+~P1(f328(f328(f330(x73572),x73575),f328(f170(x73572),x73574))) % 154.70/154.56 [7358]~P1(f328(f328(f242(a875),x73581),f328(x73583,x73585)))+P1(f328(f328(f242(a875),x73581),f152(x73582,x73583,x73584)))+~P1(f328(f328(f330(x73582),x73585),f328(f170(x73582),x73584))) % 154.70/154.56 [7761]P1(f328(x77611,x77612))+~P1(f328(x77611,x77613))+~P1(f328(f328(f330(x77614),x77612),f328(f170(x77614),f168(x77614,x77615,x77613)))) % 154.70/154.56 [7762]P1(f328(x77621,x77622))+~P1(f328(x77621,x77623))+~P1(f328(f328(f330(x77624),x77623),f328(f170(x77624),f168(x77624,x77625,x77622)))) % 154.70/154.56 [7767]~P107(x77671)+P1(f328(f328(f242(f882(x77671,a870)),f299(x77671,x77672,x77673)),f299(x77671,x77674,x77675)))+P1(f328(f328(f242(x77671),x77672),x77673)) % 154.70/154.56 [7790]~P5(x77901)+P1(f328(f328(f242(x77901),f328(f328(f42(x77902,x77901),x77903),x77904)),f328(x77904,x77905)))+~P1(f328(f328(f330(x77902),x77905),x77903)) % 154.70/154.56 [7858]~P27(x78581,x78582,x78584,x78583)+E(f328(f77(x78581,x78582,x78583,x78584),f328(x78584,x78585)),x78585)+~P1(f328(f328(f330(x78581),x78585),x78583)) % 154.70/154.56 [8052]~P1(f328(x80521,x80525))+P1(f328(x80521,f348(x80521,x80522,x80523,x80524)))+~P1(f328(f328(f330(x80524),x80525),x80523)) % 154.70/154.56 [8053]~P1(f328(x80531,x80535))+P1(f328(x80531,f348(x80531,x80532,x80533,x80534)))+~P1(f328(f328(f330(x80534),x80535),x80532)) % 154.70/154.56 [8152]P1(f328(f61(x81521),x81522))+~P1(f328(f61(x81523),x81524))+~P1(f328(f328(f242(f882(x81521,a870)),x81522),f328(f307(x81523,x81521,x81525),x81524))) % 154.70/154.56 [8326]E(x83261,x83262)+~P27(x83263,x83264,x83265,f328(f328(f114(f882(x83263,a870)),f328(f170(x83263),x83261)),f328(f170(x83263),x83262)))+~E(f328(f328(f151(x83263,x83264),x83265),x83261),f328(f328(f151(x83263,x83264),x83265),x83262)) % 154.70/154.56 [8380]~P107(x83801)+~P1(f328(f328(f243(f882(x83801,a870)),f299(x83801,x83804,x83805)),f299(x83801,x83802,x83803)))+P1(f328(f328(f242(x83801),x83802),x83803)) % 154.70/154.56 [8445]~P27(x84451,x84454,x84455,f251(f882(x84451,a870)))+~P1(f328(f328(f330(x84454),f328(x84455,x84452)),f328(f307(x84451,x84454,x84455),x84453)))+P1(f328(f328(f330(x84451),x84452),x84453)) % 154.70/154.56 [8521]P1(f328(x85211,x85212))+~P1(f328(x85211,f831(x85211,x85213,x85214,x85215)))+~P1(f328(f328(f330(x85215),x85212),x85214)) % 154.70/154.56 [8522]P1(f328(x85221,x85222))+~P1(f328(x85221,f831(x85221,x85223,x85224,x85225)))+~P1(f328(f328(f330(x85225),x85222),x85223)) % 154.70/154.56 [8810]~P27(x88102,x88103,x88101,x88104)+E(f328(x88101,f328(f77(x88102,x88103,x88104,x88101),x88105)),x88105)+~P1(f328(f328(f330(x88103),x88105),f328(f307(x88102,x88103,x88101),x88104))) % 154.70/154.56 [8914]E(x89141,f117(x89142))+E(f328(f328(f148(x89142),x89143),f695(x89144,x89143,x89145,x89141,x89142)),x89141)+~E(f328(f328(f125(x89142),x89141),x89145),f328(f328(f148(x89142),x89143),x89144)) % 154.70/154.56 [8915]E(x89151,f117(x89152))+E(f328(f328(f148(x89152),x89153),f696(x89154,x89151,x89155,x89153,x89152)),x89151)+~E(f328(f328(f125(x89152),x89151),x89154),f328(f328(f148(x89152),x89153),x89155)) % 154.70/154.56 [8933]E(f328(f328(f148(x89332),x89333),f695(x89334,x89333,x89331,x89335,x89332)),x89335)+~E(f328(f328(f125(x89332),x89335),x89331),f328(f328(f148(x89332),x89333),x89334))+E(x89331,f328(f328(f148(x89332),x89333),x89334)) % 154.70/154.56 [8934]E(f328(f328(f148(x89341),x89342),f696(x89344,x89345,x89343,x89342,x89341)),x89345)+~E(f328(f328(f125(x89341),x89345),x89344),f328(f328(f148(x89341),x89342),x89343))+E(f328(f328(f148(x89341),x89342),x89343),x89344) % 154.70/154.56 [9015]~E(f328(f307(x90153,x90152,x90154),f251(f882(x90153,a870))),f251(f882(x90152,a870)))+~E(f328(f307(x90151,x90153,x90155),f251(f882(x90151,a870))),f251(f882(x90153,a870)))+E(f328(f307(x90151,x90152,f328(f73(x90153,x90152,x90151,x90154),x90155)),f251(f882(x90151,a870))),f251(f882(x90152,a870))) % 154.70/154.56 [9384]E(x93841,f117(x93842))+~E(f328(f328(f125(x93842),x93841),x93843),f328(f328(f148(x93842),x93845),x93844))+E(f328(f328(f125(x93842),f696(x93843,x93841,x93844,x93845,x93842)),x93843),x93844) % 154.70/154.56 [9385]E(x93851,f117(x93852))+~E(f328(f328(f125(x93852),x93851),x93855),f328(f328(f148(x93852),x93854),x93853))+E(f328(f328(f125(x93852),f695(x93853,x93854,x93855,x93851,x93852)),x93855),x93853) % 154.70/154.56 [9392]E(f328(f328(f125(x93922),f695(x93924,x93923,x93921,x93925,x93922)),x93921),x93924)+~E(f328(f328(f125(x93922),x93925),x93921),f328(f328(f148(x93922),x93923),x93924))+E(x93921,f328(f328(f148(x93922),x93923),x93924)) % 154.70/154.56 [9393]~E(f328(f328(f125(x93931),x93935),x93934),f328(f328(f148(x93931),x93932),x93933))+E(f328(f328(f125(x93931),f696(x93934,x93935,x93933,x93932,x93931)),x93934),x93933)+E(f328(f328(f148(x93931),x93932),x93933),x93934) % 154.70/154.56 [9394]E(f328(f328(f125(x93941),x93945),f698(x93943,x93942,x93944,x93945,x93941)),x93942)+E(f328(f328(f125(x93941),x93942),f697(x93943,x93942,x93944,x93945,x93941)),x93945)+~E(f328(f328(f125(x93941),x93945),x93944),f328(f328(f125(x93941),x93942),x93943)) % 154.70/154.56 [9427]~P105(x94271)+P16(x94271,f328(f328(f151(x94272,x94271),x94273),f146(x94272,x94271,x94273,x94274,x94275)))+~P16(x94271,f328(f328(f151(x94272,x94271),x94273),x94275)) % 154.70/154.56 [9438]~P55(x94385,x94381,x94384,x94383)+P1(f328(f328(x94381,x94382),f560(x94383,x94384,x94381,x94385,x94382)))+~P1(f328(f328(f330(x94385),x94382),x94384)) % 154.70/154.56 [9544]~P1(f328(f328(f330(f881(x95441,x95441)),f328(f328(f263(x95441,x95441),x95445),x95443)),f304(x95441,x95444)))+P1(f328(f328(f330(f881(x95441,x95441)),f328(f328(f263(x95441,x95441),x95442),x95443)),f328(f328(f285(x95441,x95441,x95441),x95444),f304(x95441,x95444))))+~P1(f328(f328(f330(f881(x95441,x95441)),f328(f328(f263(x95441,x95441),x95442),x95445)),f328(f328(f285(x95441,x95441,x95441),x95444),f304(x95441,x95444)))) % 154.70/154.56 [9545]~P1(f328(f328(f330(f881(x95451,x95451)),f328(f328(f263(x95451,x95451),x95452),x95455)),f304(x95451,x95454)))+P1(f328(f328(f330(f881(x95451,x95451)),f328(f328(f263(x95451,x95451),x95452),x95453)),f328(f328(f285(x95451,x95451,x95451),x95454),f304(x95451,x95454))))+~P1(f328(f328(f330(f881(x95451,x95451)),f328(f328(f263(x95451,x95451),x95455),x95453)),f328(f328(f285(x95451,x95451,x95451),x95454),f304(x95451,x95454)))) % 154.70/154.56 [9548]P1(f328(f328(f330(f881(f876(x95481),f876(x95481))),f328(f328(f263(f876(x95481),f876(x95481)),x95482),x95483)),f155(x95481,f304(x95481,x95484))))+~P1(f328(f328(f330(f881(f876(x95481),f876(x95481))),f328(f328(f263(f876(x95481),f876(x95481)),x95482),x95485)),f155(x95481,f304(x95481,x95484))))+~P1(f328(f328(f330(f881(f876(x95481),f876(x95481))),f328(f328(f263(f876(x95481),f876(x95481)),x95485),x95483)),f155(x95481,f304(x95481,x95484)))) % 154.70/154.56 [9552]E(f328(f328(f125(x95521),x95522),f697(x95523,x95522,x95524,x95525,x95521)),x95525)+E(f328(f328(f125(x95521),f698(x95523,x95522,x95524,x95525,x95521)),x95523),x95524)+~E(f328(f328(f125(x95521),x95522),x95523),f328(f328(f125(x95521),x95525),x95524)) % 154.70/154.56 [9553]E(f328(f328(f125(x95531),x95532),f698(x95533,x95534,x95535,x95532,x95531)),x95534)+E(f328(f328(f125(x95531),f697(x95533,x95534,x95535,x95532,x95531)),x95535),x95533)+~E(f328(f328(f125(x95531),x95532),x95535),f328(f328(f125(x95531),x95534),x95533)) % 154.70/154.56 [9607]P1(f328(f328(f330(f881(x96071,x96071)),f328(f328(f263(x96071,x96071),x96072),x96073)),f328(f328(f285(x96071,x96071,x96071),x96074),f304(x96071,x96074))))+~P1(f328(f328(f330(f881(x96071,x96071)),f328(f328(f263(x96071,x96071),x96072),x96075)),f328(f328(f285(x96071,x96071,x96071),x96074),f304(x96071,x96074))))+~P1(f328(f328(f330(f881(x96071,x96071)),f328(f328(f263(x96071,x96071),x96075),x96073)),f328(f328(f285(x96071,x96071,x96071),x96074),f304(x96071,x96074)))) % 154.70/154.56 [9634]P36(x96341,x96342,x96343,x96344,x96345)+~E(f328(f193(f876(x96341)),x96344),f328(f193(f876(x96342)),x96345))+~P1(f328(f328(f267(x96341,x96342,a870),x96343),f737(x96345,x96344,x96343,x96342,x96341))) % 154.70/154.56 [9635]P36(x96351,x96352,x96353,x96354,x96355)+~E(f328(f193(f876(x96351)),x96354),f328(f193(f876(x96352)),x96355))+~P1(f328(f328(f267(x96351,x96352,a870),x96353),f738(x96353,x96355,x96354,x96352,x96351))) % 154.70/154.56 [9640]E(f328(f328(f125(x96401),f697(x96402,x96403,x96404,x96405,x96401)),x96404),x96402)+~E(f328(f328(f125(x96401),x96403),x96402),f328(f328(f125(x96401),x96405),x96404))+E(f328(f328(f125(x96401),f698(x96402,x96403,x96404,x96405,x96401)),x96402),x96404) % 154.70/154.56 [9655]~P105(x96552)+E(f328(f328(f145(x96551,x96552,x96553),x96554),x96555),f328(f328(f148(x96551),x96554),x96555))+P1(f328(f328(f330(x96551),f787(x96554,x96553,x96555,x96551,x96552)),f328(f170(x96551),x96555))) % 154.70/154.56 [9660]~P55(x96601,x96604,x96603,x96602)+~P1(f328(f328(f330(x96601),x96605),x96603))+P1(f328(f328(f330(x96601),f560(x96602,x96603,x96604,x96601,x96605)),x96602)) % 154.70/154.56 [9781]~P1(f328(f328(f330(f881(f882(x97811,a870),f882(x97811,a870))),f328(f328(f263(f882(x97811,a870),f882(x97811,a870)),x97814),x97813)),f319(x97811,x97812)))+~P1(f328(f328(f330(x97811),x97815),x97814))+P1(f328(f328(f330(x97811),f619(x97812,x97813,x97814,x97811,x97815)),x97813)) % 154.70/154.56 [9793]~P105(x97932)+E(f328(f328(f145(x97931,x97932,x97933),x97934),x97935),f328(f328(f148(x97931),x97934),x97935))+~P1(f328(f328(f242(x97932),f328(x97933,x97934)),f328(x97933,f787(x97934,x97933,x97935,x97931,x97932)))) % 154.70/154.56 [9983]P36(x99831,x99832,x99833,x99834,x99835)+~E(f328(f193(f876(x99831)),x99834),f328(f193(f876(x99832)),x99835))+~P1(f328(f328(x99833,f328(f328(f162(x99831),x99834),f739(x99835,x99834,x99833,x99832,x99831))),f328(f328(f162(x99832),x99835),f739(x99835,x99834,x99833,x99832,x99831)))) % 154.70/154.56 [9984]P36(x99841,x99842,x99843,x99844,x99845)+~E(f328(f193(f876(x99841)),x99844),f328(f193(f876(x99842)),x99845))+~P1(f328(f328(x99843,f328(f328(f162(x99841),x99844),f777(x99843,x99845,x99842,x99844,x99841))),f328(f328(f162(x99842),x99845),f777(x99843,x99845,x99842,x99844,x99841)))) % 154.70/154.56 [6540]~P19(x65402,x65405,x65401)+~P1(f328(f61(x65402),x65404))+E(f328(x65401,f328(f328(f306(x65402),x65403),x65404)),f328(f328(f64(x65402,x65402,x65405),x65403),x65404)) % 154.70/154.56 [6541]~E(x65413,x65414)+~E(x65412,x65415)+E(f328(f328(f306(x65411),x65412),f328(f328(f306(x65411),x65413),f192(f882(x65411,a870)))),f328(f328(f306(x65411),x65414),f328(f328(f306(x65411),x65415),f192(f882(x65411,a870))))) % 154.70/154.56 [6551]P1(f328(x65512,x65515))+E(f175(x65511,x65512,f328(f328(f125(x65511),x65513),x65514)),f175(x65511,x65512,x65513))+~P1(f328(f328(f330(x65511),x65515),f328(f170(x65511),x65513))) % 154.70/154.56 [6588]E(f328(x65881,x65882),f192(f882(x65883,a870)))+~E(f328(f328(f41(x65884,f882(x65883,a870)),x65885),x65881),f192(f882(x65883,a870)))+~P1(f328(f328(f330(x65884),x65882),x65885)) % 154.70/154.56 [6589]E(f328(x65891,x65892),f251(f882(x65893,a870)))+~E(f328(f328(f42(x65894,f882(x65893,a870)),x65895),x65891),f251(f882(x65893,a870)))+~P1(f328(f328(f330(x65894),x65892),x65895)) % 154.70/154.56 [7096]~E(x70962,x70964)+~P141(x70961)+E(f328(f328(f80(x70961),f328(f328(f81(x70961),x70962),x70963)),f328(f328(f81(x70961),x70964),x70965)),f328(f328(f80(x70961),f328(f328(f81(x70961),x70962),x70965)),f328(f328(f81(x70961),x70964),x70963))) % 154.70/154.56 [7156]~P5(x71561)+~P1(f328(f328(f330(x71564),x71563),x71565))+P1(f328(f328(f242(x71561),f328(x71562,x71563)),f328(f328(f41(x71564,x71561),x71565),x71562))) % 154.70/154.56 [7208]~P108(x72081)+P1(f328(f328(f242(x72081),f328(x72082,x72083)),f328(x72084,x72083)))+~P1(f328(f328(f242(f882(x72085,x72081)),x72082),x72084)) % 154.70/154.56 [7325]E(x73251,x73252)+E(x73253,x73251)+~E(f328(f328(f306(x73254),x73251),f328(f328(f306(x73254),x73255),f192(f882(x73254,a870)))),f328(f328(f306(x73254),x73252),f328(f328(f306(x73254),x73253),f192(f882(x73254,a870))))) % 154.70/154.56 [7326]E(x73261,x73262)+E(x73263,x73261)+~E(f328(f328(f306(x73264),x73263),f328(f328(f306(x73264),x73262),f192(f882(x73264,a870)))),f328(f328(f306(x73264),x73265),f328(f328(f306(x73264),x73261),f192(f882(x73264,a870))))) % 154.70/154.56 [7327]E(x73271,x73272)+E(x73271,x73273)+~E(f328(f328(f306(x73274),x73273),f328(f328(f306(x73274),x73272),f192(f882(x73274,a870)))),f328(f328(f306(x73274),x73275),f328(f328(f306(x73274),x73271),f192(f882(x73274,a870))))) % 154.70/154.56 [7328]E(x73281,x73282)+E(x73281,x73283)+~E(f328(f328(f306(x73284),x73281),f328(f328(f306(x73284),x73285),f192(f882(x73284,a870)))),f328(f328(f306(x73284),x73282),f328(f328(f306(x73284),x73283),f192(f882(x73284,a870))))) % 154.70/154.56 [7572]~P1(f328(f328(f328(a198,x75721),x75723),x75725))+~P1(f328(f328(f328(a198,x75722),x75725),x75724))+P1(f328(f328(f328(a198,f33(x75721,x75722)),x75723),x75724)) % 154.70/154.56 [7868]P27(x78681,x78682,x78683,x78684)+~P27(x78681,x78682,x78683,x78685)+~P1(f328(f328(f242(f882(x78681,a870)),x78684),x78685)) % 154.70/154.56 [7875]~P1(f328(f328(f242(a875),x78755),x78753))+~P1(f328(f328(f328(f328(a200,x78751),x78752),x78755),x78754))+P1(f328(f328(f328(f328(a200,x78751),x78752),x78753),x78754)) % 154.70/154.56 [8042]E(x80421,x80422)+~E(f328(f307(x80423,x80424,x80425),x80421),f328(f307(x80423,x80424,x80425),x80422))+~P27(x80423,x80424,x80425,f328(f328(f114(f882(x80423,a870)),x80421),x80422)) % 154.70/154.56 [8117]P1(f328(x81172,x81174))+E(f328(f328(f135(x81171),f328(f193(f876(x81171)),f175(x81171,x81172,x81173))),x81173),f328(f328(f148(x81171),x81174),x81175))+~E(f328(f328(f125(x81171),f175(x81171,x81172,x81173)),f328(f328(f148(x81171),x81174),x81175)),x81173) % 154.70/154.56 [8149]~P27(x81491,x81492,x81493,x81495)+~P27(x81491,x81492,x81493,x81494)+P27(x81491,x81492,x81493,f328(f328(f105(f882(x81491,a870)),x81494),x81495)) % 154.70/154.56 [8168]P1(f328(x81681,x81682))+~P1(f328(f328(f328(a198,x81684),x81682),x81685))+P1(f328(f328(f328(a198,f30(x81681,x81683,x81684)),x81682),x81685)) % 154.70/154.56 [8205]~P1(f328(x82051,x82054))+~P1(f328(f328(f328(a198,x82052),x82054),x82055))+P1(f328(f328(f328(a198,f30(x82051,x82052,x82053)),x82054),x82055)) % 154.70/154.56 [8268]~P66(x82681)+E(f328(f328(f80(x82681),f328(x82682,x82683)),f328(f163(x82681),f328(f328(f151(x82684,x82681),x82682),f167(x82684,x82683,x82685)))),f328(f163(x82681),f328(f328(f151(x82684,x82681),x82682),x82685)))+~P1(f328(f328(f330(x82684),x82683),f328(f170(x82684),x82685))) % 154.70/154.56 [8356]~P105(x83561)+~P16(x83561,f328(f328(f151(x83562,x83561),x83563),x83565))+P16(x83561,f328(f328(f151(x83562,x83561),x83563),f328(f328(f145(x83562,x83561,x83563),x83564),x83565))) % 154.70/154.56 [8441]~P5(x84411)+P1(f328(f328(f242(x84411),f328(f328(f41(x84412,x84411),x84413),x84414)),f328(f328(f41(x84412,x84411),x84415),x84414)))+~P1(f328(f328(f242(f882(x84412,a870)),x84413),x84415)) % 154.70/154.56 [8442]~P5(x84421)+P1(f328(f328(f242(x84421),f328(f328(f42(x84422,x84421),x84423),x84424)),f328(f328(f42(x84422,x84421),x84425),x84424)))+~P1(f328(f328(f242(f882(x84422,a870)),x84425),x84423)) % 154.70/154.56 [8474]~P105(x84743)+P1(f328(f134(x84741),x84742))+~P1(f328(f134(x84741),f328(f328(f145(x84741,x84743,x84744),x84745),x84742))) % 154.70/154.56 [8543]P1(f328(x85431,x85432))+P1(f328(f328(f328(a198,x85433),x85432),x85434))+~P1(f328(f328(f328(a198,f30(x85431,x85435,x85433)),x85432),x85434)) % 154.70/154.56 [8561]~P1(f328(x85614,x85612))+P1(f328(f328(f328(a198,x85611),x85612),x85613))+~P1(f328(f328(f328(a198,f30(x85614,x85611,x85615)),x85612),x85613)) % 154.70/154.56 [8623]~P105(x86231)+~P1(f328(f328(f330(x86232),x86233),f328(f170(x86232),x86234)))+~P1(f328(f134(x86232),f328(f328(f145(x86232,x86231,x86235),x86233),x86234))) % 154.70/154.56 [8640]P1(f328(f328(f328(a198,x86401),x86402),x86403))+P1(f328(f328(f328(a198,x86404),x86402),x86403))+~P1(f328(f328(f328(a198,f30(x86405,x86401,x86404)),x86402),x86403)) % 154.70/154.56 [8706]~P105(x87061)+P16(x87061,f328(f328(f151(x87062,x87061),x87063),x87064))+~P16(x87061,f328(f328(f151(x87062,x87061),x87063),f328(f328(f145(x87062,x87061,x87063),x87065),x87064))) % 154.70/154.56 [8798]~P105(x87982)+E(f328(f328(f145(x87981,x87982,x87983),x87984),x87985),f146(x87981,x87982,x87983,x87984,x87985))+P1(f328(f328(f330(x87982),f328(x87983,x87984)),f328(f307(x87981,x87982,x87983),f328(f170(x87981),x87985)))) % 154.70/154.56 [8872]~P105(x88722)+E(f146(x88721,x88722,x88723,x88724,x88725),x88725)+~P1(f328(f328(f330(x88722),f328(x88723,x88724)),f328(f307(x88721,x88722,x88723),f328(f170(x88721),x88725)))) % 154.70/154.56 [8886]~P27(x88862,x88861,x88863,x88865)+P1(f328(f328(f243(f882(x88861,a870)),f328(f307(x88862,x88861,x88863),x88864)),f328(f307(x88862,x88861,x88863),x88865)))+~P1(f328(f328(f243(f882(x88862,a870)),x88864),x88865)) % 154.70/154.56 [9057]~P27(x90571,x90572,x90573,f251(f882(x90571,a870)))+~P1(f328(f328(f242(f882(x90572,a870)),x90574),f328(f307(x90571,x90572,x90573),x90575)))+P1(f328(f328(f242(f882(x90571,a870)),f328(f308(x90571,x90572,x90573),x90574)),x90575)) % 154.70/154.56 [9080]~E(f328(f307(x90803,x90801,x90804),f251(f882(x90803,a870))),f251(f882(x90801,a870)))+P1(f328(f328(f242(f882(x90801,a870)),x90802),f328(f307(x90803,x90801,x90804),x90805)))+~P1(f328(f328(f242(f882(x90803,a870)),f328(f308(x90803,x90801,x90804),x90802)),x90805)) % 154.70/154.56 [9104]~E(f328(f235(x91042),x91044),f328(f328(f176(x91041,x91042),x91045),x91043))+~P1(f328(f134(x91041),f328(f328(f151(f881(x91041,x91042),x91041),f262(x91041,x91042)),x91045)))+P1(f328(f328(f330(f881(x91041,x91042)),f328(f328(f263(x91041,x91042),x91043),x91044)),f328(f170(f881(x91041,x91042)),x91045))) % 154.70/154.56 [9186]~P27(x91861,x91864,x91865,f251(f882(x91861,a870)))+~P1(f328(f328(f242(f882(x91864,a870)),f328(f307(x91861,x91864,x91865),x91862)),f328(f307(x91861,x91864,x91865),x91863)))+P1(f328(f328(f242(f882(x91861,a870)),x91862),x91863)) % 154.70/154.56 [9251]E(f328(f235(x92511),x92512),f328(f328(f176(x92513,x92511),x92514),x92515))+~P1(f328(f134(x92513),f328(f328(f151(f881(x92513,x92511),x92513),f262(x92513,x92511)),x92514)))+~P1(f328(f328(f330(f881(x92513,x92511)),f328(f328(f263(x92513,x92511),x92515),x92512)),f328(f170(f881(x92513,x92511)),x92514))) % 154.70/154.56 [9253]E(f328(f328(f176(x92531,x92532),x92533),x92534),f328(f235(x92532),x92535))+~P1(f328(f134(x92531),f328(f328(f151(f881(x92531,x92532),x92531),f262(x92531,x92532)),x92533)))+~P1(f328(f328(f330(f881(x92531,x92532)),f328(f328(f263(x92531,x92532),x92534),x92535)),f328(f170(f881(x92531,x92532)),x92533))) % 154.70/154.56 [9308]~P77(x93081)+~E(f328(x93083,f756(x93083,x93084,x93085,x93082,x93081)),f2(x93081))+E(f328(f163(x93081),f328(f328(f151(x93082,x93081),x93083),f328(f133(x93082,x93084),x93085))),f328(f163(x93081),f328(f328(f151(x93082,x93081),x93083),x93085))) % 154.70/154.56 [9485]~P18(x94851,x94852,x94853)+~P1(f328(f61(x94851),x94855))+P1(f328(f66(x94851,x94852,x94853,x94854,x94855),f328(f328(f64(x94851,x94852,x94853),x94854),x94855))) % 154.70/154.56 [9565]P1(f328(x95651,f658(x95652,x95651,x95653,x95654,x95655)))+~P1(f328(f328(f242(f882(x95655,a870)),x95654),x95653))+P1(f328(f328(f242(f882(x95655,a870)),f328(f328(f105(f882(x95655,a870)),x95654),f328(f248(x95655),x95651))),f328(f328(f105(f882(x95655,a870)),x95653),f328(f248(x95655),x95652)))) % 154.70/154.56 [9579]~P77(x95791)+~P1(f328(x95794,f756(x95793,x95794,x95795,x95792,x95791)))+E(f328(f163(x95791),f328(f328(f151(x95792,x95791),x95793),f328(f133(x95792,x95794),x95795))),f328(f163(x95791),f328(f328(f151(x95792,x95791),x95793),x95795))) % 154.70/154.56 [9658]~P5(x96585)+P1(f328(f328(f330(x96581),f350(x96582,x96583,x96581,x96584,x96585)),x96583))+P1(f328(f328(f242(x96585),x96584),f328(f328(f42(x96581,x96585),x96583),x96582))) % 154.70/154.56 [9661]~P77(x96611)+E(f328(f163(x96611),f328(f328(f151(x96612,x96611),x96613),f328(f133(x96612,x96614),x96615))),f328(f163(x96611),f328(f328(f151(x96612,x96611),x96613),x96615)))+P1(f328(f328(f330(x96612),f756(x96613,x96614,x96615,x96612,x96611)),f328(f170(x96612),x96615))) % 154.70/154.56 [9671]~P1(f328(x96715,f658(x96715,x96713,x96714,x96712,x96711)))+~P1(f328(f328(f242(f882(x96711,a870)),x96712),x96714))+P1(f328(f328(f242(f882(x96711,a870)),f328(f328(f105(f882(x96711,a870)),x96712),f328(f248(x96711),x96713))),f328(f328(f105(f882(x96711,a870)),x96714),f328(f248(x96711),x96715)))) % 154.70/154.56 [9706]P36(x97061,x97062,x97063,x97064,x97065)+~E(f328(f193(f876(x97062)),x97065),f328(f193(f876(x97061)),x97064))+P1(f328(f328(f243(a875),f739(x97065,x97064,x97063,x97062,x97061)),f328(f193(f876(x97061)),x97064))) % 154.70/154.56 [9707]P36(x97071,x97072,x97073,x97074,x97075)+~E(f328(f193(f876(x97072)),x97075),f328(f193(f876(x97071)),x97074))+P1(f328(f328(f243(a875),f777(x97073,x97075,x97072,x97074,x97071)),f328(f193(f876(x97071)),x97074))) % 154.70/154.56 [9740]P1(f328(f328(f330(x97401),f658(x97402,x97403,x97404,x97405,x97401)),x97405))+~P1(f328(f328(f242(f882(x97401,a870)),x97405),x97404))+P1(f328(f328(f242(f882(x97401,a870)),f328(f328(f105(f882(x97401,a870)),x97405),f328(f248(x97401),x97403))),f328(f328(f105(f882(x97401,a870)),x97404),f328(f248(x97401),x97402)))) % 154.70/154.56 [9794]~P5(x97941)+~P1(f328(f328(f242(x97941),x97942),f328(x97945,f350(x97945,x97944,x97943,x97942,x97941))))+P1(f328(f328(f242(x97941),x97942),f328(f328(f42(x97943,x97941),x97944),x97945))) % 154.70/154.56 [9827]~P73(x98271)+~P1(f328(f61(x98272),x98275))+E(f328(f328(f328(f65(x98271,x98272,f81(x98271)),f328(f328(f18(x98272,x98271,x98271),f328(f328(f8(x98271,f882(x98271,x98271),x98272),f81(x98271)),x98273)),x98274)),f78(x98271)),x98275),f328(f328(f81(x98271),f328(f328(f328(f65(x98271,x98272,f81(x98271)),x98273),f78(x98271)),x98275)),f328(f328(f328(f65(x98271,x98272,f81(x98271)),x98274),f78(x98271)),x98275))) % 154.70/154.56 [9890]~P1(f328(f328(f330(f881(f882(x98901,a870),f882(x98901,a870))),f328(f328(f263(f882(x98901,a870),f882(x98901,a870)),x98905),x98904)),f319(x98901,x98903)))+~P1(f328(f328(f330(x98901),x98902),x98905))+P1(f328(f328(f330(f881(x98901,x98901)),f328(f328(f263(x98901,x98901),x98902),f619(x98903,x98904,x98905,x98901,x98902))),x98903)) % 154.70/154.56 [10018]~P1(f328(f328(f330(f881(f876(x100181),f876(x100181))),f328(f328(f263(f876(x100181),f876(x100181)),f328(f328(f125(x100181),x100185),x100182)),f328(f328(f125(x100181),x100185),x100183))),f144(x100181,x100184)))+P1(f328(f328(f330(f881(f876(x100181),f876(x100181))),f328(f328(f263(f876(x100181),f876(x100181)),x100182),x100183)),f144(x100181,x100184)))+P1(f328(f328(f330(f881(x100181,x100181)),f328(f328(f263(x100181,x100181),f704(x100184,x100183,x100182,x100185,x100181)),f704(x100184,x100183,x100182,x100185,x100181))),x100184)) % 154.70/154.56 [7136]~E(f328(f193(f876(x71361)),x71363),f328(f193(f876(x71362)),x71364))+E(f328(f328(f176(x71361,x71362),f328(f328(f180(x71361,x71362),x71363),x71364)),x71365),f205(x71362))+P1(f328(f328(f330(x71361),x71365),f328(f170(x71361),x71363))) % 154.70/154.56 [7211]~E(x72113,x72115)+E(f328(f328(f162(x72111),f328(f328(f156(x72111,x72112),x72113),x72114)),x72115),x72114)+~P1(f328(f328(f243(a875),x72113),f328(f193(f876(x72111)),x72112))) % 154.70/154.56 [7320]~E(f328(f328(f125(x73201),x73202),x73204),f328(f328(f125(x73201),x73203),x73205))+E(f328(f328(f173(x73201),f328(f193(f876(x73201)),x73202)),x73203),x73202)+P1(f328(f328(f242(a875),f328(f193(f876(x73201)),x73203)),f328(f193(f876(x73201)),x73202))) % 154.70/154.56 [7337]~E(x73375,x73372)+P1(f328(x73371,x73372))+P1(f328(f328(f328(f328(a200,f32(x73371,x73373)),x73372),x73374),x73375)) % 154.70/154.56 [7829]~E(f328(f328(f125(x78291),x78292),x78294),f328(f328(f125(x78291),x78293),x78295))+E(f328(f328(f173(x78291),f328(f193(f876(x78291)),x78292)),x78293),x78292)+~P1(f328(f328(f242(a875),f328(f193(f876(x78291)),x78292)),f328(f193(f876(x78291)),x78293))) % 154.70/154.56 [7853]~P1(f328(f61(x78531),f328(x78534,x78535)))+~P1(f328(f328(f330(x78532),x78535),x78533))+P1(f328(f61(x78531),f328(f328(f42(x78532,f882(x78531,a870)),x78533),x78534))) % 154.70/154.56 [7906]~E(f328(f193(f876(x79061)),x79062),f328(f193(f876(x79063)),x79064))+~E(f328(f328(f176(x79061,x79063),f328(f328(f180(x79061,x79063),x79062),x79064)),x79065),f205(x79063))+~P1(f328(f328(f330(x79061),x79065),f328(f170(x79061),x79062))) % 154.70/154.56 [8027]~P41(x80271,x80273,x80275)+~P41(x80271,x80272,x80274)+P41(x80271,f328(f328(f114(f882(x80271,a870)),x80272),x80273),f328(f328(f114(f882(f881(x80271,x80271),a870)),x80274),x80275)) % 154.70/154.56 [8028]~P41(x80281,x80283,x80285)+~P41(x80281,x80282,x80284)+P41(x80281,f328(f328(f105(f882(x80281,a870)),x80282),x80283),f328(f328(f105(f882(f881(x80281,x80281),a870)),x80284),x80285)) % 154.70/154.56 [8111]E(x81111,x81112)+P1(f328(x81113,x81111))+~P1(f328(f328(f328(f328(a200,f32(x81113,x81114)),x81111),x81115),x81112)) % 154.70/154.56 [8392]E(f328(f328(f263(x83921,x83922),f328(f328(f162(x83921),x83923),x83924)),f328(f328(f162(x83922),x83925),x83924)),f328(f328(f162(f881(x83921,x83922)),f328(f328(f180(x83921,x83922),x83923),x83925)),x83924))+~P1(f328(f328(f243(a875),x83924),f328(f193(f876(x83921)),x83923)))+~P1(f328(f328(f243(a875),x83924),f328(f193(f876(x83922)),x83925))) % 154.70/154.56 [8553]~P41(x85531,x85533,x85534)+P1(f328(f328(f330(x85531),x85532),x85533))+~P1(f328(f328(f330(f881(x85531,x85531)),f328(f328(f263(x85531,x85531),x85535),x85532)),x85534)) % 154.70/154.56 [8554]~P41(x85541,x85543,x85544)+P1(f328(f328(f330(x85541),x85542),x85543))+~P1(f328(f328(f330(f881(x85541,x85541)),f328(f328(f263(x85541,x85541),x85542),x85545)),x85544)) % 154.70/154.56 [8555]~P8(x85551,x85553,x85554)+P1(f328(f328(f330(x85551),x85552),x85553))+~P1(f328(f328(f330(f881(x85551,x85551)),f328(f328(f263(x85551,x85551),x85555),x85552)),x85554)) % 154.70/154.56 [8556]~P8(x85561,x85563,x85564)+P1(f328(f328(f330(x85561),x85562),x85563))+~P1(f328(f328(f330(f881(x85561,x85561)),f328(f328(f263(x85561,x85561),x85562),x85565)),x85564)) % 154.70/154.56 [8820]~P8(x88201,x88205,x88202)+E(f328(f282(x88201,x88201,x88202),f328(f328(f306(x88201),x88203),f192(f882(x88201,a870)))),f328(f282(x88201,x88201,x88202),f328(f328(f306(x88201),x88204),f192(f882(x88201,a870)))))+~P1(f328(f328(f330(f881(x88201,x88201)),f328(f328(f263(x88201,x88201),x88203),x88204)),x88202)) % 154.70/154.56 [8901]~P1(f328(f328(f328(f328(a200,x89012),x89013),x89014),x89015))+~P1(f328(f328(f328(f328(a200,f32(x89011,x89012)),x89015),x89014),x89013))+P1(f328(f328(f328(f328(a200,f32(x89011,x89012)),x89013),x89014),x89013)) % 154.70/154.56 [9012]P1(f328(x90121,x90122))+~P1(f328(f328(f330(x90123),x90122),x90125))+P1(f328(f328(f330(x90123),f831(x90121,x90124,x90125,x90123)),f328(f328(f114(f882(x90123,a870)),x90125),x90124))) % 154.70/154.56 [9013]P1(f328(x90131,x90132))+~P1(f328(f328(f330(x90133),x90132),x90134))+P1(f328(f328(f330(x90133),f831(x90131,x90134,x90135,x90133)),f328(f328(f114(f882(x90133,a870)),x90135),x90134))) % 154.70/154.56 [9021]~P1(f328(x90212,x90215))+~P1(f328(f328(f330(x90211),x90215),x90214))+P1(f328(f328(f330(x90211),f348(x90212,x90213,x90214,x90211)),f328(f328(f114(f882(x90211,a870)),x90214),x90213))) % 154.70/154.56 [9022]~P1(f328(x90222,x90225))+~P1(f328(f328(f330(x90221),x90225),x90223))+P1(f328(f328(f330(x90221),f348(x90222,x90223,x90224,x90221)),f328(f328(f114(f882(x90221,a870)),x90224),x90223))) % 154.70/154.56 [9037]~P1(f328(f328(f242(f882(x90371,a870)),x90373),x90375))+~P1(f328(f328(f242(f882(x90371,a870)),x90372),x90374))+P1(f328(f328(f242(f882(x90371,a870)),f328(f328(f114(f882(x90371,a870)),x90372),x90373)),f328(f328(f114(f882(x90371,a870)),x90374),x90375))) % 154.70/154.56 [9038]~P1(f328(f328(f242(f882(x90381,a870)),x90385),x90383))+~P1(f328(f328(f242(f882(x90381,a870)),x90382),x90384))+P1(f328(f328(f242(f882(x90381,a870)),f328(f328(f22(f882(x90381,a870)),x90382),x90383)),f328(f328(f22(f882(x90381,a870)),x90384),x90385))) % 154.70/154.56 [9039]~P1(f328(f328(f242(f882(x90391,a870)),x90393),x90395))+~P1(f328(f328(f242(f882(x90391,a870)),x90392),x90394))+P1(f328(f328(f242(f882(x90391,a870)),f328(f328(f105(f882(x90391,a870)),x90392),x90393)),f328(f328(f105(f882(x90391,a870)),x90394),x90395))) % 154.70/154.56 [9129]~E(f328(f193(f876(x91291)),x91293),f328(f193(f876(x91292)),x91294))+E(f328(f328(f176(x91291,x91292),f328(f328(f180(x91291,x91292),x91293),x91294)),x91295),f328(f235(x91292),f713(x91295,x91294,x91292,x91293,x91291)))+~P1(f328(f328(f330(x91291),x91295),f328(f170(x91291),x91293))) % 154.70/154.56 [9133]P1(f328(f328(f330(f881(x91331,x91331)),f328(f328(f263(x91331,x91331),x91332),x91333)),f322(x91331,x91334,x91335)))+~P1(f328(f328(f242(a875),f328(x91334,x91332)),f328(x91334,x91333)))+~P1(f328(f328(f330(f881(x91331,x91331)),f328(f328(f263(x91331,x91331),x91332),x91333)),x91335)) % 154.70/154.56 [9318]P1(f328(f328(f330(f881(x93181,x93181)),f328(f328(f263(x93181,x93181),x93182),x93183)),f304(x93181,x93184)))+~P1(f328(f328(f330(f881(x93181,x93181)),f328(f328(f263(x93181,x93181),x93182),x93185)),f304(x93181,x93184)))+~P1(f328(f328(f330(f881(x93181,x93181)),f328(f328(f263(x93181,x93181),x93185),x93183)),x93184)) % 154.70/154.56 [9319]P1(f328(f328(f330(f881(x93191,x93191)),f328(f328(f263(x93191,x93191),x93192),x93193)),f304(x93191,x93194)))+~P1(f328(f328(f330(f881(x93191,x93191)),f328(f328(f263(x93191,x93191),x93195),x93193)),f304(x93191,x93194)))+~P1(f328(f328(f330(f881(x93191,x93191)),f328(f328(f263(x93191,x93191),x93192),x93195)),x93194)) % 154.70/154.56 [9416]E(x94161,x94162)+E(f328(a116,f640(x94163,x94164,x94161,x94162,x94165)),x94164)+~P1(f328(f328(f330(f881(x94165,x94165)),f328(f328(f263(x94165,x94165),x94162),x94161)),f328(f328(f187(f881(x94165,x94165),a870),x94164),x94163))) % 154.70/154.56 [9417]E(x94171,x94172)+E(f328(a116,f642(x94173,x94174,x94171,x94172,x94175)),x94174)+~P1(f328(f328(f330(f881(x94175,x94175)),f328(f328(f263(x94175,x94175),x94172),x94171)),f328(f328(f187(f881(x94175,x94175),a870),x94174),x94173))) % 154.70/154.56 [9418]E(x94181,f2(a875))+E(f328(a116,f640(x94182,x94181,x94183,x94184,x94185)),x94181)+~P1(f328(f328(f330(f881(x94185,x94185)),f328(f328(f263(x94185,x94185),x94184),x94183)),f328(f328(f187(f881(x94185,x94185),a870),x94181),x94182))) % 154.70/154.56 [9419]E(x94191,f2(a875))+E(f328(a116,f642(x94192,x94191,x94193,x94194,x94195)),x94191)+~P1(f328(f328(f330(f881(x94195,x94195)),f328(f328(f263(x94195,x94195),x94194),x94193)),f328(f328(f187(f881(x94195,x94195),a870),x94191),x94192))) % 154.70/154.56 [9435]P1(f328(f328(f330(f881(x94351,x94351)),f328(f328(f263(x94351,x94351),x94352),x94353)),f328(f328(f285(x94351,x94351,x94351),x94354),f304(x94351,x94354))))+~P1(f328(f328(f330(f881(x94351,x94351)),f328(f328(f263(x94351,x94351),x94352),x94355)),x94354))+~P1(f328(f328(f330(f881(x94351,x94351)),f328(f328(f263(x94351,x94351),x94355),x94353)),x94354)) % 154.70/154.56 [9442]~P1(f328(f328(f330(f881(x94421,x94421)),f328(f328(f263(x94421,x94421),x94422),x94425)),f304(x94421,x94424)))+P1(f328(f328(f330(f881(x94421,x94421)),f328(f328(f263(x94421,x94421),x94422),x94423)),f328(f328(f285(x94421,x94421,x94421),x94424),f304(x94421,x94424))))+~P1(f328(f328(f330(f881(x94421,x94421)),f328(f328(f263(x94421,x94421),x94425),x94423)),x94424)) % 154.70/154.56 [9481]~P8(x94811,x94815,x94812)+~P1(f328(f328(f330(f881(x94811,x94811)),f328(f328(f263(x94811,x94811),x94813),x94814)),x94812))+P1(f328(f328(f242(f882(x94811,a870)),f328(f282(x94811,x94811,x94812),f328(f328(f306(x94811),x94813),f192(f882(x94811,a870))))),f328(f282(x94811,x94811,x94812),f328(f328(f306(x94811),x94814),f192(f882(x94811,a870)))))) % 154.70/154.56 [9503]E(x95031,x95032)+P1(f328(f328(f328(f328(a200,x95033),x95031),x95034),f345(x95032,x95034,x95031,x95033,x95035)))+~P1(f328(f328(f328(f328(a200,f32(x95035,x95033)),x95031),x95034),x95032)) % 154.70/154.56 [9507]~P1(f328(x95075,x95072))+P1(f328(f328(f328(f328(a200,x95071),x95072),x95073),f345(x95074,x95073,x95072,x95071,x95075)))+~P1(f328(f328(f328(f328(a200,f32(x95075,x95071)),x95072),x95073),x95074)) % 154.70/154.56 [9537]P1(f328(f328(f330(f881(x95371,x95371)),f328(f328(f263(x95371,x95371),x95372),x95373)),f328(f328(f285(x95371,x95371,x95371),x95374),f304(x95371,x95374))))+~P1(f328(f328(f330(f881(x95371,x95371)),f328(f328(f263(x95371,x95371),x95372),x95375)),f328(f328(f285(x95371,x95371,x95371),x95374),f304(x95371,x95374))))+~P1(f328(f328(f330(f881(x95371,x95371)),f328(f328(f263(x95371,x95371),x95375),x95373)),x95374)) % 154.70/154.56 [9538]P1(f328(f328(f330(f881(x95381,x95381)),f328(f328(f263(x95381,x95381),x95382),x95383)),f328(f328(f285(x95381,x95381,x95381),x95384),f304(x95381,x95384))))+~P1(f328(f328(f330(f881(x95381,x95381)),f328(f328(f263(x95381,x95381),x95385),x95383)),f328(f328(f285(x95381,x95381,x95381),x95384),f304(x95381,x95384))))+~P1(f328(f328(f330(f881(x95381,x95381)),f328(f328(f263(x95381,x95381),x95382),x95385)),x95384)) % 154.70/154.56 [9588]~P1(f328(f66(x95881,x95881,x95884,x95882,x95883),x95885))+P1(f328(f328(f330(x95881),x95882),x95883))+P1(f328(f62(x95881,x95884,f328(f328(f306(x95881),x95882),x95883)),x95885)) % 154.70/154.56 [9627]~E(f328(f307(x96273,x96272,x96275),x96274),x96271)+E(x96271,f192(f882(x96272,a870)))+P1(f328(f328(f242(f882(x96273,a870)),f328(f307(x96272,x96273,f429(x96274,x96273,x96272,x96271)),x96271)),x96274)) % 154.70/154.56 [9674]~P5(x96745)+P1(f328(f328(f330(x96741),f351(x96742,x96743,x96744,x96741,x96745)),x96744))+P1(f328(f328(f242(x96745),f328(f328(f41(x96741,x96745),x96744),x96743)),x96742)) % 154.70/154.56 [9726]P36(x97261,x97262,x97263,x97264,x97265)+~E(f328(f193(f876(x97261)),x97264),f328(f193(f876(x97262)),x97265))+P1(f328(f328(f330(f881(x97261,x97262)),f737(x97265,x97264,x97263,x97262,x97261)),f328(f170(f881(x97261,x97262)),f328(f328(f180(x97261,x97262),x97264),x97265)))) % 154.70/154.56 [9727]P36(x97271,x97272,x97273,x97274,x97275)+~E(f328(f193(f876(x97271)),x97274),f328(f193(f876(x97272)),x97275))+P1(f328(f328(f330(f881(x97271,x97272)),f738(x97273,x97275,x97274,x97272,x97271)),f328(f170(f881(x97271,x97272)),f328(f328(f180(x97271,x97272),x97274),x97275)))) % 154.70/154.56 [9857]E(x98571,x98572)+P1(f328(f328(f328(f328(a200,f32(x98573,x98574)),f345(x98571,x98575,x98572,x98574,x98573)),x98575),x98571))+~P1(f328(f328(f328(f328(a200,f32(x98573,x98574)),x98572),x98575),x98571)) % 154.70/154.56 [9859]~P1(f328(x98591,x98595))+P1(f328(f328(f328(f328(a200,f32(x98591,x98592)),f345(x98593,x98594,x98595,x98592,x98591)),x98594),x98593))+~P1(f328(f328(f328(f328(a200,f32(x98591,x98592)),x98595),x98594),x98593)) % 154.70/154.56 [9867]E(x98671,x98672)+P1(f328(f328(f330(f881(x98673,x98673)),f328(f328(f263(x98673,x98673),x98671),f643(x98674,x98675,x98672,x98671,x98673))),x98674))+~P1(f328(f328(f330(f881(x98673,x98673)),f328(f328(f263(x98673,x98673),x98671),x98672)),f328(f328(f187(f881(x98673,x98673),a870),x98675),x98674))) % 154.70/154.56 [9868]E(x98681,f2(a875))+P1(f328(f328(f330(f881(x98682,x98682)),f328(f328(f263(x98682,x98682),x98683),f643(x98684,x98681,x98685,x98683,x98682))),x98684))+~P1(f328(f328(f330(f881(x98682,x98682)),f328(f328(f263(x98682,x98682),x98683),x98685)),f328(f328(f187(f881(x98682,x98682),a870),x98681),x98684))) % 154.70/154.56 [9911]~P5(x99111)+~P1(f328(f328(f242(x99111),f328(x99114,f351(x99115,x99114,x99113,x99112,x99111))),x99115))+P1(f328(f328(f242(x99111),f328(f328(f41(x99112,x99111),x99113),x99114)),x99115)) % 154.70/154.56 [9953]E(x99531,x99532)+P1(f328(f328(f330(f881(x99533,x99533)),f328(f328(f263(x99533,x99533),f641(x99534,x99535,x99531,x99532,x99533)),x99531)),x99534))+~P1(f328(f328(f330(f881(x99533,x99533)),f328(f328(f263(x99533,x99533),x99532),x99531)),f328(f328(f187(f881(x99533,x99533),a870),x99535),x99534))) % 154.70/154.56 [9954]E(x99541,f2(a875))+P1(f328(f328(f330(f881(x99542,x99542)),f328(f328(f263(x99542,x99542),f641(x99543,x99541,x99544,x99545,x99542)),x99544)),x99543))+~P1(f328(f328(f330(f881(x99542,x99542)),f328(f328(f263(x99542,x99542),x99545),x99544)),f328(f328(f187(f881(x99542,x99542),a870),x99541),x99543))) % 154.70/154.56 [9958]E(x99581,x99582)+P1(f328(f328(f330(f881(x99583,x99583)),f328(f328(f263(x99583,x99583),x99581),f641(x99584,x99585,x99582,x99581,x99583))),f328(f328(f187(f881(x99583,x99583),a870),f640(x99584,x99585,x99582,x99581,x99583)),x99584)))+~P1(f328(f328(f330(f881(x99583,x99583)),f328(f328(f263(x99583,x99583),x99581),x99582)),f328(f328(f187(f881(x99583,x99583),a870),x99585),x99584))) % 154.70/154.56 [9959]E(x99591,f2(a875))+P1(f328(f328(f330(f881(x99592,x99592)),f328(f328(f263(x99592,x99592),x99593),f641(x99594,x99591,x99595,x99593,x99592))),f328(f328(f187(f881(x99592,x99592),a870),f640(x99594,x99591,x99595,x99593,x99592)),x99594)))+~P1(f328(f328(f330(f881(x99592,x99592)),f328(f328(f263(x99592,x99592),x99593),x99595)),f328(f328(f187(f881(x99592,x99592),a870),x99591),x99594))) % 154.70/154.56 [10009]E(x100091,x100092)+P1(f328(f328(f330(f881(x100093,x100093)),f328(f328(f263(x100093,x100093),f643(x100094,x100095,x100091,x100092,x100093)),x100091)),f328(f328(f187(f881(x100093,x100093),a870),f642(x100094,x100095,x100091,x100092,x100093)),x100094)))+~P1(f328(f328(f330(f881(x100093,x100093)),f328(f328(f263(x100093,x100093),x100092),x100091)),f328(f328(f187(f881(x100093,x100093),a870),x100095),x100094))) % 154.70/154.56 [10010]E(x100101,f2(a875))+P1(f328(f328(f330(f881(x100102,x100102)),f328(f328(f263(x100102,x100102),f643(x100103,x100101,x100104,x100105,x100102)),x100104)),f328(f328(f187(f881(x100102,x100102),a870),f642(x100103,x100101,x100104,x100105,x100102)),x100103)))+~P1(f328(f328(f330(f881(x100102,x100102)),f328(f328(f263(x100102,x100102),x100105),x100104)),f328(f328(f187(f881(x100102,x100102),a870),x100101),x100103))) % 154.70/154.56 [10043]~P66(x100432)+~P1(f328(f61(x100431),x100435))+E(f328(f328(f6(x100431,x100432),f328(f328(f7(x100431,x100432,x100432),f328(f328(f18(x100431,x100432,f882(x100432,x100432)),f328(f328(f8(a870,f882(x100432,f882(x100432,x100432)),x100431),f100(x100432)),f328(f328(f7(x100431,f882(x100431,a870),a870),f330(x100431)),x100433))),x100434)),f2(x100432))),x100435),f328(f328(f6(x100431,x100432),x100434),f328(f328(f105(f882(x100431,a870)),x100435),x100433))) % 154.70/154.56 [8620]~P66(x86201)+~P1(f328(f61(x86204),x86205))+E(f328(f328(f80(x86201),f328(x86202,x86203)),f328(f328(f6(x86204,x86201),x86202),f328(f328(f22(f882(x86204,a870)),x86205),f328(f328(f306(x86204),x86203),f192(f882(x86204,a870)))))),f328(f328(f6(x86204,x86201),x86202),f328(f328(f306(x86204),x86203),x86205))) % 154.70/154.56 [8621]~P73(x86211)+~P1(f328(f61(x86214),x86215))+E(f328(f328(f81(x86211),f328(x86212,x86213)),f328(f328(f9(x86214,x86211),x86212),f328(f328(f22(f882(x86214,a870)),x86215),f328(f328(f306(x86214),x86213),f192(f882(x86214,a870)))))),f328(f328(f9(x86214,x86211),x86212),f328(f328(f306(x86214),x86213),x86215))) % 154.70/154.56 [8942]~P105(x89422)+~P16(x89422,f328(f166(x89422),f328(f328(f151(x89421,x89422),x89424),x89425)))+E(f328(f133(x89421,f328(f328(f8(x89422,a870,x89421),f328(f243(x89422),x89423)),x89424)),x89425),f175(x89421,f328(f328(f8(x89422,a870,x89421),f328(f243(x89422),x89423)),x89424),x89425)) % 154.70/154.56 [8969]~P66(x89691)+E(f328(f328(f80(x89691),f328(f328(f6(a875,x89691),x89692),f299(a875,x89693,x89694))),f328(f328(f6(a875,x89691),x89692),f299(a875,f328(f328(f80(a875),x89694),f78(a875)),f328(f328(f80(a875),x89694),x89695)))),f328(f328(f6(a875,x89691),x89692),f299(a875,x89693,f328(f328(f80(a875),x89694),x89695))))+~P1(f328(f328(f242(a875),x89693),f328(f328(f80(a875),x89694),f78(a875)))) % 154.70/154.56 [8970]~P1(f328(f328(f330(x89701),x89704),x89705))+~P1(f328(f328(f242(f882(x89701,a870)),f328(f170(x89701),x89702)),x89705))+P1(f328(f328(f242(f882(x89701,a870)),f328(f170(x89701),f328(f328(f156(x89701,x89702),x89703),x89704))),x89705)) % 154.70/154.56 [9196]~P5(x91962)+~P1(f328(f61(x91961),x91965))+E(f328(f328(f64(x91961,x91962,f328(f328(f8(x91962,f882(x91962,x91962),x91961),f114(x91962)),x91963)),x91964),x91965),f328(f328(f114(x91962),x91964),f328(f328(f41(x91961,x91962),x91965),x91963))) % 154.70/154.56 [9197]~P5(x91972)+~P1(f328(f61(x91971),x91975))+E(f328(f328(f64(x91971,x91972,f328(f328(f8(x91972,f882(x91972,x91972),x91971),f105(x91972)),x91973)),x91974),x91975),f328(f328(f105(x91972),x91974),f328(f328(f42(x91971,x91972),x91975),x91973))) % 154.70/154.56 [9244]E(f328(x92441,x92442),f328(x92441,x92443))+P1(f328(f328(f243(a875),f328(x92441,x92442)),f328(x92441,x92443)))+~P1(f328(f328(f330(f881(x92444,x92444)),f328(f328(f263(x92444,x92444),x92442),x92443)),f150(x92444,f328(f328(f148(f882(x92444,a875)),x92441),x92445)))) % 154.70/154.56 [9275]~E(f328(x92754,x92752),f328(x92754,x92753))+~P1(f328(f328(f330(f881(x92751,x92751)),f328(f328(f263(x92751,x92751),x92752),x92753)),f150(x92751,x92755)))+P1(f328(f328(f330(f881(x92751,x92751)),f328(f328(f263(x92751,x92751),x92752),x92753)),f150(x92751,f328(f328(f148(f882(x92751,a875)),x92754),x92755)))) % 154.70/154.56 [9297]~P27(x92971,x92972,x92973,x92975)+P27(x92971,x92972,x92973,f328(f328(f306(x92971),x92974),x92975))+P1(f328(f328(f330(x92972),f328(x92973,x92974)),f328(f307(x92971,x92972,x92973),f328(f328(f22(f882(x92971,a870)),x92975),f328(f328(f306(x92971),x92974),f192(f882(x92971,a870))))))) % 154.70/154.56 [9301]P1(f328(x93012,x93015))+~P1(f328(f328(f330(x93011),x93015),f328(f170(x93011),x93013)))+E(f328(f328(f135(x93011),f328(f193(f876(x93011)),f175(x93011,x93012,f328(f328(f125(x93011),x93013),x93014)))),f328(f328(f125(x93011),x93013),x93014)),f328(f328(f125(x93011),f328(f328(f135(x93011),f328(f193(f876(x93011)),f175(x93011,x93012,x93013))),x93013)),x93014)) % 154.70/154.56 [9304]~P1(f328(f328(f330(f881(x93041,x93041)),f328(f328(f263(x93041,x93041),x93042),x93043)),f150(x93041,x93045)))+~P1(f328(f328(f242(a875),f328(x93044,x93042)),f328(x93044,x93043)))+P1(f328(f328(f330(f881(x93041,x93041)),f328(f328(f263(x93041,x93041),x93042),x93043)),f150(x93041,f328(f328(f148(f882(x93041,a875)),x93044),x93045)))) % 154.70/154.56 [9369]P1(f328(f328(f330(f881(x93694,x93694)),f328(f328(f263(x93694,x93694),x93692),x93693)),f150(x93694,x93695)))+P1(f328(f328(f243(a875),f328(x93691,x93692)),f328(x93691,x93693)))+~P1(f328(f328(f330(f881(x93694,x93694)),f328(f328(f263(x93694,x93694),x93692),x93693)),f150(x93694,f328(f328(f148(f882(x93694,a875)),x93691),x93695)))) % 154.70/154.56 [9510]~P1(f328(f328(f330(f881(f876(x95101),f876(x95101))),f328(f328(f263(f876(x95101),f876(x95101)),x95102),x95104)),f155(x95101,x95105)))+~P1(f328(f328(f243(a875),x95103),f328(f193(f876(x95101)),x95102)))+P1(f328(f328(f330(f881(x95101,x95101)),f328(f328(f263(x95101,x95101),f328(f328(f162(x95101),x95102),x95103)),f328(f328(f162(x95101),x95104),x95103))),x95105)) % 154.70/154.56 [9754]E(x97541,f2(a1))+~P1(f328(f48(x97543,x97541),f328(f328(f263(a1,a1),x97544),x97545)))+P1(f328(f48(f328(f328(f81(a1),x97542),x97543),x97541),f328(f328(f263(a1,a1),f328(f328(f80(a1),f328(f328(f81(a1),x97542),x97544)),f328(f328(f38(a1),f328(f328(f81(a1),x97542),x97545)),x97541))),f44(a1,f328(f328(f81(a1),x97542),x97545),x97541)))) % 154.70/154.56 [9756]~P1(f328(f328(f243(a875),f2(a875)),x97563))+~P1(f328(f47(x97562,x97563),f328(f328(f263(a875,a875),x97564),x97565)))+P1(f328(f47(f328(f328(f81(a875),x97561),x97562),x97563),f328(f328(f263(a875,a875),f328(f328(f80(a875),f328(f328(f81(a875),x97561),x97564)),f328(f328(f38(a875),f328(f328(f81(a875),x97561),x97565)),x97563))),f44(a875,f328(f328(f81(a875),x97561),x97565),x97563)))) % 154.70/154.56 [10066]~P66(x100662)+~P1(f328(f61(x100661),x100664))+E(f328(f328(f6(x100661,x100662),x100663),f328(f248(x100661),f328(f328(f18(x100661,a870,a870),f328(f328(f8(a870,f882(a870,a870),x100661),a326),f328(f328(f7(x100661,f882(x100661,a870),a870),f330(x100661)),x100664))),f328(f328(f7(x100661,f882(x100661,a870),a870),f330(x100661)),x100665)))),f328(f328(f6(x100661,x100662),f328(f328(f7(x100661,x100662,x100662),f328(f328(f18(x100661,x100662,f882(x100662,x100662)),f328(f328(f8(a870,f882(x100662,f882(x100662,x100662)),x100661),f100(x100662)),f328(f328(f7(x100661,f882(x100661,a870),a870),f330(x100661)),x100665))),x100663)),f2(x100662))),x100664)) % 154.70/154.56 [8249]~E(f328(f328(f125(x82491),x82492),x82495),f328(f328(f125(x82491),x82493),x82494))+E(f328(f328(f125(x82491),f328(f328(f135(x82491),f328(f193(f876(x82491)),x82492)),x82493)),x82494),x82495)+P1(f328(f328(f242(a875),f328(f193(f876(x82491)),x82493)),f328(f193(f876(x82491)),x82492))) % 154.70/154.56 [8444]~E(f328(f328(f125(x84442),x84443),x84441),f328(f328(f125(x84442),x84444),x84445))+E(x84441,f328(f328(f125(x84442),f328(f328(f135(x84442),f328(f193(f876(x84442)),x84443)),x84444)),x84445))+~P1(f328(f328(f242(a875),f328(f193(f876(x84442)),x84443)),f328(f193(f876(x84442)),x84444))) % 154.70/154.56 [8533]~E(f328(f328(f80(a875),f328(f328(f81(a875),x85333),x85334)),x85331),f328(f328(f80(a875),f328(f328(f81(a875),x85332),x85334)),x85335))+~P1(f328(f328(f242(a875),x85333),x85332))+E(x85331,f328(f328(f80(a875),f328(f328(f81(a875),f328(f328(f22(a875),x85332),x85333)),x85334)),x85335)) % 154.70/154.56 [8534]~E(f328(f328(f80(a875),f328(f328(f81(a875),x85341),x85343)),x85344),f328(f328(f80(a875),f328(f328(f81(a875),x85342),x85343)),x85345))+~P1(f328(f328(f242(a875),x85342),x85341))+E(f328(f328(f80(a875),f328(f328(f81(a875),f328(f328(f22(a875),x85341),x85342)),x85343)),x85344),x85345) % 154.70/154.56 [8699]E(f328(f328(f80(a875),f328(f328(f81(a875),x86991),x86992)),x86993),f328(f328(f80(a875),f328(f328(f81(a875),x86994),x86992)),x86995))+~P1(f328(f328(f242(a875),x86994),x86991))+~E(x86995,f328(f328(f80(a875),f328(f328(f81(a875),f328(f328(f22(a875),x86991),x86994)),x86992)),x86993)) % 154.70/154.56 [8700]E(f328(f328(f80(a875),f328(f328(f81(a875),x87001),x87002)),x87003),f328(f328(f80(a875),f328(f328(f81(a875),x87004),x87002)),x87005))+~P1(f328(f328(f242(a875),x87004),x87001))+~E(f328(f328(f80(a875),f328(f328(f81(a875),f328(f328(f22(a875),x87001),x87004)),x87002)),x87003),x87005) % 154.70/154.56 [9564]~P60(x95642)+~P1(f328(f61(x95641),x95645))+E(f328(f328(f9(x95641,x95642),f328(f328(f18(x95641,x95642,x95642),f328(f328(f8(x95642,f882(x95642,x95642),x95641),f286(x95642)),x95643)),x95644)),x95645),f328(f328(f286(x95642),f328(f328(f9(x95641,x95642),x95643),x95645)),f328(f328(f9(x95641,x95642),x95644),x95645))) % 154.70/154.56 [9690]~E(f644(x96905,x96904,x96903,x96902,x96901),f645(x96905,x96904,x96903,x96902,x96901))+P1(f328(f328(f330(f881(x96901,x96901)),f328(f328(f263(x96901,x96901),x96902),x96903)),f304(x96901,x96904)))+~P1(f328(f328(f330(f881(x96901,x96901)),f328(f328(f263(x96901,x96901),x96902),x96903)),f304(x96901,f328(f328(f114(f882(f881(x96901,x96901),a870)),x96904),x96905)))) % 154.70/154.56 [9691]~E(f649(x96915,x96914,x96913,x96912,x96911),f646(x96915,x96914,x96913,x96912,x96911))+P1(f328(f328(f330(f881(x96911,x96911)),f328(f328(f263(x96911,x96911),x96912),x96913)),f304(x96911,x96914)))+~P1(f328(f328(f330(f881(x96911,x96911)),f328(f328(f263(x96911,x96911),x96912),x96913)),f304(x96911,f328(f328(f114(f882(f881(x96911,x96911),a870)),x96914),x96915)))) % 154.70/154.56 [9901]P1(f328(f328(f330(f881(x99011,x99011)),f328(f328(f263(x99011,x99011),x99012),f645(x99015,x99014,x99013,x99012,x99011))),f304(x99011,x99014)))+P1(f328(f328(f330(f881(x99011,x99011)),f328(f328(f263(x99011,x99011),x99012),x99013)),f304(x99011,x99014)))+~P1(f328(f328(f330(f881(x99011,x99011)),f328(f328(f263(x99011,x99011),x99012),x99013)),f304(x99011,f328(f328(f114(f882(f881(x99011,x99011),a870)),x99014),x99015)))) % 154.70/154.56 [9980]P1(f328(f328(f330(f881(x99801,x99801)),f328(f328(f263(x99801,x99801),f646(x99805,x99804,x99803,x99802,x99801)),x99803)),f304(x99801,x99804)))+P1(f328(f328(f330(f881(x99801,x99801)),f328(f328(f263(x99801,x99801),x99802),x99803)),f304(x99801,x99804)))+~P1(f328(f328(f330(f881(x99801,x99801)),f328(f328(f263(x99801,x99801),x99802),x99803)),f304(x99801,f328(f328(f114(f882(f881(x99801,x99801),a870)),x99804),x99805)))) % 154.70/154.56 [10016]P1(f328(f328(f330(f881(x100161,x100161)),f328(f328(f263(x100161,x100161),x100162),x100163)),f304(x100161,x100164)))+P1(f328(f328(f330(f881(x100161,x100161)),f328(f328(f263(x100161,x100161),f645(x100165,x100164,x100163,x100162,x100161)),f644(x100165,x100164,x100163,x100162,x100161))),x100165))+~P1(f328(f328(f330(f881(x100161,x100161)),f328(f328(f263(x100161,x100161),x100162),x100163)),f304(x100161,f328(f328(f114(f882(f881(x100161,x100161),a870)),x100164),x100165)))) % 154.70/154.56 [10017]P1(f328(f328(f330(f881(x100171,x100171)),f328(f328(f263(x100171,x100171),x100172),x100173)),f304(x100171,x100174)))+P1(f328(f328(f330(f881(x100171,x100171)),f328(f328(f263(x100171,x100171),f649(x100175,x100174,x100173,x100172,x100171)),f646(x100175,x100174,x100173,x100172,x100171))),x100175))+~P1(f328(f328(f330(f881(x100171,x100171)),f328(f328(f263(x100171,x100171),x100172),x100173)),f304(x100171,f328(f328(f114(f882(f881(x100171,x100171),a870)),x100174),x100175)))) % 154.70/154.56 [10138]~P1(f328(f328(f330(f881(f876(x101381),f876(x101381))),f328(f328(f263(f876(x101381),f876(x101381)),x101384),x101385)),f155(x101381,x101382)))+~P1(f328(f328(f330(f881(x101381,x101381)),x101383),f328(f170(f881(x101381,x101381)),f328(f328(f180(x101381,x101381),x101384),x101385))))+P1(f328(f328(f267(x101381,x101381,a870),f328(f328(f7(x101381,f882(f881(x101381,x101381),a870),f882(x101381,a870)),f328(f328(f8(f882(x101381,f882(f882(f881(x101381,x101381),a870),a870)),f882(f882(f881(x101381,x101381),a870),f882(x101381,a870)),x101381),f7(x101381,f882(f881(x101381,x101381),a870),a870)),f328(f328(f8(f882(x101381,f881(x101381,x101381)),f882(x101381,f882(f882(f881(x101381,x101381),a870),a870)),x101381),f328(f8(f881(x101381,x101381),f882(f882(f881(x101381,x101381),a870),a870),x101381),f330(f881(x101381,x101381)))),f263(x101381,x101381)))),x101382)),x101383)) % 154.70/154.56 [9592]~P1(f328(f328(f242(a875),x95923),x95922))+~P1(f328(f328(f243(a875),f328(f328(f80(a875),f328(f328(f81(a875),x95923),x95924)),x95921)),f328(f328(f80(a875),f328(f328(f81(a875),x95922),x95924)),x95925)))+P1(f328(f328(f243(a875),x95921),f328(f328(f80(a875),f328(f328(f81(a875),f328(f328(f22(a875),x95922),x95923)),x95924)),x95925))) % 154.70/154.56 [9593]~P1(f328(f328(f242(a875),x95933),x95932))+~P1(f328(f328(f242(a875),f328(f328(f80(a875),f328(f328(f81(a875),x95933),x95934)),x95931)),f328(f328(f80(a875),f328(f328(f81(a875),x95932),x95934)),x95935)))+P1(f328(f328(f242(a875),x95931),f328(f328(f80(a875),f328(f328(f81(a875),f328(f328(f22(a875),x95932),x95933)),x95934)),x95935))) % 154.70/154.56 [9611]~P1(f328(f328(f242(a875),x96111),x96114))+P1(f328(f328(f243(a875),f328(f328(f80(a875),f328(f328(f81(a875),x96111),x96112)),x96113)),f328(f328(f80(a875),f328(f328(f81(a875),x96114),x96112)),x96115)))+~P1(f328(f328(f243(a875),x96113),f328(f328(f80(a875),f328(f328(f81(a875),f328(f328(f22(a875),x96114),x96111)),x96112)),x96115))) % 154.70/154.56 [9612]~P1(f328(f328(f242(a875),x96121),x96124))+P1(f328(f328(f242(a875),f328(f328(f80(a875),f328(f328(f81(a875),x96121),x96122)),x96123)),f328(f328(f80(a875),f328(f328(f81(a875),x96124),x96122)),x96125)))+~P1(f328(f328(f242(a875),x96123),f328(f328(f80(a875),f328(f328(f81(a875),f328(f328(f22(a875),x96124),x96121)),x96122)),x96125))) % 154.70/154.56 [9724]~P1(f328(f328(f242(a875),x97242),x97241))+~P1(f328(f328(f243(a875),f328(f328(f80(a875),f328(f328(f81(a875),x97241),x97243)),x97244)),f328(f328(f80(a875),f328(f328(f81(a875),x97242),x97243)),x97245)))+P1(f328(f328(f243(a875),f328(f328(f80(a875),f328(f328(f81(a875),f328(f328(f22(a875),x97241),x97242)),x97243)),x97244)),x97245)) % 154.70/154.56 [9725]~P1(f328(f328(f242(a875),x97252),x97251))+~P1(f328(f328(f242(a875),f328(f328(f80(a875),f328(f328(f81(a875),x97251),x97253)),x97254)),f328(f328(f80(a875),f328(f328(f81(a875),x97252),x97253)),x97255)))+P1(f328(f328(f242(a875),f328(f328(f80(a875),f328(f328(f81(a875),f328(f328(f22(a875),x97251),x97252)),x97253)),x97254)),x97255)) % 154.70/154.56 [9778]~P1(f328(f328(f242(a875),x97784),x97781))+P1(f328(f328(f243(a875),f328(f328(f80(a875),f328(f328(f81(a875),x97781),x97782)),x97783)),f328(f328(f80(a875),f328(f328(f81(a875),x97784),x97782)),x97785)))+~P1(f328(f328(f243(a875),f328(f328(f80(a875),f328(f328(f81(a875),f328(f328(f22(a875),x97781),x97784)),x97782)),x97783)),x97785)) % 154.70/154.56 [9779]~P1(f328(f328(f242(a875),x97794),x97791))+P1(f328(f328(f242(a875),f328(f328(f80(a875),f328(f328(f81(a875),x97791),x97792)),x97793)),f328(f328(f80(a875),f328(f328(f81(a875),x97794),x97792)),x97795)))+~P1(f328(f328(f242(a875),f328(f328(f80(a875),f328(f328(f81(a875),f328(f328(f22(a875),x97791),x97794)),x97792)),x97793)),x97795)) % 154.70/154.56 [10001]~P14(x100011,x100012,x100015,x100013)+~P1(f328(f328(f330(f881(x100011,x100011)),x100014),x100015))+P1(f328(f328(f267(x100011,x100011,a870),f328(f328(f7(x100011,f882(x100011,x100012),f882(x100011,a870)),f328(f328(f8(f882(x100012,a870),f882(f882(x100011,x100012),f882(x100011,a870)),x100011),f8(x100012,a870,x100011)),f328(f328(f8(x100012,f882(x100012,a870),x100011),a325),x100013))),x100013)),x100014)) % 154.70/154.56 [6782]~E(f328(x67824,x67825),f205(x67822))+E(f328(f183(x67821,x67822,x67823,x67824),x67825),f328(f235(x67822),x67826))+~E(f328(x67823,x67825),f328(f235(x67822),x67826)) % 154.70/154.56 [6884]~E(f328(x68843,x68846),f205(x68841))+E(f328(f237(f879(x68841),x68842,f205(x68841),x68843),f328(x68844,x68845)),f205(x68841))+~E(f328(x68844,x68845),f328(f235(x68842),x68846)) % 154.70/154.56 [7466]E(f328(x74661,x74662),f205(x74663))+~E(f328(f183(x74665,x74663,x74666,x74661),x74662),f328(f235(x74663),x74664))+E(f328(x74661,x74662),f328(f235(x74663),x74664)) % 154.70/154.56 [7502]~E(f328(f183(x75026,x75023,x75025,x75021),x75022),f328(f235(x75023),x75024))+E(f328(x75021,x75022),f328(f235(x75023),x75024))+E(f328(x75025,x75022),f328(f235(x75023),x75024)) % 154.70/154.56 [8407]~P21(x84076,x84071,x84072,x84074)+E(f328(f73(x84071,x84071,x84071,f328(x84072,x84073)),f328(x84074,x84075)),f328(f73(x84071,x84071,x84071,f328(x84074,x84075)),f328(x84072,x84073)))+~P1(f328(f61(x84076),x84075)) % 154.70/154.56 [8832]~P27(x88321,x88323,x88325,x88326)+~P27(x88323,x88322,x88324,f328(f307(x88321,x88323,x88325),x88326))+P27(x88321,x88322,f328(f73(x88323,x88322,x88321,x88324),x88325),x88326) % 154.70/154.56 [9401]~P1(f328(f328(x94013,x94012),x94016))+~P1(f328(f328(x94014,x94015),x94012))+P1(f328(f328(f330(x94011),x94012),f296(x94011,x94013,x94014,x94015,x94016))) % 154.70/154.56 [9402]~P1(f328(f328(x94024,x94022),x94026))+~P1(f328(f328(x94023,x94025),x94022))+P1(f328(f328(f330(x94021),x94022),f293(x94021,x94023,x94024,x94025,x94026))) % 154.70/154.56 [9511]E(x95111,x95112)+E(x95113,x95114)+~P1(f328(f328(f330(f881(f876(x95115),f876(x95115))),f328(f328(f263(f876(x95115),f876(x95115)),f328(f328(f148(x95115),x95113),x95111)),f328(f328(f148(x95115),x95114),x95112))),f154(x95115,x95116))) % 154.70/154.56 [9520]~E(x95202,x95204)+P1(f328(f328(f330(f881(f876(x95201),f876(x95201))),f328(f328(f263(f876(x95201),f876(x95201)),f328(f328(f148(x95201),x95202),x95203)),f328(f328(f148(x95201),x95204),x95205))),f142(x95201,x95206)))+~P1(f328(f328(f330(f881(f876(x95201),f876(x95201))),f328(f328(f263(f876(x95201),f876(x95201)),x95203),x95205)),f142(x95201,x95206))) % 154.70/154.56 [9521]~E(x95212,x95214)+P1(f328(f328(f330(f881(f876(x95211),f876(x95211))),f328(f328(f263(f876(x95211),f876(x95211)),f328(f328(f148(x95211),x95212),x95213)),f328(f328(f148(x95211),x95214),x95215))),f144(x95211,x95216)))+~P1(f328(f328(f330(f881(f876(x95211),f876(x95211))),f328(f328(f263(f876(x95211),f876(x95211)),x95213),x95215)),f144(x95211,x95216))) % 154.70/154.56 [9522]~E(x95222,x95224)+P1(f328(f328(f330(f881(f876(x95221),f876(x95221))),f328(f328(f263(f876(x95221),f876(x95221)),f328(f328(f148(x95221),x95222),x95223)),f328(f328(f148(x95221),x95224),x95225))),f154(x95221,x95226)))+~P1(f328(f328(f330(f881(f876(x95221),f876(x95221))),f328(f328(f263(f876(x95221),f876(x95221)),x95223),x95225)),f154(x95221,x95226))) % 154.70/154.56 [9523]~E(x95232,x95234)+P1(f328(f328(f330(f881(f876(x95231),f876(x95231))),f328(f328(f263(f876(x95231),f876(x95231)),f328(f328(f125(x95231),x95232),x95233)),f328(f328(f125(x95231),x95234),x95235))),f154(x95231,x95236)))+~P1(f328(f328(f330(f881(f876(x95231),f876(x95231))),f328(f328(f263(f876(x95231),f876(x95231)),x95233),x95235)),f154(x95231,x95236))) % 154.70/154.56 [9524]~E(x95243,x95245)+P1(f328(f328(f330(f881(f876(x95241),f876(x95241))),f328(f328(f263(f876(x95241),f876(x95241)),f328(f328(f125(x95241),x95242),x95243)),f328(f328(f125(x95241),x95244),x95245))),f154(x95241,x95246)))+~P1(f328(f328(f330(f881(f876(x95241),f876(x95241))),f328(f328(f263(f876(x95241),f876(x95241)),x95242),x95244)),f154(x95241,x95246))) % 154.70/154.56 [9580]E(x95801,x95802)+P1(f328(f328(f330(f881(f876(x95803),f876(x95803))),f328(f328(f263(f876(x95803),f876(x95803)),x95801),x95802)),f154(x95803,x95804)))+~P1(f328(f328(f330(f881(f876(x95803),f876(x95803))),f328(f328(f263(f876(x95803),f876(x95803)),f328(f328(f148(x95803),x95805),x95801)),f328(f328(f148(x95803),x95806),x95802))),f154(x95803,x95804))) % 154.70/154.56 [9728]~E(x97283,x97285)+P1(f328(f328(f330(f881(f876(x97281),f876(x97281))),f328(f328(f263(f876(x97281),f876(x97281)),f328(f328(f125(x97281),x97282),f328(f328(f148(x97281),x97283),f117(x97281)))),f328(f328(f125(x97281),x97284),f328(f328(f148(x97281),x97285),f117(x97281))))),f154(x97281,x97286)))+~P1(f328(f328(f330(f881(f876(x97281),f876(x97281))),f328(f328(f263(f876(x97281),f876(x97281)),x97282),x97284)),f154(x97281,x97286))) % 154.70/154.56 [9744]E(f328(x97441,x97442),f205(x97443))+~E(f328(f237(f879(x97446),x97443,f205(x97446),x97444),f328(x97441,x97442)),f205(x97446))+E(f328(x97444,f770(x97442,x97441,x97444,x97445,x97446,x97443)),f205(x97446)) % 154.70/154.56 [9745]E(f328(x97451,x97452),f205(x97453))+~E(f328(f237(f879(x97456),x97453,f205(x97456),x97454),f328(x97451,x97452)),f205(x97456))+E(f328(f235(x97453),f770(x97452,x97451,x97454,x97455,x97456,x97453)),f328(x97451,x97452)) % 154.70/154.56 [9782]E(x97821,x97822)+E(x97823,x97824)+~P1(f328(f328(f330(f881(f876(x97825),f876(x97825))),f328(f328(f263(f876(x97825),f876(x97825)),f328(f328(f125(x97825),x97823),f328(f328(f148(x97825),x97821),f117(x97825)))),f328(f328(f125(x97825),x97824),f328(f328(f148(x97825),x97822),f117(x97825))))),f154(x97825,x97826))) % 154.70/154.56 [9807]E(x98071,x98072)+~P1(f328(f328(f330(f881(f876(x98073),f876(x98073))),f328(f328(f263(f876(x98073),f876(x98073)),f328(f328(f125(x98073),x98071),f328(f328(f148(x98073),x98075),f117(x98073)))),f328(f328(f125(x98073),x98072),f328(f328(f148(x98073),x98076),f117(x98073))))),f154(x98073,x98074)))+P1(f328(f328(f330(f881(f876(x98073),f876(x98073))),f328(f328(f263(f876(x98073),f876(x98073)),x98071),x98072)),f154(x98073,x98074))) % 154.70/154.56 [9843]~P1(f328(f328(f330(f881(f882(x98431,a870),f882(x98431,a870))),f328(f328(f263(f882(x98431,a870),f882(x98431,a870)),x98432),x98434)),f319(x98431,x98436)))+~P1(f328(f328(f330(f881(f882(x98431,a870),f882(x98431,a870))),f328(f328(f263(f882(x98431,a870),f882(x98431,a870)),x98433),x98435)),f319(x98431,x98436)))+P1(f328(f328(f330(f881(f882(x98431,a870),f882(x98431,a870))),f328(f328(f263(f882(x98431,a870),f882(x98431,a870)),f328(f328(f114(f882(x98431,a870)),x98432),x98433)),f328(f328(f114(f882(x98431,a870)),x98434),x98435))),f319(x98431,x98436))) % 154.70/154.56 [5233]~E(f328(x52333,x52336),x52335)+~E(x52334,f328(f235(x52331),x52336))+E(f328(f328(f206(x52331,x52332),x52333),x52334),f328(f235(x52332),x52335)) % 154.70/154.56 [5645]~E(f328(f328(f125(x56451),x56456),x56453),x56455)+E(f328(f328(f125(x56451),x56452),x56453),f328(f328(f148(x56451),x56454),x56455))+~E(x56452,f328(f328(f148(x56451),x56454),x56456)) % 154.70/154.56 [5646]~E(f328(f328(f125(x56461),x56466),x56463),x56465)+E(f328(f328(f125(x56461),x56462),x56463),f328(f328(f125(x56461),x56464),x56465))+~E(x56462,f328(f328(f125(x56461),x56464),x56466)) % 154.70/154.56 [5648]E(f328(f328(f125(x56481),x56482),x56483),f328(f328(f148(x56481),x56484),x56485))+~E(f328(f328(f148(x56481),x56484),x56486),x56482)+~E(x56485,f328(f328(f125(x56481),x56486),x56483)) % 154.70/154.56 [5650]~E(f328(f328(f125(x56501),x56502),x56506),x56504)+E(f328(f328(f125(x56501),x56502),x56503),f328(f328(f125(x56501),x56504),x56505))+~E(x56503,f328(f328(f125(x56501),x56506),x56505)) % 154.70/154.56 [6776]E(f328(x67761,x67762),f328(x67763,x67762))+~E(f328(f328(f151(x67764,x67765),x67761),x67766),f328(f328(f151(x67764,x67765),x67763),x67766))+~P1(f328(f328(f330(x67764),x67762),f328(f170(x67764),x67766))) % 154.70/154.56 [7159]~P21(x71594,x71595,x71596,x71591)+E(f328(f328(x71591,x71592),x71593),f328(f328(f64(x71594,x71595,x71596),x71593),x71592))+~P1(f328(f61(x71594),x71592)) % 154.70/154.56 [7227]~E(x72272,f328(x72274,x72276))+~P1(f328(f328(f330(x72273),x72276),x72275))+P1(f328(f328(f330(x72271),x72272),f328(f307(x72273,x72271,x72274),x72275))) % 154.70/154.56 [7228]~E(f328(x72284,x72282),x72286)+~P1(f328(f328(f330(x72283),x72286),x72285))+P1(f328(f328(f330(x72281),x72282),f328(f308(x72281,x72283,x72284),x72285))) % 154.70/154.56 [7683]~P34(x76831,x76832,x76834,x76836)+P34(x76831,x76832,f328(f328(f148(x76831),x76833),x76834),f328(f328(f148(x76831),x76835),x76836))+~P1(f328(f328(x76832,x76833),x76835)) % 154.70/154.56 [8707]~P53(x87074,x87075,x87071,x87072,x87076)+E(f328(x87071,f328(x87072,x87073)),x87073)+~P1(f328(f328(f330(x87075),x87073),x87076)) % 154.70/154.56 [9513]E(x95131,x95132)+E(f328(f193(f876(x95133)),x95134),f328(f193(f876(x95133)),x95135))+~P1(f328(f328(f330(f881(f876(x95133),f876(x95133))),f328(f328(f263(f876(x95133),f876(x95133)),f328(f328(f148(x95133),x95131),x95134)),f328(f328(f148(x95133),x95132),x95135))),f142(x95133,x95136))) % 154.70/154.56 [9576]~P18(x95761,x95762,x95763)+E(f328(f328(f64(x95761,x95762,x95763),x95764),x95765),x95766)+~P1(f328(f66(x95761,x95762,x95763,x95764,x95765),x95766)) % 154.70/154.56 [9583]E(f328(f193(f876(x95831)),x95832),f328(f193(f876(x95831)),x95833))+P1(f328(f328(f330(f881(f876(x95831),f876(x95831))),f328(f328(f263(f876(x95831),f876(x95831)),x95832),x95833)),f142(x95831,x95834)))+~P1(f328(f328(f330(f881(f876(x95831),f876(x95831))),f328(f328(f263(f876(x95831),f876(x95831)),f328(f328(f148(x95831),x95835),x95832)),f328(f328(f148(x95831),x95836),x95833))),f142(x95831,x95834))) % 154.70/154.56 [9605]~P1(f328(f328(f330(f881(x96051,x96051)),f328(f328(f263(x96051,x96051),x96052),x96054)),f304(x96051,x96056)))+P1(f328(f328(f330(f881(f876(x96051),f876(x96051))),f328(f328(f263(f876(x96051),f876(x96051)),f328(f328(f148(x96051),x96052),x96053)),f328(f328(f148(x96051),x96054),x96055))),f304(f876(x96051),f154(x96051,x96056))))+~P1(f328(f328(f330(f881(f876(x96051),f876(x96051))),f328(f328(f263(f876(x96051),f876(x96051)),x96053),x96055)),f304(f876(x96051),f154(x96051,x96056)))) % 154.70/154.56 [9788]~P1(f328(x97882,x97886))+~E(f328(f133(x97881,x97882),x97883),f328(f328(f148(x97881),x97884),x97885))+~P1(f328(f328(f330(x97881),x97886),f328(f170(x97881),f786(x97885,x97884,x97883,x97882,x97881)))) % 154.70/154.56 [9789]~P1(f328(x97894,x97896))+~E(f328(f328(f148(x97891),x97892),x97893),f328(f133(x97891,x97894),x97895))+~P1(f328(f328(f330(x97891),x97896),f328(f170(x97891),f789(x97895,x97894,x97893,x97892,x97891)))) % 154.70/154.56 [10094]~P66(x100942)+E(f328(f328(f6(x100941,x100942),f328(f328(f8(f882(x100943,a870),x100942,x100941),f328(f6(x100943,x100942),x100944)),f328(f328(f8(f882(x100943,a870),f882(x100943,a870),x100941),f248(x100943)),f328(f328(f8(f882(x100943,a870),f882(x100943,a870),x100941),f328(f18(x100943,a870,a870),f328(f328(f8(a870,f882(a870,a870),x100943),a326),f328(f328(f7(x100943,f882(x100943,a870),a870),f330(x100943)),x100945)))),f328(f7(x100943,x100941,a870),f328(f328(f8(x100941,f882(x100941,a870),x100943),a325),x100946)))))),f328(f307(x100943,x100941,x100946),x100945)),f328(f328(f6(x100943,x100942),x100944),x100945))+~P1(f328(f61(x100943),x100945)) % 154.70/154.56 [6834]~P105(x68343)+P1(f328(x68342,x68345))+E(f328(f133(x68341,x68342),f328(f328(f145(x68341,x68343,x68344),x68345),x68346)),f328(f133(x68341,x68342),x68346)) % 154.70/154.56 [6836]P1(f328(x68361,x68362))+~E(f164(x68363,x68361,x68364),f328(f328(f263(f876(x68363),f876(x68363)),x68365),x68366))+~P1(f328(f328(f330(x68363),x68362),f328(f170(x68363),x68365))) % 154.70/154.56 [6881]~P1(f328(x68812,x68816))+~E(f164(x68811,x68812,x68813),f328(f328(f263(f876(x68811),f876(x68811)),x68814),x68815))+~P1(f328(f328(f330(x68811),x68816),f328(f170(x68811),x68815))) % 154.70/154.56 [7546]~P17(x75461,x75462,x75463)+~P1(f328(f61(x75461),x75466))+E(f328(f328(f64(x75461,x75462,x75463),x75464),f328(f328(f306(x75461),x75465),x75466)),f328(f328(f64(x75461,x75462,x75463),f328(f328(x75463,x75465),x75464)),x75466)) % 154.70/154.56 [7598]~P105(x75982)+~P1(f328(f328(f242(x75982),f328(x75983,x75984)),f328(x75983,x75985)))+E(f328(f328(f145(x75981,x75982,x75983),x75984),f328(f328(f148(x75981),x75985),x75986)),f328(f328(f148(x75981),x75984),f328(f328(f148(x75981),x75985),x75986))) % 154.70/154.56 [7713]E(x77131,x77132)+~E(f328(f328(f265(x77133,x77134),x77131),f328(f16(f882(x77134,a870),x77133),x77135)),f328(f328(f265(x77133,x77134),x77132),f328(f16(f882(x77134,a870),x77133),x77135)))+~P1(f328(f328(f330(x77134),x77136),x77135)) % 154.70/154.56 [7780]~P17(x77801,x77802,x77803)+~P1(f328(f61(x77801),x77806))+E(f328(f328(f64(x77801,x77802,x77803),x77804),f328(f328(f306(x77801),x77805),x77806)),f328(f328(x77803,x77805),f328(f328(f64(x77801,x77802,x77803),x77804),x77806))) % 154.70/154.56 [7898]~P18(x78981,x78982,x78983)+~P1(f328(f61(x78981),x78986))+E(f328(f328(f64(x78981,x78982,x78983),f328(f328(x78983,x78984),x78985)),x78986),f328(f328(x78983,x78984),f328(f328(f64(x78981,x78982,x78983),x78985),x78986))) % 154.70/154.56 [7967]~P22(x79672,x79675,x79676,x79671)+~P1(f328(f61(x79672),x79674))+E(f328(x79671,f328(f328(f306(x79672),x79673),x79674)),f328(f73(x79675,x79675,x79675,f328(x79671,x79674)),f328(x79676,x79673))) % 154.70/154.56 [7999]~P105(x79992)+P1(f328(f328(f242(x79992),f328(x79993,x79994)),f328(x79993,x79995)))+E(f328(f328(f145(x79991,x79992,x79993),x79994),f328(f328(f148(x79991),x79995),x79996)),f328(f328(f148(x79991),x79995),f328(f328(f145(x79991,x79992,x79993),x79994),x79996))) % 154.70/154.56 [8141]~E(f328(f193(f876(x81411)),x81415),f328(f193(f876(x81412)),x81416))+~E(f328(f193(f876(x81411)),x81413),f328(f193(f876(x81412)),x81414))+E(f328(f328(f125(f881(x81411,x81412)),f328(f328(f180(x81411,x81412),x81413),x81414)),f328(f328(f180(x81411,x81412),x81415),x81416)),f328(f328(f180(x81411,x81412),f328(f328(f125(x81411),x81413),x81415)),f328(f328(f125(x81412),x81414),x81416))) % 154.70/154.56 [8264]~E(x82642,f328(f307(x82643,x82641,x82644),x82646))+P1(f328(f328(f242(f882(x82641,a870)),x82642),f328(f307(x82643,x82641,x82644),x82645)))+~P1(f328(f328(f242(f882(x82643,a870)),x82646),x82645)) % 154.70/154.56 [8365]~P105(x83655)+E(f328(x83651,x83652),f328(x83651,x83653))+E(f328(f328(f145(x83654,x83655,x83651),x83652),f328(f328(f145(x83654,x83655,x83651),x83653),x83656)),f328(f328(f145(x83654,x83655,x83651),x83653),f328(f328(f145(x83654,x83655,x83651),x83652),x83656))) % 154.70/154.56 [8400]~P27(x84003,x84001,x84004,x84005)+P27(x84003,x84001,f328(f328(f328(f72(x84003,x84001),x84004),x84006),x84002),x84005)+P1(f328(f328(f330(x84001),x84002),f328(f307(x84003,x84001,x84004),x84005))) % 154.70/154.56 [8545]~P1(f328(f328(f330(x85452),x85454),f328(x85456,x85453)))+~P1(f328(f328(f330(x85451),x85453),x85455))+P1(f328(f328(f330(f881(x85451,x85452)),f328(f328(f263(x85451,x85452),x85453),x85454)),f328(f328(f265(x85451,x85452),x85455),x85456))) % 154.70/154.56 [9010]~P66(x90102)+~P27(x90104,x90101,x90105,x90106)+E(f328(f328(f6(x90101,x90102),x90103),f328(f307(x90104,x90101,x90105),x90106)),f328(f328(f6(x90104,x90102),f328(f73(x90101,x90102,x90104,x90103),x90105)),x90106)) % 154.70/154.56 [9011]~P73(x90112)+~P27(x90114,x90111,x90115,x90116)+E(f328(f328(f9(x90111,x90112),x90113),f328(f307(x90114,x90111,x90115),x90116)),f328(f328(f9(x90114,x90112),f328(f73(x90111,x90112,x90114,x90113),x90115)),x90116)) % 154.70/154.56 [9059]~P36(x90592,x90595,x90591,x90593,x90596)+P1(f328(f328(x90591,f328(f328(f162(x90592),x90593),x90594)),f328(f328(f162(x90595),x90596),x90594)))+~P1(f328(f328(f243(a875),x90594),f328(f193(f876(x90595)),x90596))) % 154.70/154.56 [9060]~P36(x90602,x90605,x90601,x90603,x90606)+P1(f328(f328(x90601,f328(f328(f162(x90602),x90603),x90604)),f328(f328(f162(x90605),x90606),x90604)))+~P1(f328(f328(f243(a875),x90604),f328(f193(f876(x90602)),x90603))) % 154.70/154.56 [9271]~P21(x92713,x92711,x92716,x92712)+~P1(f328(f61(x92713),x92714))+E(f328(f73(x92711,x92711,x92711,f328(x92712,f328(f328(f22(f882(x92713,a870)),x92714),f328(f328(f306(x92713),x92715),f192(f882(x92713,a870)))))),f328(x92716,x92715)),f328(x92712,f328(f328(f306(x92713),x92715),x92714))) % 154.70/154.56 [9881]~E(f328(f307(x98812,x98814,x98816),f251(f882(x98812,a870))),f251(f882(x98814,a870)))+~E(f328(f307(x98811,x98813,x98815),f251(f882(x98811,a870))),f251(f882(x98813,a870)))+E(f328(f307(f881(x98811,x98812),f881(x98813,x98814),f268(x98811,x98813,x98812,x98814,x98815,x98816)),f251(f882(f881(x98811,x98812),a870))),f251(f882(f881(x98813,x98814),a870))) % 154.70/154.56 [9929]~P27(x99293,x99294,x99295,f328(x99296,f451(x99296,x99295,x99294,x99293,x99292,x99291)))+P27(x99293,x99294,x99295,f328(f328(f42(x99292,f882(x99293,a870)),x99291),x99296))+E(x99291,f192(f882(x99292,a870))) % 154.70/154.56 [9987]P27(x99876,x99875,x99874,f328(f328(f42(x99872,f882(x99876,a870)),x99871),x99873))+E(x99871,f192(f882(x99872,a870)))+P1(f328(f328(f330(x99872),f451(x99873,x99874,x99875,x99876,x99872,x99871)),x99871)) % 154.70/154.56 [9992]P1(f328(f328(f330(x99921),f616(x99922,x99923,x99924,x99925,x99926,x99921)),x99926))+P1(f328(f328(f242(f882(f881(x99921,x99924),a870)),f328(f328(f265(x99921,x99924),x99926),x99923)),f328(f328(f265(x99921,x99924),x99925),x99922)))+~P1(f328(f328(f242(f882(x99921,a870)),x99926),x99925)) % 154.70/154.56 [10030]P26(x100306,x100305,f328(f328(f306(f874(x100306)),f328(f328(f328(f92(x100306),x100301),x100303),x100302)),f192(f882(f874(x100306),a870))))+~P26(x100306,x100305,f328(f328(f306(f874(x100306)),f328(f328(f328(f92(x100306),x100304),x100303),x100302)),f192(f882(f874(x100306),a870))))+P1(f328(f328(x100301,f383(x100301,x100302,x100303,x100304,x100305,x100306)),f392(x100301,x100302,x100303,x100304,x100305,x100306))) % 154.70/154.56 [10031]P26(x100316,x100315,f328(f328(f306(f874(x100316)),f328(f328(f328(f92(x100316),x100314),x100313),x100312)),f192(f882(f874(x100316),a870))))+~P26(x100316,x100315,f328(f328(f306(f874(x100316)),f328(f328(f328(f92(x100316),x100314),x100313),x100311)),f192(f882(f874(x100316),a870))))+P1(f328(f328(x100311,f404(x100312,x100311,x100313,x100314,x100315,x100316)),f418(x100312,x100311,x100313,x100314,x100315,x100316))) % 154.70/154.56 [10069]~P26(x100691,x100692,f328(f328(f306(f874(x100691)),f328(f328(f328(f92(x100691),x100693),x100694),x100696)),f192(f882(f874(x100691),a870))))+P26(x100691,x100692,f328(f328(f306(f874(x100691)),f328(f328(f328(f92(x100691),x100693),x100694),x100695)),f192(f882(f874(x100691),a870))))+~P1(f328(f328(x100695,f404(x100695,x100696,x100694,x100693,x100692,x100691)),f418(x100695,x100696,x100694,x100693,x100692,x100691))) % 154.70/154.56 [10070]~P26(x100701,x100702,f328(f328(f306(f874(x100701)),f328(f328(f328(f92(x100701),x100706),x100704),x100705)),f192(f882(f874(x100701),a870))))+P26(x100701,x100702,f328(f328(f306(f874(x100701)),f328(f328(f328(f92(x100701),x100703),x100704),x100705)),f192(f882(f874(x100701),a870))))+~P1(f328(f328(x100706,f383(x100703,x100705,x100704,x100706,x100702,x100701)),f392(x100703,x100705,x100704,x100706,x100702,x100701))) % 154.70/154.56 [10105]~P1(f328(f328(f242(f882(x101052,a870)),f328(x101054,f616(x101056,x101054,x101052,x101055,x101053,x101051))),f328(x101056,f616(x101056,x101054,x101052,x101055,x101053,x101051))))+~P1(f328(f328(f242(f882(x101051,a870)),x101053),x101055))+P1(f328(f328(f242(f882(f881(x101051,x101052),a870)),f328(f328(f265(x101051,x101052),x101053),x101054)),f328(f328(f265(x101051,x101052),x101055),x101056))) % 154.70/154.56 [7733]~P1(f328(x77331,x77335))+~P1(f328(x77336,x77334))+P1(f328(x77331,f328(f266(x77332,x77333),f328(f328(f263(x77332,x77333),x77334),x77335)))) % 154.70/154.56 [7734]~P1(f328(x77341,x77344))+~P1(f328(x77346,x77345))+P1(f328(x77341,f328(f262(x77342,x77343),f328(f328(f263(x77342,x77343),x77344),x77345)))) % 154.70/154.56 [7755]~E(f328(f193(f876(x77551)),x77553),f328(f193(f876(x77554)),x77555))+~E(f328(f328(f176(x77551,x77554),f328(f328(f180(x77551,x77554),x77553),x77555)),x77552),f328(f235(x77554),x77556))+P1(f328(f328(f330(x77551),x77552),f328(f170(x77551),x77553))) % 154.70/154.56 [7785]~P1(f328(f328(x77854,x77856),x77855))+~P1(f328(f328(f330(x77851),x77856),x77853))+P1(f328(f328(f328(f41(x77851,f882(x77852,a870)),x77853),x77854),x77855)) % 154.70/154.56 [8088]~P1(f328(f328(f330(x80881),x80882),f328(x80885,x80886)))+~P1(f328(f328(f330(x80883),x80886),x80884))+P1(f328(f328(f330(x80881),x80882),f328(f328(f41(x80883,f882(x80881,a870)),x80884),x80885))) % 154.70/154.56 [8132]P1(f328(f328(x81321,x81322),x81323))+~P1(f328(f328(x81324,x81322),x81323))+~P1(f328(f328(f242(f882(x81325,f882(x81326,a870))),x81324),x81321)) % 154.70/154.56 [8287]P1(f328(f328(x82871,x82872),x82873))+~P1(f328(f328(f330(x82874),x82872),x82875))+~P1(f328(f328(f328(f42(x82874,f882(x82876,a870)),x82875),x82871),x82873)) % 154.70/154.56 [8423]P1(f328(f328(f330(x84231),x84232),f328(x84233,x84234)))+~P1(f328(f328(f330(x84235),x84234),x84236))+~P1(f328(f328(f330(x84231),x84232),f328(f328(f42(x84235,f882(x84231,a870)),x84236),x84233))) % 154.70/154.56 [8617]~P1(f328(f328(f328(f328(a200,x86171),x86173),x86174),x86176))+~P1(f328(f328(f328(f328(a200,x86172),x86176),x86174),x86175))+P1(f328(f328(f328(f328(a200,f33(x86171,x86172)),x86173),x86174),x86175)) % 154.70/154.56 [8689]~P14(x86894,x86895,x86896,x86891)+E(f328(x86891,x86892),f328(x86891,x86893))+~P1(f328(f328(f330(f881(x86894,x86894)),f328(f328(f263(x86894,x86894),x86892),x86893)),x86896)) % 154.70/154.56 [8720]P1(f328(f328(f242(f882(x87201,a870)),x87202),f328(x87203,x87204)))+~P1(f328(f328(f330(x87205),x87204),x87206))+~P1(f328(f328(f242(f882(x87201,a870)),x87202),f328(f328(f42(x87205,f882(x87201,a870)),x87206),x87203))) % 154.70/154.56 [8748]~P51(x87483,x87484,f328(f283(x87484,x87483),x87485))+E(x87481,f192(f882(x87482,a870)))+E(f328(f328(f42(x87482,f882(x87483,a870)),x87481),f328(f328(f8(f882(x87484,a870),f882(x87483,a870),x87482),f282(x87484,x87483,x87485)),x87486)),f328(f282(x87484,x87483,x87485),f328(f328(f42(x87482,f882(x87484,a870)),x87481),x87486))) % 154.70/154.56 [8823]P1(f328(f328(f330(x88231),x88232),f328(f282(x88233,x88231,x88234),x88235)))+~P1(f328(f328(f330(x88233),x88236),x88235))+~P1(f328(f328(f330(f881(x88233,x88231)),f328(f328(f263(x88233,x88231),x88236),x88232)),x88234)) % 154.70/154.56 [8941]P1(f328(x89411,x89412))+~P1(f328(f328(f328(f328(a200,x89414),x89412),x89415),x89416))+P1(f328(f328(f328(f328(a200,f30(x89411,x89413,x89414)),x89412),x89415),x89416)) % 154.70/154.56 [8958]~P1(f328(x89581,x89584))+~P1(f328(f328(f328(f328(a200,x89582),x89584),x89585),x89586))+P1(f328(f328(f328(f328(a200,f30(x89581,x89582,x89583)),x89584),x89585),x89586)) % 154.70/154.56 [9135]P1(f328(f328(f242(f882(x91351,a870)),f328(f282(x91352,x91351,x91353),x91354)),f328(f282(x91352,x91351,x91355),x91356)))+~P1(f328(f328(f242(f882(x91352,a870)),x91354),x91356))+~P1(f328(f328(f242(f882(f881(x91352,x91351),a870)),x91353),x91355)) % 154.70/154.56 [9223]P1(f328(x92231,x92232))+P1(f328(f328(f328(f328(a200,x92233),x92232),x92234),x92235))+~P1(f328(f328(f328(f328(a200,f30(x92231,x92236,x92233)),x92232),x92234),x92235)) % 154.70/154.56 [9228]~P1(f328(x92285,x92282))+P1(f328(f328(f328(f328(a200,x92281),x92282),x92283),x92284))+~P1(f328(f328(f328(f328(a200,f30(x92285,x92281,x92286)),x92282),x92283),x92284)) % 154.70/154.56 [9278]P1(f328(f328(f328(f328(a200,x92781),x92782),x92783),x92784))+P1(f328(f328(f328(f328(a200,x92785),x92782),x92783),x92784))+~P1(f328(f328(f328(f328(a200,f30(x92786,x92781,x92785)),x92782),x92783),x92784)) % 154.70/154.56 [9320]~P1(f328(f328(f330(x93202),x93206),x93204))+~P1(f328(f328(f242(f882(x93201,a870)),x93203),x93205))+P1(f328(f328(f242(f882(f881(x93201,x93202),a870)),f328(f328(f265(x93201,x93202),x93203),f328(f16(f882(x93202,a870),x93201),x93204))),f328(f328(f265(x93201,x93202),x93205),f328(f16(f882(x93202,a870),x93201),x93204)))) % 154.70/154.56 [9333]~P36(x93331,x93332,x93333,x93335,x93336)+P1(f328(f328(f267(x93331,x93332,a870),x93333),x93334))+~P1(f328(f328(f330(f881(x93331,x93332)),x93334),f328(f170(f881(x93331,x93332)),f328(f328(f180(x93331,x93332),x93335),x93336)))) % 154.70/154.56 [9467]~E(x94673,x94675)+P1(f328(f328(f330(f881(f876(x94671),f876(x94671))),f328(f328(f263(f876(x94671),f876(x94671)),f328(f328(f148(x94671),x94672),x94673)),f328(f328(f148(x94671),x94674),x94675))),f154(x94671,x94676)))+~P1(f328(f328(f330(f881(x94671,x94671)),f328(f328(f263(x94671,x94671),x94672),x94674)),x94676)) % 154.70/154.56 [9473]~E(f328(f193(f876(x94731)),x94735),f328(f193(f876(x94732)),x94736))+E(f185(x94731,x94732,f186(x94731,x94732,x94733,f328(f328(f22(f882(x94731,a870)),x94734),f328(f170(x94731),x94735))),x94735,x94736),f186(x94731,x94732,f185(x94731,x94732,x94733,x94735,x94736),x94734))+~P1(f328(f328(f242(f882(x94731,a870)),f328(f170(x94731),x94735)),x94734)) % 154.70/154.56 [9474]~E(f328(f193(f876(x94741)),x94743),f328(f193(f876(x94741)),x94745))+P1(f328(f328(f330(f881(f876(x94741),f876(x94741))),f328(f328(f263(f876(x94741),f876(x94741)),f328(f328(f148(x94741),x94742),x94743)),f328(f328(f148(x94741),x94744),x94745))),f142(x94741,x94746)))+~P1(f328(f328(f330(f881(x94741,x94741)),f328(f328(f263(x94741,x94741),x94742),x94744)),x94746)) % 154.70/154.56 [9504]P1(f328(f328(f330(f881(x95041,x95041)),f328(f328(f263(x95041,x95041),x95042),x95043)),f328(f328(f187(f881(x95041,x95041),a870),f328(a116,x95044)),x95045)))+~P1(f328(f328(f330(f881(x95041,x95041)),f328(f328(f263(x95041,x95041),x95046),x95043)),x95045))+~P1(f328(f328(f330(f881(x95041,x95041)),f328(f328(f263(x95041,x95041),x95042),x95046)),f328(f328(f187(f881(x95041,x95041),a870),x95044),x95045))) % 154.70/154.56 [9505]P1(f328(f328(f330(f881(x95051,x95051)),f328(f328(f263(x95051,x95051),x95052),x95053)),f328(f328(f187(f881(x95051,x95051),a870),f328(a116,x95054)),x95055)))+~P1(f328(f328(f330(f881(x95051,x95051)),f328(f328(f263(x95051,x95051),x95052),x95056)),x95055))+~P1(f328(f328(f330(f881(x95051,x95051)),f328(f328(f263(x95051,x95051),x95056),x95053)),f328(f328(f187(f881(x95051,x95051),a870),x95054),x95055))) % 154.70/154.56 [9509]~P1(f328(f328(f330(x95094),x95095),x95096))+P1(f328(f328(f242(f882(x95091,a870)),x95092),x95093))+~P1(f328(f328(f242(f882(f881(x95091,x95094),a870)),f328(f328(f265(x95091,x95094),x95092),f328(f16(f882(x95094,a870),x95091),x95096))),f328(f328(f265(x95091,x95094),x95093),f328(f16(f882(x95094,a870),x95091),x95096)))) % 154.70/154.56 [9554]E(x95541,x95542)+~P1(f328(f328(f330(f881(f876(x95543),f876(x95543))),f328(f328(f263(f876(x95543),f876(x95543)),f328(f328(f148(x95543),x95541),x95545)),f328(f328(f148(x95543),x95542),x95546))),f142(x95543,x95544)))+P1(f328(f328(f330(f881(x95543,x95543)),f328(f328(f263(x95543,x95543),x95541),x95542)),x95544)) % 154.70/154.56 [9555]E(x95551,x95552)+~P1(f328(f328(f330(f881(f876(x95553),f876(x95553))),f328(f328(f263(f876(x95553),f876(x95553)),f328(f328(f148(x95553),x95551),x95555)),f328(f328(f148(x95553),x95552),x95556))),f144(x95553,x95554)))+P1(f328(f328(f330(f881(x95553,x95553)),f328(f328(f263(x95553,x95553),x95551),x95552)),x95554)) % 154.70/154.56 [9556]E(x95561,x95562)+~P1(f328(f328(f330(f881(f876(x95563),f876(x95563))),f328(f328(f263(f876(x95563),f876(x95563)),f328(f328(f148(x95563),x95561),x95565)),f328(f328(f148(x95563),x95562),x95566))),f154(x95563,x95564)))+P1(f328(f328(f330(f881(x95563,x95563)),f328(f328(f263(x95563,x95563),x95561),x95562)),x95564)) % 154.70/154.56 [9591]P1(f328(f328(f330(f881(f876(x95911),f876(x95911))),f328(f328(f263(f876(x95911),f876(x95911)),f328(f328(f148(x95911),x95912),x95913)),f328(f328(f148(x95911),x95914),x95915))),f155(x95911,x95916)))+~P1(f328(f328(f330(f881(f876(x95911),f876(x95911))),f328(f328(f263(f876(x95911),f876(x95911)),x95913),x95915)),f155(x95911,x95916)))+~P1(f328(f328(f330(f881(x95911,x95911)),f328(f328(f263(x95911,x95911),x95912),x95914)),x95916)) % 154.70/154.56 [9609]P1(f328(x96091,x96092))+~P1(f328(x96091,f731(x96091,x96093,x96094,x96095,x96096)))+~P1(f328(f328(f330(x96096),x96092),f328(f328(f41(x96095,f882(x96096,a870)),x96094),x96093))) % 154.70/154.56 [9614]~P1(f328(f328(f330(f881(f876(x96141),f876(x96141))),f328(f328(f263(f876(x96141),f876(x96141)),f328(f328(f148(x96141),x96142),x96145)),f328(f328(f148(x96141),x96143),x96146))),f142(x96141,x96144)))+P1(f328(f328(f330(f881(f876(x96141),f876(x96141))),f328(f328(f263(f876(x96141),f876(x96141)),x96145),x96146)),f142(x96141,x96144)))+P1(f328(f328(f330(f881(x96141,x96141)),f328(f328(f263(x96141,x96141),x96142),x96143)),x96144)) % 154.70/154.56 [9615]~P1(f328(f328(f330(f881(f876(x96151),f876(x96151))),f328(f328(f263(f876(x96151),f876(x96151)),f328(f328(f148(x96151),x96152),x96155)),f328(f328(f148(x96151),x96153),x96156))),f144(x96151,x96154)))+P1(f328(f328(f330(f881(f876(x96151),f876(x96151))),f328(f328(f263(f876(x96151),f876(x96151)),x96155),x96156)),f144(x96151,x96154)))+P1(f328(f328(f330(f881(x96151,x96151)),f328(f328(f263(x96151,x96151),x96152),x96153)),x96154)) % 154.70/154.56 [9616]~P1(f328(f328(f330(f881(f876(x96161),f876(x96161))),f328(f328(f263(f876(x96161),f876(x96161)),f328(f328(f148(x96161),x96162),x96165)),f328(f328(f148(x96161),x96163),x96166))),f154(x96161,x96164)))+P1(f328(f328(f330(f881(f876(x96161),f876(x96161))),f328(f328(f263(f876(x96161),f876(x96161)),x96165),x96166)),f154(x96161,x96164)))+P1(f328(f328(f330(f881(x96161,x96161)),f328(f328(f263(x96161,x96161),x96162),x96163)),x96164)) % 154.70/154.56 [9700]P1(f328(x97001,x97002))+P1(f328(f328(f330(x97003),f725(x97001,x97004,x97005,x97003,x97006)),x97005))+~P1(f328(f328(f330(x97006),x97002),f328(f328(f41(x97003,f882(x97006,a870)),x97005),x97004))) % 154.70/154.56 [9711]~E(x97112,x97114)+P1(f328(f328(f330(f881(f876(x97111),f876(x97111))),f328(f328(f263(f876(x97111),f876(x97111)),f328(f328(f125(x97111),x97112),f328(f328(f148(x97111),x97113),f117(x97111)))),f328(f328(f125(x97111),x97114),f328(f328(f148(x97111),x97115),f117(x97111))))),f154(x97111,x97116)))+~P1(f328(f328(f330(f881(x97111,x97111)),f328(f328(f263(x97111,x97111),x97113),x97115)),x97116)) % 154.70/154.56 [9798]E(x97981,x97982)+~P1(f328(f328(f330(f881(f876(x97983),f876(x97983))),f328(f328(f263(f876(x97983),f876(x97983)),f328(f328(f125(x97983),x97985),f328(f328(f148(x97983),x97981),f117(x97983)))),f328(f328(f125(x97983),x97986),f328(f328(f148(x97983),x97982),f117(x97983))))),f154(x97983,x97984)))+P1(f328(f328(f330(f881(x97983,x97983)),f328(f328(f263(x97983,x97983),x97981),x97982)),x97984)) % 154.70/154.56 [9826]~P1(f328(f328(f330(f881(f876(x98261),f876(x98261))),f328(f328(f263(f876(x98261),f876(x98261)),f328(f328(f125(x98261),x98265),f328(f328(f148(x98261),x98262),f117(x98261)))),f328(f328(f125(x98261),x98266),f328(f328(f148(x98261),x98263),f117(x98261))))),f154(x98261,x98264)))+P1(f328(f328(f330(f881(f876(x98261),f876(x98261))),f328(f328(f263(f876(x98261),f876(x98261)),x98265),x98266)),f154(x98261,x98264)))+P1(f328(f328(f330(f881(x98261,x98261)),f328(f328(f263(x98261,x98261),x98262),x98263)),x98264)) % 154.70/154.56 [9844]P1(f328(x98441,x98442))+P1(f328(f328(f330(x98443),f731(x98441,x98444,x98445,x98446,x98443)),f328(x98444,f725(x98441,x98444,x98445,x98446,x98443))))+~P1(f328(f328(f330(x98443),x98442),f328(f328(f41(x98446,f882(x98443,a870)),x98445),x98444))) % 154.70/154.56 [8838]~P18(x88383,x88384,x88381)+~P1(f328(f61(x88383),x88386))+E(f328(f328(x88381,x88382),f328(f328(f64(x88383,x88384,x88381),x88385),f328(f328(f22(f882(x88383,a870)),x88386),f328(f328(f306(x88383),x88382),f192(f882(x88383,a870)))))),f328(f328(f64(x88383,x88384,x88381),x88385),f328(f328(f306(x88383),x88382),x88386))) % 154.70/154.56 [8924]~E(f328(f328(f176(x89241,x89242),x89244),x89245),f328(f235(x89242),x89246))+~P1(f328(f328(x89243,x89245),x89246))+E(f328(f328(f176(x89241,x89242),f328(f133(f881(x89241,x89242),f328(f267(x89241,x89242,a870),x89243)),x89244)),x89245),f328(f235(x89242),x89246)) % 154.70/154.56 [9142]~P1(f328(f328(f330(x91425),x91423),x91426))+P1(f328(f328(f242(f882(x91421,a870)),f328(x91422,x91423)),x91424))+~P1(f328(f328(f242(f882(x91421,a870)),f328(f328(f41(x91425,f882(x91421,a870)),x91426),x91422)),x91424)) % 154.70/154.56 [9771]~P8(x97711,x97715,x97714)+P1(f328(f328(f330(f881(x97711,x97711)),f328(f328(f263(x97711,x97711),x97712),x97713)),x97714))+~P1(f328(f328(f330(x97711),x97716),f328(f328(f105(f882(x97711,a870)),f328(f282(x97711,x97711,x97714),f328(f328(f306(x97711),x97712),f192(f882(x97711,a870))))),f328(f282(x97711,x97711,x97714),f328(f328(f306(x97711),x97713),f192(f882(x97711,a870))))))) % 154.70/154.56 [8584]~P103(x85842)+~E(f328(f328(f80(x85842),f328(f328(f81(x85842),x85844),x85845)),x85841),f328(f328(f80(x85842),f328(f328(f81(x85842),x85843),x85845)),x85846))+E(x85841,f328(f328(f80(x85842),f328(f328(f81(x85842),f328(f328(f22(x85842),x85843),x85844)),x85845)),x85846)) % 154.70/154.56 [8585]~P103(x85851)+~E(f328(f328(f80(x85851),f328(f328(f81(x85851),x85852),x85854)),x85855),f328(f328(f80(x85851),f328(f328(f81(x85851),x85853),x85854)),x85856))+E(f328(f328(f80(x85851),f328(f328(f81(x85851),f328(f328(f22(x85851),x85852),x85853)),x85854)),x85855),x85856) % 154.70/154.56 [8751]~P103(x87511)+E(f328(f328(f80(x87511),f328(f328(f81(x87511),x87512),x87513)),x87514),f328(f328(f80(x87511),f328(f328(f81(x87511),x87515),x87513)),x87516))+~E(x87516,f328(f328(f80(x87511),f328(f328(f81(x87511),f328(f328(f22(x87511),x87512),x87515)),x87513)),x87514)) % 154.70/154.56 [8752]~P103(x87521)+E(f328(f328(f80(x87521),f328(f328(f81(x87521),x87522),x87523)),x87524),f328(f328(f80(x87521),f328(f328(f81(x87521),x87525),x87523)),x87526))+~E(f328(f328(f80(x87521),f328(f328(f81(x87521),f328(f328(f22(x87521),x87522),x87525)),x87523)),x87524),x87526) % 154.70/154.56 [9082]~P1(f328(f328(x90824,x90825),x90826))+~P1(f328(f328(x90823,x90825),x90826))+P1(f328(f328(f328(f328(f105(f882(x90821,f882(x90822,a870))),x90823),x90824),x90825),x90826)) % 154.70/154.56 [9341]P1(f328(f328(x93411,x93412),x93413))+P1(f328(f328(x93414,x93412),x93413))+~P1(f328(f328(f328(f328(f114(f882(x93415,f882(x93416,a870))),x93414),x93411),x93412),x93413)) % 154.70/154.56 [9629]~P127(x96291)+~P1(f328(f328(f243(x96291),f328(f328(f80(x96291),f328(f328(f81(x96291),x96294),x96295)),x96292)),f328(f328(f80(x96291),f328(f328(f81(x96291),x96293),x96295)),x96296)))+P1(f328(f328(f243(x96291),x96292),f328(f328(f80(x96291),f328(f328(f81(x96291),f328(f328(f22(x96291),x96293),x96294)),x96295)),x96296))) % 154.70/154.56 [9630]~P127(x96301)+~P1(f328(f328(f242(x96301),f328(f328(f80(x96301),f328(f328(f81(x96301),x96304),x96305)),x96302)),f328(f328(f80(x96301),f328(f328(f81(x96301),x96303),x96305)),x96306)))+P1(f328(f328(f242(x96301),x96302),f328(f328(f80(x96301),f328(f328(f81(x96301),f328(f328(f22(x96301),x96303),x96304)),x96305)),x96306))) % 154.70/154.56 [9653]~P127(x96531)+P1(f328(f328(f243(x96531),f328(f328(f80(x96531),f328(f328(f81(x96531),x96532),x96533)),x96534)),f328(f328(f80(x96531),f328(f328(f81(x96531),x96535),x96533)),x96536)))+~P1(f328(f328(f243(x96531),x96534),f328(f328(f80(x96531),f328(f328(f81(x96531),f328(f328(f22(x96531),x96535),x96532)),x96533)),x96536))) % 154.70/154.56 [9654]~P127(x96541)+P1(f328(f328(f242(x96541),f328(f328(f80(x96541),f328(f328(f81(x96541),x96542),x96543)),x96544)),f328(f328(f80(x96541),f328(f328(f81(x96541),x96545),x96543)),x96546)))+~P1(f328(f328(f242(x96541),x96544),f328(f328(f80(x96541),f328(f328(f81(x96541),f328(f328(f22(x96541),x96545),x96542)),x96543)),x96546))) % 154.70/154.56 [9759]~P127(x97591)+~P1(f328(f328(f243(x97591),f328(f328(f80(x97591),f328(f328(f81(x97591),x97592),x97594)),x97595)),f328(f328(f80(x97591),f328(f328(f81(x97591),x97593),x97594)),x97596)))+P1(f328(f328(f243(x97591),f328(f328(f80(x97591),f328(f328(f81(x97591),f328(f328(f22(x97591),x97592),x97593)),x97594)),x97595)),x97596)) % 154.70/154.56 [9760]~P127(x97601)+~P1(f328(f328(f242(x97601),f328(f328(f80(x97601),f328(f328(f81(x97601),x97602),x97604)),x97605)),f328(f328(f80(x97601),f328(f328(f81(x97601),x97603),x97604)),x97606)))+P1(f328(f328(f242(x97601),f328(f328(f80(x97601),f328(f328(f81(x97601),f328(f328(f22(x97601),x97602),x97603)),x97604)),x97605)),x97606)) % 154.70/154.56 [9809]~P127(x98091)+P1(f328(f328(f243(x98091),f328(f328(f80(x98091),f328(f328(f81(x98091),x98092),x98093)),x98094)),f328(f328(f80(x98091),f328(f328(f81(x98091),x98095),x98093)),x98096)))+~P1(f328(f328(f243(x98091),f328(f328(f80(x98091),f328(f328(f81(x98091),f328(f328(f22(x98091),x98092),x98095)),x98093)),x98094)),x98096)) % 154.70/154.56 [9810]~P127(x98101)+P1(f328(f328(f242(x98101),f328(f328(f80(x98101),f328(f328(f81(x98101),x98102),x98103)),x98104)),f328(f328(f80(x98101),f328(f328(f81(x98101),x98105),x98103)),x98106)))+~P1(f328(f328(f242(x98101),f328(f328(f80(x98101),f328(f328(f81(x98101),f328(f328(f22(x98101),x98102),x98105)),x98103)),x98104)),x98106)) % 154.70/154.56 [9981]~P66(x99812)+~P1(f328(f61(x99811),x99816))+E(f328(f328(f6(x99811,x99812),f328(f328(f18(x99811,x99812,x99812),f328(f328(f18(x99811,x99812,f882(x99812,x99812)),f328(f328(f8(a870,f882(x99812,f882(x99812,x99812)),x99811),f100(x99812)),x99813)),x99814)),x99815)),x99816),f328(f328(f80(x99812),f328(f328(f6(x99811,x99812),x99814),f328(f328(f105(f882(x99811,a870)),x99816),f328(f248(x99811),x99813)))),f328(f328(f6(x99811,x99812),x99815),f328(f328(f105(f882(x99811,a870)),x99816),f328(f79(f882(x99811,a870)),f328(f248(x99811),x99813)))))) % 154.70/154.56 [10039]P1(f328(f328(f330(x100392),x100394),x100396))+P1(f328(f328(f330(x100392),x100395),x100396))+E(f328(f308(x100391,x100392,f328(f328(f7(x100391,x100392,x100392),f328(f328(f7(x100391,x100392,f882(x100392,x100392)),f328(f328(f8(a870,f882(x100392,f882(x100392,x100392)),x100391),f100(x100392)),f328(f328(f7(x100391,f882(x100391,a870),a870),f330(x100391)),x100393))),x100394)),x100395)),x100396),f192(f882(x100391,a870))) % 154.70/154.56 [10040]P1(f328(f328(f330(x100402),x100405),x100406))+~P1(f328(f328(f330(x100402),x100404),x100406))+E(f328(f308(x100401,x100402,f328(f328(f7(x100401,x100402,x100402),f328(f328(f7(x100401,x100402,f882(x100402,x100402)),f328(f328(f8(a870,f882(x100402,f882(x100402,x100402)),x100401),f100(x100402)),f328(f328(f7(x100401,f882(x100401,a870),a870),f330(x100401)),x100403))),x100404)),x100405)),x100406),x100403) % 154.70/154.56 [10041]P1(f328(f328(f330(x100412),x100414),x100416))+~P1(f328(f328(f330(x100412),x100415),x100416))+E(f328(f308(x100411,x100412,f328(f328(f7(x100411,x100412,x100412),f328(f328(f7(x100411,x100412,f882(x100412,x100412)),f328(f328(f8(a870,f882(x100412,f882(x100412,x100412)),x100411),f100(x100412)),f328(f328(f7(x100411,f882(x100411,a870),a870),f330(x100411)),x100413))),x100414)),x100415)),x100416),f328(f79(f882(x100411,a870)),x100413)) % 154.70/154.56 [10042]~P1(f328(f328(f330(x100422),x100424),x100426))+~P1(f328(f328(f330(x100422),x100425),x100426))+E(f328(f308(x100421,x100422,f328(f328(f7(x100421,x100422,x100422),f328(f328(f7(x100421,x100422,f882(x100422,x100422)),f328(f328(f8(a870,f882(x100422,f882(x100422,x100422)),x100421),f100(x100422)),f328(f328(f7(x100421,f882(x100421,a870),a870),f330(x100421)),x100423))),x100424)),x100425)),x100426),f251(f882(x100421,a870))) % 154.70/154.56 [10173]P26(x101731,x101732,f328(f328(f306(f874(x101731)),f328(f328(f328(f92(x101731),f328(x101733,x101734)),f328(a26,x101734)),f328(x101735,x101734))),f192(f882(f874(x101731),a870))))+~P1(f328(f328(f330(a873),x101734),x101736))+~P26(x101731,f328(f328(f114(f882(f874(x101731),a870)),x101732),f328(f307(a873,f874(x101731),f328(f328(f18(a873,f882(x101731,f882(a872,a870)),f874(x101731)),f328(f328(f18(a873,a871,f882(f882(x101731,f882(a872,a870)),f874(x101731))),f328(f328(f8(f882(x101731,f882(a872,a870)),f882(a871,f882(f882(x101731,f882(a872,a870)),f874(x101731))),a873),f92(x101731)),x101733)),a26)),x101735)),x101736)),f328(f307(a873,f874(x101731),f328(f328(f18(a873,f882(x101731,f882(a872,a870)),f874(x101731)),f328(f328(f18(a873,a871,f882(f882(x101731,f882(a872,a870)),f874(x101731))),f328(f328(f8(f882(x101731,f882(a872,a870)),f882(a871,f882(f882(x101731,f882(a872,a870)),f874(x101731))),a873),f92(x101731)),x101733)),f328(f328(f8(f879(a871),a871,a873),f239(a871)),a28))),x101735)),x101736)) % 154.70/154.56 [8614]E(x86141,x86142)+~P53(x86144,x86145,x86143,x86146,x86147)+~E(f328(x86143,x86141),f328(x86143,x86142)) % 154.70/154.56 [6987]E(f328(f237(f879(x69871),x69872,f205(x69871),x69873),f328(x69874,x69875)),f328(f235(x69871),x69876))+~E(f328(x69874,x69875),f328(f235(x69872),x69877))+~E(f328(x69873,x69877),f328(f235(x69871),x69876)) % 154.70/154.56 [8645]~P11(x86456,x86455,x86457,x86454,x86451)+E(f328(f328(x86451,x86452),x86453),x86454)+P1(f328(f61(x86455),x86453)) % 154.70/154.56 [9494]P44(x94941,x94942,x94943,x94944,x94945,f328(f328(x94943,x94946),x94947))+~E(f328(f328(x94943,x94946),x94947),x94944)+~E(x94945,f192(f882(x94941,a870))) % 154.70/154.56 [9675]~P1(f328(x96756,x96753))+~P1(f328(f328(f330(f881(x96752,x96752)),f328(f328(f263(x96752,x96752),x96754),x96755)),f328(x96757,x96753)))+P1(f328(f328(f330(f881(f881(x96751,x96752),f881(x96751,x96752))),f328(f328(f263(f881(x96751,x96752),f881(x96751,x96752)),f328(f328(f263(x96751,x96752),x96753),x96754)),f328(f328(f263(x96751,x96752),x96753),x96755))),f280(x96751,x96752,x96756,x96757))) % 154.70/154.56 [10096]~P44(x100962,x100967,x100963,x100966,x100961,f328(f328(x100963,x100965),x100964))+E(f328(f328(x100963,f845(x100964,x100965,x100961,x100966,x100963,x100967,x100962)),f846(x100964,x100965,x100961,x100966,x100963,x100967,x100962)),f328(f328(x100963,x100965),x100964))+E(x100961,f192(f882(x100962,a870))) % 154.70/154.56 [10097]~P44(x100977,x100976,x100971,x100974,x100975,f328(f328(x100971,x100972),x100973))+E(f328(f328(x100971,f845(x100973,x100972,x100975,x100974,x100971,x100976,x100977)),f846(x100973,x100972,x100975,x100974,x100971,x100976,x100977)),f328(f328(x100971,x100972),x100973))+E(f328(f328(x100971,x100972),x100973),x100974) % 154.70/154.56 [9180]~P36(x91801,x91802,x91803,x91805,x91807)+P36(x91801,x91802,x91803,f328(f328(f148(x91801),x91804),x91805),f328(f328(f148(x91802),x91806),x91807))+~P1(f328(f328(x91803,x91804),x91806)) % 154.70/154.56 [9198]P36(x91981,x91982,x91983,x91984,x91985)+~P36(x91981,x91982,x91983,f328(f328(f125(x91981),x91986),x91984),f328(f328(f125(x91982),x91987),x91985))+~E(f328(f193(f876(x91981)),x91986),f328(f193(f876(x91982)),x91987)) % 154.70/154.56 [9199]P36(x91991,x91992,x91993,x91994,x91995)+~P36(x91991,x91992,x91993,f328(f328(f125(x91991),x91994),x91996),f328(f328(f125(x91992),x91995),x91997))+~E(f328(f193(f876(x91991)),x91994),f328(f193(f876(x91992)),x91995)) % 154.70/154.56 [9404]~P36(x94041,x94042,x94043,x94045,x94047)+~P36(x94041,x94042,x94043,x94044,x94046)+P36(x94041,x94042,x94043,f328(f328(f125(x94041),x94044),x94045),f328(f328(f125(x94042),x94046),x94047)) % 154.70/154.56 [9748]~P1(f328(f66(x97481,x97484,x97485,x97486,x97483),x97487))+P1(f328(f66(x97481,x97484,x97485,x97486,f328(f328(f306(x97481),x97482),x97483)),f328(f328(x97485,x97482),x97487)))+P1(f328(f328(f330(x97481),x97482),x97483)) % 154.70/154.56 [9879]~P27(x98793,x98791,x98794,f251(f882(x98793,a870)))+E(f328(f328(f176(x98791,x98792),f328(f328(f151(f881(x98793,x98792),f881(x98791,x98792)),f328(f267(x98793,x98792,f881(x98791,x98792)),f328(f328(f8(x98791,f882(x98792,f881(x98791,x98792)),x98793),f263(x98791,x98792)),x98794))),x98795)),f328(x98794,x98796)),f328(f235(x98792),x98797))+~E(f328(f328(f176(x98793,x98792),x98795),x98796),f328(f235(x98792),x98797)) % 154.70/154.56 [10118]~P44(x101182,x101187,x101186,x101185,x101181,f328(f328(x101186,x101184),x101183))+E(x101181,f192(f882(x101182,a870)))+P1(f328(f328(f330(x101182),f845(x101183,x101184,x101181,x101185,x101186,x101187,x101182)),x101181)) % 154.70/154.56 [10119]~P44(x101195,x101197,x101191,x101194,x101196,f328(f328(x101191,x101192),x101193))+E(f328(f328(x101191,x101192),x101193),x101194)+P1(f328(f328(f330(x101195),f845(x101193,x101192,x101196,x101194,x101191,x101197,x101195)),x101196)) % 154.70/154.56 [6775]~E(x67755,x67757)+~E(x67756,x67754)+E(f328(f328(f328(f328(f72(x67751,f879(x67752)),x67753),x67754),f328(f235(x67752),x67755)),x67756),f328(f235(x67752),x67757)) % 154.70/154.56 [6903]E(x69031,x69032)+~E(f328(x69035,x69031),f328(f235(x69034),x69037))+E(f328(f328(f328(f328(f72(x69033,f879(x69034)),x69035),x69032),f328(f235(x69034),x69036)),x69031),f328(f235(x69034),x69037)) % 154.70/154.56 [7623]E(x76231,x76232)+~E(x76233,x76234)+~E(f328(f328(f328(f328(f72(x76235,f879(x76236)),x76237),x76234),f328(f235(x76236),x76231)),x76233),f328(f235(x76236),x76232)) % 154.70/154.56 [7689]E(x76891,x76892)+E(f328(x76893,x76894),f328(f235(x76895),x76891))+~E(f328(f328(f328(f328(f72(x76896,f879(x76895)),x76893),x76897),f328(f235(x76895),x76892)),x76894),f328(f235(x76895),x76891)) % 154.70/154.56 [7690]E(x76901,x76902)+E(f328(x76903,x76901),f328(f235(x76904),x76905))+~E(f328(f328(f328(f328(f72(x76906,f879(x76904)),x76903),x76902),f328(f235(x76904),x76907)),x76901),f328(f235(x76904),x76905)) % 154.70/154.56 [8863]~P23(x88634,x88635,x88636,x88637,x88631)+~P1(f328(f61(x88635),x88633))+E(f328(f328(x88631,x88632),x88633),f328(f328(f328(f65(x88634,x88635,x88636),x88632),x88637),x88633)) % 154.70/154.56 [8864]~P11(x88644,x88645,x88646,x88647,x88641)+~P1(f328(f61(x88645),x88643))+E(f328(f328(x88641,x88642),x88643),f328(f328(f328(f65(x88644,x88645,x88646),x88642),x88647),x88643)) % 154.70/154.56 [9460]~P26(x94601,x94602,f328(f328(f306(f874(x94601)),f328(f328(f328(f92(x94601),x94603),x94604),x94607)),f192(f882(f874(x94601),a870))))+P26(x94601,x94602,f328(f328(f306(f874(x94601)),f328(f328(f328(f92(x94601),x94603),f33(x94604,x94605)),x94606)),f192(f882(f874(x94601),a870))))+~P26(x94601,x94602,f328(f328(f306(f874(x94601)),f328(f328(f328(f92(x94601),x94607),x94605),x94606)),f192(f882(f874(x94601),a870)))) % 154.70/154.56 [9648]~P25(x96483,x96484,x96485,x96487,x96486,x96481)+~P1(f328(f61(x96484),x96482))+E(f328(x96481,x96482),f328(f328(f328(f65(x96483,x96484,x96485),x96486),x96487),x96482)) % 154.70/154.56 [9804]P44(x98041,x98042,x98043,x98044,x98045,f328(f328(x98043,x98046),x98047))+~P44(x98041,x98042,x98043,x98044,f328(f328(f22(f882(x98041,a870)),x98045),f328(f328(f306(x98041),x98046),f192(f882(x98041,a870)))),x98047)+~P1(f328(f328(f330(x98041),x98046),x98045)) % 154.70/154.56 [10071]~P26(x100711,x100712,f328(f328(f306(f874(x100711)),f328(f328(f328(f92(x100711),f95(x100711,x100713,x100714)),x100715),x100717)),f192(f882(f874(x100711),a870))))+P26(x100711,x100712,f328(f328(f306(f874(x100711)),f328(f328(f328(f92(x100711),x100713),f30(x100714,x100715,x100716)),x100717)),f192(f882(f874(x100711),a870))))+~P26(x100711,x100712,f328(f328(f306(f874(x100711)),f328(f328(f328(f92(x100711),f95(x100711,x100713,f328(f73(a870,a870,a872,a323),x100714))),x100716),x100717)),f192(f882(f874(x100711),a870)))) % 154.70/154.56 [10144]~P44(x101442,x101443,x101444,x101445,x101441,f328(f328(x101444,x101447),x101446))+P44(x101442,x101443,x101444,x101445,f328(f328(f22(f882(x101442,a870)),x101441),f328(f328(f306(x101442),f845(x101446,x101447,x101441,x101445,x101444,x101443,x101442)),f192(f882(x101442,a870)))),f846(x101446,x101447,x101441,x101445,x101444,x101443,x101442))+E(x101441,f192(f882(x101442,a870))) % 154.70/154.56 [10145]~P44(x101455,x101456,x101451,x101454,x101457,f328(f328(x101451,x101452),x101453))+P44(x101455,x101456,x101451,x101454,f328(f328(f22(f882(x101455,a870)),x101457),f328(f328(f306(x101455),f845(x101453,x101452,x101457,x101454,x101451,x101456,x101455)),f192(f882(x101455,a870)))),f846(x101453,x101452,x101457,x101454,x101451,x101456,x101455))+E(f328(f328(x101451,x101452),x101453),x101454) % 154.70/154.56 [9187]E(f185(x91871,x91872,x91873,x91874,f328(f328(f156(x91872,x91875),x91876),x91877)),f185(x91871,x91872,x91873,x91874,x91875))+~P1(f328(f328(f243(a875),x91876),f328(f193(f876(x91872)),x91875)))+~P1(f328(f328(f242(a875),f328(f193(f876(x91871)),x91874)),x91876)) % 154.70/154.56 [9482]P1(f328(f328(f242(f882(f881(x94821,x94822),a870)),f328(f328(f285(x94821,x94823,x94822),x94824),x94825)),f328(f328(f285(x94821,x94823,x94822),x94826),x94827)))+~P1(f328(f328(f242(f882(f881(x94823,x94822),a870)),x94825),x94827))+~P1(f328(f328(f242(f882(f881(x94821,x94823),a870)),x94824),x94826)) % 154.70/154.56 [9815]~P1(f328(f328(f330(x98151),x98156),x98155))+P1(f328(f66(x98151,x98152,x98153,x98154,x98155),f328(f328(x98153,x98156),x98157)))+~P1(f328(f66(x98151,x98152,x98153,x98154,f328(f328(f22(f882(x98151,a870)),x98155),f328(f328(f306(x98151),x98156),f192(f882(x98151,a870))))),x98157)) % 154.70/154.56 [10204]~P139(x102041)+~P27(f881(x102042,x102043),x102041,f328(f267(x102042,x102043,x102041),f328(f328(f7(x102042,f882(x102043,x102041),f882(x102043,x102041)),f328(f328(f8(f882(x102041,x102041),f882(f882(x102043,x102041),f882(x102043,x102041)),x102042),f8(x102041,x102041,x102043)),f328(f328(f8(x102041,f882(x102041,x102041),x102042),f81(x102041)),x102044))),x102045)),f328(f328(f265(x102042,x102043),x102046),f328(f16(f882(x102043,a870),x102042),x102047)))+E(f328(f328(f6(x102041,x102041),f34(x102041)),f328(f248(x102041),f328(f328(f8(f882(x102042,a870),a870,x102041),f87(x102042)),f328(f328(f8(f882(x102042,f882(x102043,a870)),f882(x102042,a870),x102041),f328(f8(f882(x102043,a870),a870,x102042),f87(x102043))),f328(f328(f7(x102041,f882(x102042,f882(x102043,a870)),f882(x102042,f882(x102043,a870))),f328(f328(f8(f882(x102042,f882(f882(x102043,a870),f882(x102043,a870))),f882(f882(x102042,f882(x102043,a870)),f882(x102042,f882(x102043,a870))),x102041),f18(x102042,f882(x102043,a870),f882(x102043,a870))),f328(f328(f8(f882(x102042,f882(x102043,f882(a870,a870))),f882(x102042,f882(f882(x102043,a870),f882(x102043,a870))),x102041),f328(f8(f882(x102043,f882(a870,a870)),f882(f882(x102043,a870),f882(x102043,a870)),x102042),f18(x102043,a870,a870))),f328(f328(f8(f882(x102042,f882(x102043,a870)),f882(x102042,f882(x102043,f882(a870,a870))),x102041),f328(f8(f882(x102043,a870),f882(x102043,f882(a870,a870)),x102042),f328(f8(a870,f882(a870,a870),x102043),a326))),f328(f328(f7(x102041,f882(x102042,f882(x102043,x102041)),f882(x102042,f882(x102043,a870))),f328(f328(f8(f882(f882(x102043,x102041),f882(x102043,a870)),f882(f882(x102042,f882(x102043,x102041)),f882(x102042,f882(x102043,a870))),x102041),f8(f882(x102043,x102041),f882(x102043,a870),x102042)),f328(f328(f8(f882(x102041,a870),f882(f882(x102043,x102041),f882(x102043,a870)),x102041),f8(x102041,a870,x102043)),a325))),f328(f328(f7(x102042,f882(x102043,x102041),f882(x102043,x102041)),f328(f328(f8(f882(x102041,x102041),f882(f882(x102043,x102041),f882(x102043,x102041)),x102042),f8(x102041,x102041,x102043)),f328(f328(f8(x102041,f882(x102041,x102041),x102042),f81(x102041)),x102044))),x102045)))))),f328(f328(f7(x102042,f882(x102043,a870),f882(x102043,a870)),f328(f328(f8(f882(a870,a870),f882(f882(x102043,a870),f882(x102043,a870)),x102042),f8(a870,a870,x102043)),f328(f328(f8(a870,f882(a870,a870),x102042),a326),f328(f328(f7(x102042,f882(x102042,a870),a870),f330(x102042)),x102046)))),f328(f328(f7(x102043,f882(x102043,a870),a870),f330(x102043)),x102047))))))),f328(f328(f81(x102041),f328(f328(f6(x102042,x102041),x102044),x102046)),f328(f328(f6(x102043,x102041),x102045),x102047))) % 154.70/154.57 [9646]~P1(f328(f328(x96464,x96466),x96468))+~P1(f328(f328(x96465,x96468),x96467))+P1(f328(f328(f264(x96461,x96462,x96463,x96464,x96465),x96466),x96467)) % 154.70/154.57 [9248]~P21(x92488,x92481,x92483,x92485)+~P1(f328(f61(x92488),x92486))+E(f328(f73(x92481,x92481,x92482,f328(x92483,x92484)),f328(f73(x92481,x92481,x92482,f328(x92485,x92486)),x92487)),f328(f73(x92481,x92481,x92482,f328(x92485,x92486)),f328(f73(x92481,x92481,x92482,f328(x92483,x92484)),x92487))) % 154.70/154.57 [9636]~P24(x96367,x96362,x96365,x96368,x96366,x96361)+~P1(f328(f61(x96362),x96364))+E(f328(x96361,f328(f328(f306(x96362),x96363),x96364)),f328(f328(x96365,f328(x96366,x96363)),f328(x96361,x96364))) % 154.70/154.57 [9757]~P27(x97572,x97574,x97576,x97578)+~P27(x97571,x97573,x97575,x97577)+P27(f881(x97571,x97572),f881(x97573,x97574),f268(x97571,x97573,x97572,x97574,x97575,x97576),f328(f328(f265(x97571,x97572),x97577),f328(f16(f882(x97572,a870),x97571),x97578))) % 154.70/154.57 [9428]P1(f328(f328(f330(f881(x94281,x94282)),f328(f328(f263(x94281,x94282),x94283),x94284)),f328(f328(f285(x94281,x94285,x94282),x94286),x94287)))+~P1(f328(f328(f330(f881(x94281,x94285)),f328(f328(f263(x94281,x94285),x94283),x94288)),x94286))+~P1(f328(f328(f330(f881(x94285,x94282)),f328(f328(f263(x94285,x94282),x94288),x94284)),x94287)) % 154.70/154.57 [9617]~P1(f328(f328(f242(f882(f881(x96173,x96172),a870)),x96175),f328(f328(f265(x96173,x96172),x96178),f328(f16(f882(x96172,a870),x96173),x96177))))+~P1(f328(f328(f242(f882(f881(x96171,x96173),a870)),x96174),f328(f328(f265(x96171,x96173),x96176),f328(f16(f882(x96173,a870),x96171),x96178))))+P1(f328(f328(f242(f882(f881(x96171,x96172),a870)),f328(f328(f285(x96171,x96173,x96172),x96174),x96175)),f328(f328(f265(x96171,x96172),x96176),f328(f16(f882(x96172,a870),x96171),x96177)))) % 154.70/154.57 [9670]~E(x96703,x96705)+P1(f328(f328(f330(f881(f881(x96701,x96702),f881(x96701,x96702))),f328(f328(f263(f881(x96701,x96702),f881(x96701,x96702)),f328(f328(f263(x96701,x96702),x96703),x96704)),f328(f328(f263(x96701,x96702),x96705),x96706))),f320(x96701,x96702,x96707,x96708)))+~P1(f328(f328(f330(f881(x96702,x96702)),f328(f328(f263(x96702,x96702),x96704),x96706)),x96708)) % 154.70/154.57 [9780]E(x97801,x97802)+~P1(f328(f328(f330(f881(f881(x97803,x97805),f881(x97803,x97805))),f328(f328(f263(f881(x97803,x97805),f881(x97803,x97805)),f328(f328(f263(x97803,x97805),x97801),x97806)),f328(f328(f263(x97803,x97805),x97802),x97807))),f320(x97803,x97805,x97804,x97808)))+P1(f328(f328(f330(f881(x97803,x97803)),f328(f328(f263(x97803,x97803),x97801),x97802)),x97804)) % 154.70/154.57 [9797]~P1(f328(f328(f330(f881(f881(x97971,x97975),f881(x97971,x97975))),f328(f328(f263(f881(x97971,x97975),f881(x97971,x97975)),f328(f328(f263(x97971,x97975),x97972),x97976)),f328(f328(f263(x97971,x97975),x97973),x97977))),f320(x97971,x97975,x97974,x97978)))+P1(f328(f328(f330(f881(x97971,x97971)),f328(f328(f263(x97971,x97971),x97972),x97973)),x97974))+P1(f328(f328(f330(f881(x97975,x97975)),f328(f328(f263(x97975,x97975),x97976),x97977)),x97978)) % 154.70/154.57 [9701]~P25(x97017,x97015,x97011,x97018,x97012,x97014)+~P1(f328(f61(x97015),x97016))+E(f328(f328(x97011,f328(x97012,x97013)),f328(x97014,f328(f328(f22(f882(x97015,a870)),x97016),f328(f328(f306(x97015),x97013),f192(f882(x97015,a870)))))),f328(x97014,f328(f328(f306(x97015),x97013),x97016))) % 154.70/154.57 [9206]~P1(f328(f328(f328(x92065,x92068),x92066),x92067))+~P1(f328(f328(f330(x92061),x92068),x92064))+P1(f328(f328(f328(f328(f41(x92061,f882(x92062,f882(x92063,a870))),x92064),x92065),x92066),x92067)) % 154.70/154.57 [9415]P1(f328(f328(f328(x94151,x94152),x94153),x94154))+~P1(f328(f328(f330(x94155),x94152),x94156))+~P1(f328(f328(f328(f328(f42(x94155,f882(x94157,f882(x94158,a870))),x94156),x94151),x94153),x94154)) % 154.70/154.57 [9610]~P23(x96103,x96102,x96104,x96108,x96101)+~P1(f328(f61(x96102),x96107))+E(f328(f328(x96101,f328(f328(f18(x96102,x96103,x96103),f328(f328(f8(x96103,f882(x96103,x96103),x96102),x96104),x96105)),x96106)),x96107),f328(f328(x96104,f328(f328(x96101,x96105),x96107)),f328(f328(x96101,x96106),x96107))) % 154.70/154.57 [9887]~E(f328(f307(x98872,x98874,x98876),x98878),x988710)+~E(f328(f307(x98871,x98873,x98875),x98877),x98879)+E(f328(f307(f881(x98871,x98872),f881(x98873,x98874),f268(x98871,x98873,x98872,x98874,x98875,x98876)),f328(f328(f265(x98871,x98872),x98877),f328(f16(f882(x98872,a870),x98871),x98878))),f328(f328(f265(x98873,x98874),x98879),f328(f16(f882(x98874,a870),x98873),x988710))) % 154.70/154.57 [8228]~P31(a5000)+~P9(a5000)+~P1(f328(a25,x82281))+P26(a872,f192(f882(f874(a872),a870)),f328(f328(f306(f874(a872)),f328(f328(f328(f92(a872),a325),x82281),f328(a198,x82281))),f192(f882(f874(a872),a870)))) % 154.70/154.57 [4826]~P105(x48262)+~P16(x48262,x48261)+P16(x48262,f118(x48262,x48261))+E(x48261,f117(x48262)) % 154.70/154.57 [4827]~P105(x48272)+~P16(x48272,x48271)+P16(x48272,f744(x48271,x48272))+E(x48271,f117(x48272)) % 154.70/154.57 [5060]~P5(x50602)+E(f10(x50602,x50601),f39(x50602,x50601))+E(x50601,f192(f882(x50602,a870)))+~P1(f328(f61(x50602),x50601)) % 154.70/154.57 [5061]~P5(x50612)+E(f11(x50612,x50611),f40(x50612,x50611))+E(x50611,f192(f882(x50612,a870)))+~P1(f328(f61(x50612),x50611)) % 154.70/154.57 [5221]~P105(x52212)+~P16(x52212,x52211)+E(x52211,f117(x52212))+E(f328(f328(f148(x52212),f762(x52211,x52212)),f744(x52211,x52212)),x52211) % 154.70/154.57 [6011]~P2(x60112)+E(x60111,f192(f882(x60112,a870)))+P1(f328(f328(f242(x60112),f11(x60112,x60111)),f10(x60112,x60111)))+~P1(f328(f61(x60112),x60111)) % 154.70/154.57 [6023]~P40(x60232)+~P40(x60231)+E(x60231,x60232)+~E(f328(f307(a1,a875,a108),x60231),f328(f307(a1,a875,a108),x60232)) % 154.70/154.57 [9061]~P121(x90611)+~P1(f328(f328(f330(x90611),x90612),f113(x90611)))+P1(f328(f328(f243(x90611),f328(f328(f80(x90611),f328(f328(f80(x90611),f78(x90611)),x90612)),x90612)),f2(x90611)))+~P1(f328(f328(f243(x90611),x90612),f2(x90611))) % 154.70/154.57 [9303]~P121(x93031)+~P1(f328(f328(f330(x93031),x93032),f113(x93031)))+~P1(f328(f328(f243(x93031),f328(f328(f80(x93031),f328(f328(f80(x93031),f78(x93031)),x93032)),x93032)),f2(x93031)))+P1(f328(f328(f243(x93031),x93032),f2(x93031))) % 154.70/154.57 [4882]~P139(x48822)+~P112(x48822)+E(x48821,f2(a875))+E(f328(f328(f253(x48822),f2(x48822)),x48821),f2(x48822)) % 154.70/154.57 [4886]~P139(x48861)+~P112(x48861)+~E(x48862,f2(a875))+E(f328(f328(f253(x48861),f2(x48861)),x48862),f78(x48861)) % 154.70/154.57 [5047]~P137(x50472)+E(x50471,f78(x50472))+E(x50471,f328(f79(x50472),f78(x50472)))+~E(f328(f328(f81(x50472),x50471),x50471),f78(x50472)) % 154.70/154.57 [5303]~P87(x53032)+E(x53031,f2(x53032))+E(f82(x53032,x53031),f328(f79(x53032),f78(x53032)))+P1(f328(f328(f243(x53032),f2(x53032)),x53031)) % 154.70/154.57 [5536]~P87(x55362)+E(f82(x55362,x55361),f78(x55362))+E(x55361,f2(x55362))+~P1(f328(f328(f243(x55362),f2(x55362)),x55361)) % 154.70/154.57 [5545]E(x55451,x55452)+~E(f328(f107(a875),x55451),f328(f107(a875),x55452))+P1(f328(a197,f328(f107(a1),x55452)))+P1(f328(a197,f328(f107(a1),x55451))) % 154.70/154.57 [5595]~P89(x55951)+~E(x55952,f2(x55951))+E(f328(f328(f80(x55951),x55952),x55952),f2(x55951))+~P1(f328(f328(f330(x55951),x55952),f113(x55951))) % 154.70/154.57 [5633]E(x56331,f2(a1))+~E(f328(f328(f38(a1),x56332),x56331),f2(a1))+P1(f328(f328(f243(a1),x56331),x56332))+P1(f328(f328(f243(a1),x56332),x56331)) % 154.70/154.57 [5664]E(x56641,f2(a1))+~E(f328(f328(f38(a1),x56642),x56641),f2(a1))+P1(f328(f328(f242(a1),x56642),f2(a1)))+P1(f328(f328(f243(a1),x56642),x56641)) % 154.70/154.57 [5698]E(x56981,f2(a1))+~E(f328(f328(f38(a1),x56982),x56981),f2(a1))+P1(f328(f328(f242(a1),f2(a1)),x56982))+P1(f328(f328(f243(a1),x56981),x56982)) % 154.70/154.57 [5734]~P89(x57342)+E(x57341,f2(x57342))+~E(f328(f328(f80(x57342),x57341),x57341),f2(x57342))+~P1(f328(f328(f330(x57342),x57341),f113(x57342))) % 154.70/154.57 [5794]E(f328(f107(a875),x57941),f328(f107(a875),x57942))+~E(f328(f107(a1),x57942),f2(a1))+P1(f328(a197,f328(f107(a1),x57942)))+~P1(f328(a197,f328(f107(a1),x57941))) % 154.70/154.57 [5821]~E(f328(f107(a875),x58212),f328(f107(a875),x58211))+E(f328(f107(a1),x58211),f2(a1))+P1(f328(a197,f328(f107(a1),x58211)))+~P1(f328(a197,f328(f107(a1),x58212))) % 154.70/154.57 [5830]~P105(x58302)+E(x58301,f192(f882(x58302,a870)))+~P1(f328(f61(x58302),x58301))+P1(f328(f328(f330(x58302),f14(x58302,x58301)),x58301)) % 154.70/154.57 [5831]~P105(x58312)+E(x58311,f192(f882(x58312,a870)))+~P1(f328(f61(x58312),x58311))+P1(f328(f328(f330(x58312),f15(x58312,x58311)),x58311)) % 154.70/154.57 [5991]~P121(x59911)+~P90(x59911)+P1(f328(f328(f243(x59911),f2(x59911)),f328(f107(x59911),x59912)))+~P1(f328(f328(f243(a1),a83),x59912)) % 154.70/154.57 [5992]~P121(x59921)+~P90(x59921)+P1(f328(f328(f242(x59921),f2(x59921)),f328(f107(x59921),x59922)))+~P1(f328(f328(f242(a1),a83),x59922)) % 154.70/154.57 [6010]~P121(x60101)+~P90(x60101)+E(f328(f75(x60101),f328(f107(x60101),x60102)),f328(f107(x60101),x60102))+P1(f328(f328(f243(x60101),f328(f107(x60101),x60102)),f2(x60101))) % 154.70/154.57 [6050]E(x60501,x60502)+~E(f328(a108,x60501),f328(a108,x60502))+~P1(f328(f328(f242(a1),f2(a1)),x60502))+~P1(f328(f328(f242(a1),f2(a1)),x60501)) % 154.70/154.57 [6249]~P90(x62492)+~P121(x62492)+~P1(f328(f328(f243(x62492),f2(x62492)),f328(f107(x62492),x62491)))+P1(f328(f328(f243(a1),a83),x62491)) % 154.70/154.57 [6250]~P90(x62502)+~P121(x62502)+~P1(f328(f328(f242(x62502),f2(x62502)),f328(f107(x62502),x62501)))+P1(f328(f328(f242(a1),a83),x62501)) % 154.70/154.57 [6255]~P121(x62551)+~P90(x62551)+P1(f328(f328(f243(x62551),f328(f107(x62551),x62552)),f2(x62551)))+~P1(f328(f328(f243(a1),x62552),a83)) % 154.70/154.57 [6256]~P121(x62561)+~P90(x62561)+P1(f328(f328(f242(x62561),f328(f107(x62561),x62562)),f2(x62561)))+~P1(f328(f328(f242(a1),x62562),a83)) % 154.70/154.57 [6562]~P90(x65622)+~P121(x65622)+~P1(f328(f328(f243(x65622),f328(f107(x65622),x65621)),f2(x65622)))+P1(f328(f328(f243(a1),x65621),a83)) % 154.70/154.57 [6563]~P90(x65632)+~P121(x65632)+~P1(f328(f328(f242(x65632),f328(f107(x65632),x65631)),f2(x65632)))+P1(f328(f328(f242(a1),x65631),a83)) % 154.70/154.57 [6655]~P121(x66551)+~P90(x66551)+E(f328(f75(x66551),f328(f107(x66551),x66552)),f328(f79(x66551),f328(f107(x66551),x66552)))+~P1(f328(f328(f243(x66551),f328(f107(x66551),x66552)),f2(x66551))) % 154.70/154.57 [6673]E(f328(f107(a875),x66731),f328(f107(a875),x66732))+~E(f328(f107(a1),x66732),f2(a1))+~P1(f328(f328(f242(a1),f328(f107(a1),x66731)),f2(a1)))+~P1(f328(a197,f328(f107(a1),x66731))) % 154.70/154.57 [7552]~P105(x75522)+E(x75521,f192(f882(x75522,a870)))+~P1(f328(f61(x75522),x75521))+P1(f328(f328(f242(x75522),f13(x75522,f240(x75522),x75521)),f12(x75522,f241(x75522),x75521))) % 154.70/154.57 [7874]~P40(x78742)+~P6(x78741)+P1(f328(f328(f330(a1),x78741),x78742))+~P1(f328(f328(f330(a875),f328(a108,x78741)),f328(f307(a1,a875,a108),x78742))) % 154.70/154.57 [8144]~P59(x81442)+P1(f328(x81441,f205(x81442)))+~P1(f328(f57(f879(x81442)),x81441))+P1(f328(f57(x81442),f328(f328(f8(f879(x81442),a870,x81442),x81441),f235(x81442)))) % 154.70/154.57 [8622]~P59(x86221)+~P1(f328(x86222,f205(x86221)))+P1(f328(f58(f879(x86221)),x86222))+~P1(f328(f58(x86221),f328(f328(f8(f879(x86221),a870,x86221),x86222),f235(x86221)))) % 154.70/154.57 [5827]~P135(x58272)+E(x58271,f2(a1))+E(f328(f79(x58272),f328(f106(x58272),f328(f79(a1),x58271))),f328(f106(x58272),x58271))+~P1(f328(f328(f243(a1),x58271),f2(a1))) % 154.70/154.57 [5900]~P89(x59001)+~P90(x59001)+~P32(x59001,f328(f107(x59001),x59002))+P32(x59001,f328(f107(x59001),f328(f328(f80(a1),x59002),x59002))) % 154.70/154.57 [6237]~P74(x62372)+E(x62371,f192(f882(x62372,a870)))+E(f15(x62372,f328(f307(x62372,x62372,f79(x62372)),x62371)),f328(f79(x62372),f14(x62372,x62371)))+~P1(f328(f61(x62372),x62371)) % 154.70/154.57 [6238]~P74(x62382)+E(x62381,f192(f882(x62382,a870)))+E(f14(x62382,f328(f307(x62382,x62382,f79(x62382)),x62381)),f328(f79(x62382),f15(x62382,x62381)))+~P1(f328(f61(x62382),x62381)) % 154.70/154.57 [6270]~P89(x62701)+~P90(x62701)+P32(x62701,f328(f107(x62701),x62702))+~P32(x62701,f328(f107(x62701),f328(f328(f80(a1),x62702),x62702))) % 154.70/154.57 [6358]E(x63581,f2(a1))+E(f328(a50,f49(f328(f79(a1),x63581),f328(f79(a1),x63582))),f45(x63581,x63582))+P1(f328(f328(f242(a1),f2(a1)),x63582))+~P1(f328(f328(f242(a1),f2(a1)),x63581)) % 154.70/154.57 [8475]~P31(a5000)+~P1(f328(a25,x84751))+P26(a872,x84752,f328(f328(f306(f874(a872)),f328(f328(f328(f92(a872),a325),x84751),f328(a198,x84751))),f192(f882(f874(a872),a870))))+P1(f328(f328(f330(a873),f475(x84751,x84752)),f182(a873,a871,a28))) % 154.70/154.57 [8668]~P40(x86682)+~P40(x86681)+P1(f328(f328(f243(f882(a875,a870)),f328(f307(a1,a875,a108),x86681)),f328(f307(a1,a875,a108),x86682)))+~P1(f328(f328(f243(f882(a1,a870)),x86681),x86682)) % 154.70/154.57 [8881]~E(f767(x88812,x88811),f768(x88812,x88811))+~P1(f328(f134(x88811),f769(x88812,x88811)))+~P1(f328(f134(f876(x88811)),x88812))+P1(f328(f134(x88811),f328(f139(f876(x88811),f876(x88811),f125(x88811),f117(x88811)),x88812))) % 154.70/154.57 [8980]~P40(x89802)+~P40(x89801)+~P1(f328(f328(f243(f882(a875,a870)),f328(f307(a1,a875,a108),x89801)),f328(f307(a1,a875,a108),x89802)))+P1(f328(f328(f243(f882(a1,a870)),x89801),x89802)) % 154.70/154.57 [8981]~P40(x89812)+~P40(x89811)+~P1(f328(f328(f242(f882(a875,a870)),f328(f307(a1,a875,a108),x89811)),f328(f307(a1,a875,a108),x89812)))+P1(f328(f328(f242(f882(a1,a870)),x89811),x89812)) % 154.70/154.57 [8987]~E(f767(x89872,x89871),f768(x89872,x89871))+~P1(f328(f134(f876(x89871)),x89872))+P1(f328(f134(x89871),f328(f139(f876(x89871),f876(x89871),f125(x89871),f117(x89871)),x89872)))+P1(f328(f328(f330(f876(x89871)),f769(x89872,x89871)),f328(f170(f876(x89871)),x89872))) % 154.70/154.57 [9028]~P1(f328(f134(x90281),f769(x90282,x90281)))+~P1(f328(f134(f876(x90281)),x90282))+P1(f328(f134(x90281),f328(f139(f876(x90281),f876(x90281),f125(x90281),f117(x90281)),x90282)))+P1(f328(f328(f330(f876(x90281)),f768(x90282,x90281)),f328(f170(f876(x90281)),x90282))) % 154.70/154.57 [9029]~P1(f328(f134(x90291),f769(x90292,x90291)))+~P1(f328(f134(f876(x90291)),x90292))+P1(f328(f134(x90291),f328(f139(f876(x90291),f876(x90291),f125(x90291),f117(x90291)),x90292)))+P1(f328(f328(f330(f876(x90291)),f767(x90292,x90291)),f328(f170(f876(x90291)),x90292))) % 154.70/154.57 [9107]~P1(f328(f134(f876(x91071)),x91072))+P1(f328(f134(x91071),f328(f139(f876(x91071),f876(x91071),f125(x91071),f117(x91071)),x91072)))+P1(f328(f328(f330(f876(x91071)),f768(x91072,x91071)),f328(f170(f876(x91071)),x91072)))+P1(f328(f328(f330(f876(x91071)),f769(x91072,x91071)),f328(f170(f876(x91071)),x91072))) % 154.70/154.57 [9108]~P1(f328(f134(f876(x91081)),x91082))+P1(f328(f134(x91081),f328(f139(f876(x91081),f876(x91081),f125(x91081),f117(x91081)),x91082)))+P1(f328(f328(f330(f876(x91081)),f767(x91082,x91081)),f328(f170(f876(x91081)),x91082)))+P1(f328(f328(f330(f876(x91081)),f769(x91082,x91081)),f328(f170(f876(x91081)),x91082))) % 154.70/154.57 [9121]~E(f328(f328(f105(f882(x91211,a870)),f328(f170(x91211),f768(x91212,x91211))),f328(f170(x91211),f767(x91212,x91211))),f192(f882(x91211,a870)))+~P1(f328(f134(x91211),f769(x91212,x91211)))+~P1(f328(f134(f876(x91211)),x91212))+P1(f328(f134(x91211),f328(f139(f876(x91211),f876(x91211),f125(x91211),f117(x91211)),x91212))) % 154.70/154.57 [9183]~E(f328(f328(f105(f882(x91831,a870)),f328(f170(x91831),f768(x91832,x91831))),f328(f170(x91831),f767(x91832,x91831))),f192(f882(x91831,a870)))+~P1(f328(f134(f876(x91831)),x91832))+P1(f328(f134(x91831),f328(f139(f876(x91831),f876(x91831),f125(x91831),f117(x91831)),x91832)))+P1(f328(f328(f330(f876(x91831)),f769(x91832,x91831)),f328(f170(f876(x91831)),x91832))) % 154.70/154.57 [9452]E(x94521,f2(a1))+E(x94522,f2(a1))+E(f328(f328(f86(a1,f881(a1,a1)),f328(f328(a224,x94522),x94521)),f328(f328(f18(a1,a1,f881(a1,a1)),f328(f328(f8(a1,f882(a1,f881(a1,a1)),a1),f263(a1,a1)),f328(f38(a1),x94522))),f328(f38(a1),x94521))),f222(x94522,x94521))+P1(f328(f328(f243(a1),x94521),f2(a1))) % 154.70/154.57 [9534]~P31(a5000)+~P1(f328(a25,x95342))+P26(a872,x95341,f328(f328(f306(f874(a872)),f328(f328(f328(f92(a872),a325),x95342),f328(a198,x95342))),f192(f882(f874(a872),a870))))+~P26(a872,x95341,f328(f328(f306(f874(a872)),f328(f328(f328(f92(a872),a325),f328(a26,f475(x95342,x95341))),f328(a198,f328(a26,f475(x95342,x95341))))),f192(f882(f874(a872),a870)))) % 154.70/154.57 [8211]~P90(x82112)+~P121(x82112)+~P1(f328(f328(f243(x82112),f328(f107(x82112),x82111)),f78(x82112)))+P1(f328(f328(f243(a1),x82111),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))) % 154.70/154.57 [8212]~P90(x82122)+~P121(x82122)+~P1(f328(f328(f242(x82122),f328(f107(x82122),x82121)),f78(x82122)))+P1(f328(f328(f242(a1),x82121),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))) % 154.70/154.57 [8484]~P121(x84841)+~P90(x84841)+P1(f328(f328(f243(x84841),f328(f107(x84841),x84842)),f78(x84841)))+~P1(f328(f328(f243(a1),x84842),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))) % 154.70/154.57 [8485]~P121(x84851)+~P90(x84851)+P1(f328(f328(f242(x84851),f328(f107(x84851),x84852)),f78(x84851)))+~P1(f328(f328(f242(a1),x84852),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))) % 154.70/154.57 [8694]~P90(x86942)+~P121(x86942)+~P1(f328(f328(f243(x86942),f78(x86942)),f328(f107(x86942),x86941)))+P1(f328(f328(f243(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),x86941)) % 154.70/154.57 [8695]~P90(x86952)+~P121(x86952)+~P1(f328(f328(f242(x86952),f78(x86952)),f328(f107(x86952),x86951)))+P1(f328(f328(f242(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),x86951)) % 154.70/154.57 [9067]~P121(x90671)+~P90(x90671)+P1(f328(f328(f243(x90671),f78(x90671)),f328(f107(x90671),x90672)))+~P1(f328(f328(f243(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),x90672)) % 154.70/154.57 [9068]~P121(x90681)+~P90(x90681)+P1(f328(f328(f242(x90681),f78(x90681)),f328(f107(x90681),x90682)))+~P1(f328(f328(f242(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),x90682)) % 154.70/154.57 [9582]~P137(x95822)+E(x95821,f78(x95822))+E(x95821,f328(f79(x95822),f78(x95822)))+~E(f328(f328(f253(x95822),x95821),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f78(x95822)) % 154.70/154.57 [9855]~P62(x98551)+~P90(x98551)+~P1(f328(f328(f243(x98551),f2(x98551)),x98552))+P1(f328(f328(f243(x98551),f2(x98551)),f328(f328(f286(x98551),x98552),f328(f107(x98551),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))) % 154.70/154.57 [9917]~P62(x99171)+~P90(x99171)+P1(f328(f328(f243(x99171),f2(x99171)),x99172))+~P1(f328(f328(f243(x99171),f2(x99171)),f328(f328(f286(x99171),x99172),f328(f107(x99171),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))) % 154.70/154.57 [10172]~P135(x101722)+E(x101721,f2(a1))+P1(f328(f328(f243(a1),x101721),f2(a1)))+E(f328(f328(f267(a1,a1,x101722),f328(f328(f7(a1,f882(a1,f882(x101722,x101722)),f882(a1,x101722)),f328(f328(f8(f882(f882(x101722,x101722),x101722),f882(f882(a1,f882(x101722,x101722)),f882(a1,x101722)),a1),f8(f882(x101722,x101722),x101722,a1)),f328(f328(f8(x101722,f882(f882(x101722,x101722),x101722),a1),f86(x101722,x101722)),f106(x101722)))),f328(f328(f7(a1,f882(x101722,x101722),f882(x101722,x101722)),f328(f328(f8(f882(x101722,f882(x101722,x101722)),f882(f882(x101722,x101722),f882(x101722,x101722)),a1),f18(x101722,x101722,x101722)),f328(f328(f7(a1,f882(x101722,x101722),f882(x101722,f882(x101722,x101722))),f328(f328(f8(f882(x101722,f882(x101722,x101722)),f882(f882(x101722,x101722),f882(x101722,f882(x101722,x101722))),a1),f8(x101722,f882(x101722,x101722),x101722)),f328(f328(f8(a870,f882(x101722,f882(x101722,x101722)),a1),f100(x101722)),f328(f328(f7(a1,a1,a870),a325),f2(a1))))),f328(f328(f18(x101722,x101722,x101722),f80(x101722)),f5(x101722))))),f328(f328(f7(x101722,x101722,x101722),f328(f328(f8(x101722,f882(x101722,x101722),x101722),f80(x101722)),f328(f328(f18(x101722,x101722,x101722),f80(x101722)),f5(x101722)))),f78(x101722))))),f45(x101721,f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f106(x101722),x101721)) % 154.70/154.57 [5216]~P59(x52163)+~P37(x52163,x52162,f55(x52163))+E(x52161,f779(x52162,x52163))+~P1(f328(x52162,x52161)) % 154.70/154.57 [5373]~P59(x53731)+P37(x53731,x53732,f55(x53731))+~E(f780(x53732,x53731,x53733),x53733)+~P1(f328(x53732,x53733)) % 154.70/154.57 [4853]~P89(x48533)+~P90(x48533)+E(x48531,x48532)+~E(f328(f107(x48533),x48531),f328(f107(x48533),x48532)) % 154.70/154.57 [5990]~P59(x59901)+P37(x59901,x59902,f55(x59901))+~P1(f328(x59902,x59903))+P1(f328(x59902,f780(x59902,x59901,x59903))) % 154.70/154.57 [6000]~P1(f328(x60001,x60002))+~P1(f328(x60001,x60003))+~P1(f328(f328(f242(a875),x60003),f411(x60002,x60001)))+P1(f328(x60001,f2(a875))) % 154.70/154.57 [6421]P144(x64212,x64211,x64213)+E(x64211,f2(a1))+P1(f328(f328(f242(a1),f2(a1)),f813(x64213,x64211,x64212)))+P1(f328(f328(f243(a1),x64211),f2(a1))) % 154.70/154.57 [6422]P143(x64222,x64221,x64223)+E(x64221,f2(a1))+P1(f328(f328(f242(a1),f2(a1)),f821(x64223,x64221,x64222)))+P1(f328(f328(f243(a1),x64221),f2(a1))) % 154.70/154.57 [6542]P143(x65421,x65422,x65423)+~P1(f328(x65421,x65423))+P1(f328(f328(f242(a1),f2(a1)),f821(x65423,x65422,x65421)))+P1(f328(f328(f243(a1),x65422),f2(a1))) % 154.70/154.57 [6568]P144(x65681,x65682,x65683)+P1(f328(f328(f242(a1),f2(a1)),f813(x65683,x65682,x65681)))+~P1(f328(x65681,f2(a1)))+P1(f328(f328(f243(a1),x65682),f2(a1))) % 154.70/154.57 [6596]P144(x65962,x65961,x65963)+E(x65961,f2(a1))+~P1(f328(x65962,f814(x65963,x65961,x65962)))+P1(f328(f328(f243(a1),x65961),f2(a1))) % 154.70/154.57 [6597]P143(x65972,x65971,x65973)+E(x65971,f2(a1))+~P1(f328(x65972,f821(x65973,x65971,x65972)))+P1(f328(f328(f243(a1),x65971),f2(a1))) % 154.70/154.57 [6698]~P5(x66981)+~P105(x66981)+~P1(f328(f328(f243(x66981),x66982),f39(x66981,x66983)))+P1(f328(f328(f243(x66981),x66982),f853(x66983,x66982,x66981))) % 154.70/154.57 [6707]P143(x67071,x67072,x67073)+~P1(f328(x67071,x67073))+~P1(f328(x67071,f821(x67073,x67072,x67071)))+P1(f328(f328(f243(a1),x67072),f2(a1))) % 154.70/154.57 [6739]P144(x67391,x67392,x67393)+~P1(f328(x67391,f814(x67393,x67392,x67391)))+~P1(f328(x67391,f2(a1)))+P1(f328(f328(f243(a1),x67392),f2(a1))) % 154.70/154.57 [6990]P144(x69902,x69901,x69903)+E(x69901,f2(a1))+P1(f328(f328(f242(a1),f2(a1)),f813(x69903,x69901,x69902)))+P1(f328(f328(f243(a1),x69901),f812(x69903,x69901,x69902))) % 154.70/154.57 [6991]P143(x69912,x69911,x69913)+E(x69911,f2(a1))+P1(f328(f328(f242(a1),f2(a1)),f821(x69913,x69911,x69912)))+P1(f328(f328(f243(a1),x69911),f820(x69913,x69911,x69912))) % 154.70/154.57 [7108]P143(x71081,x71082,x71083)+~P1(f328(x71081,x71083))+P1(f328(f328(f242(a1),f2(a1)),f821(x71083,x71082,x71081)))+P1(f328(f328(f243(a1),x71082),f820(x71083,x71082,x71081))) % 154.70/154.57 [7127]P144(x71271,x71272,x71273)+P1(f328(f328(f242(a1),f2(a1)),f813(x71273,x71272,x71271)))+P1(f328(f328(f243(a1),x71272),f812(x71273,x71272,x71271)))+~P1(f328(x71271,f2(a1))) % 154.70/154.57 [7160]P144(x71602,x71601,x71603)+E(x71601,f2(a1))+~P1(f328(x71602,f814(x71603,x71601,x71602)))+P1(f328(f328(f243(a1),x71601),f812(x71603,x71601,x71602))) % 154.70/154.57 [7161]P143(x71612,x71611,x71613)+E(x71611,f2(a1))+~P1(f328(x71612,f821(x71613,x71611,x71612)))+P1(f328(f328(f243(a1),x71611),f820(x71613,x71611,x71612))) % 154.70/154.57 [7204]P144(x72042,x72041,x72043)+E(x72041,f2(a1))+P1(f328(f328(f242(a1),f2(a1)),f813(x72043,x72041,x72042)))+~P1(f328(x72042,f819(x72043,x72041,x72042))) % 154.70/154.57 [7205]P143(x72052,x72051,x72053)+E(x72051,f2(a1))+P1(f328(f328(f242(a1),f2(a1)),f821(x72053,x72051,x72052)))+~P1(f328(x72052,f820(x72053,x72051,x72052))) % 154.70/154.57 [7293]P143(x72931,x72932,x72933)+~P1(f328(x72931,x72933))+~P1(f328(x72931,f821(x72933,x72932,x72931)))+P1(f328(f328(f243(a1),x72932),f820(x72933,x72932,x72931))) % 154.70/154.57 [7309]P144(x73091,x73092,x73093)+~P1(f328(x73091,f814(x73093,x73092,x73091)))+P1(f328(f328(f243(a1),x73092),f812(x73093,x73092,x73091)))+~P1(f328(x73091,f2(a1))) % 154.70/154.57 [7313]P143(x73131,x73132,x73133)+~P1(f328(x73131,x73133))+P1(f328(f328(f242(a1),f2(a1)),f821(x73133,x73132,x73131)))+~P1(f328(x73131,f820(x73133,x73132,x73131))) % 154.70/154.57 [7331]P144(x73311,x73312,x73313)+P1(f328(f328(f242(a1),f2(a1)),f813(x73313,x73312,x73311)))+~P1(f328(x73311,f819(x73313,x73312,x73311)))+~P1(f328(x73311,f2(a1))) % 154.70/154.57 [7355]P144(x73552,x73551,x73553)+E(x73551,f2(a1))+~P1(f328(x73552,f814(x73553,x73551,x73552)))+~P1(f328(x73552,f819(x73553,x73551,x73552))) % 154.70/154.57 [7356]P143(x73562,x73561,x73563)+E(x73561,f2(a1))+~P1(f328(x73562,f821(x73563,x73561,x73562)))+~P1(f328(x73562,f820(x73563,x73561,x73562))) % 154.70/154.57 [7447]P143(x74471,x74472,x74473)+~P1(f328(x74471,x74473))+~P1(f328(x74471,f821(x74473,x74472,x74471)))+~P1(f328(x74471,f820(x74473,x74472,x74471))) % 154.70/154.57 [7464]P144(x74641,x74642,x74643)+~P1(f328(x74641,f814(x74643,x74642,x74641)))+~P1(f328(x74641,f819(x74643,x74642,x74641)))+~P1(f328(x74641,f2(a1))) % 154.70/154.57 [7512]P144(x75122,x75121,x75123)+E(x75121,f2(a1))+P1(f328(f328(f242(a1),f2(a1)),f813(x75123,x75121,x75122)))+P1(f328(f328(f242(a1),f812(x75123,x75121,x75122)),f2(a1))) % 154.70/154.57 [7513]P143(x75132,x75131,x75133)+E(x75131,f2(a1))+P1(f328(f328(f242(a1),f2(a1)),f821(x75133,x75131,x75132)))+P1(f328(f328(f242(a1),f820(x75133,x75131,x75132)),f2(a1))) % 154.70/154.57 [7514]~P135(x75141)+~P1(f328(f328(f330(x75141),x75143),f113(x75141)))+~P1(f328(f328(f330(x75141),x75142),f113(x75141)))+P1(f328(f328(f330(x75141),f328(f328(f22(x75141),x75142),x75143)),f113(x75141))) % 154.70/154.57 [7515]~P135(x75151)+~P1(f328(f328(f330(x75151),x75153),f113(x75151)))+~P1(f328(f328(f330(x75151),x75152),f113(x75151)))+P1(f328(f328(f330(x75151),f328(f328(f80(x75151),x75152),x75153)),f113(x75151))) % 154.70/154.57 [7516]~P140(x75161)+~P1(f328(f328(f330(x75161),x75163),f190(x75161)))+~P1(f328(f328(f330(x75161),x75162),f190(x75161)))+P1(f328(f328(f330(x75161),f328(f328(f80(x75161),x75162),x75163)),f190(x75161))) % 154.70/154.57 [7517]~P135(x75171)+~P1(f328(f328(f330(x75171),x75173),f113(x75171)))+~P1(f328(f328(f330(x75171),x75172),f113(x75171)))+P1(f328(f328(f330(x75171),f328(f328(f81(x75171),x75172),x75173)),f113(x75171))) % 154.70/154.57 [7518]~P140(x75181)+~P1(f328(f328(f330(x75181),x75183),f190(x75181)))+~P1(f328(f328(f330(x75181),x75182),f190(x75181)))+P1(f328(f328(f330(x75181),f328(f328(f81(x75181),x75182),x75183)),f190(x75181))) % 154.70/154.57 [7519]~P85(x75191)+~P1(f328(f328(f243(x75191),x75193),f2(x75191)))+~P1(f328(f328(f243(x75191),x75192),f2(x75191)))+P1(f328(f328(f243(x75191),f328(f328(f80(x75191),x75192),x75193)),f2(x75191))) % 154.70/154.57 [7520]~P85(x75201)+~P1(f328(f328(f242(x75201),x75202),f2(x75201)))+~P1(f328(f328(f243(x75201),x75203),f2(x75201)))+P1(f328(f328(f243(x75201),f328(f328(f80(x75201),x75202),x75203)),f2(x75201))) % 154.70/154.57 [7521]~P85(x75211)+~P1(f328(f328(f242(x75211),x75213),f2(x75211)))+~P1(f328(f328(f243(x75211),x75212),f2(x75211)))+P1(f328(f328(f243(x75211),f328(f328(f80(x75211),x75212),x75213)),f2(x75211))) % 154.70/154.57 [7522]~P85(x75221)+~P1(f328(f328(f242(x75221),x75223),f2(x75221)))+~P1(f328(f328(f242(x75221),x75222),f2(x75221)))+P1(f328(f328(f242(x75221),f328(f328(f80(x75221),x75222),x75223)),f2(x75221))) % 154.70/154.57 [7548]P144(x75483,x75481,x75482)+E(x75481,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x75481),f814(x75482,x75481,x75483))),f813(x75482,x75481,x75483)),x75482)+P1(f328(f328(f243(a1),x75481),f2(a1))) % 154.70/154.57 [7549]P143(x75493,x75491,x75492)+E(x75491,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x75491),f822(x75492,x75491,x75493))),f821(x75492,x75491,x75493)),x75492)+P1(f328(f328(f243(a1),x75491),f2(a1))) % 154.70/154.57 [7633]P143(x76331,x76332,x76333)+~P1(f328(x76331,x76333))+P1(f328(f328(f242(a1),f2(a1)),f821(x76333,x76332,x76331)))+P1(f328(f328(f242(a1),f820(x76333,x76332,x76331)),f2(a1))) % 154.70/154.57 [7662]P144(x76621,x76622,x76623)+P1(f328(f328(f242(a1),f2(a1)),f813(x76623,x76622,x76621)))+~P1(f328(x76621,f2(a1)))+P1(f328(f328(f242(a1),f812(x76623,x76622,x76621)),f2(a1))) % 154.70/154.57 [7671]P143(x76713,x76711,x76712)+~P1(f328(x76713,x76712))+E(f328(f328(f80(a1),f328(f328(f81(a1),x76711),f822(x76712,x76711,x76713))),f821(x76712,x76711,x76713)),x76712)+P1(f328(f328(f243(a1),x76711),f2(a1))) % 154.70/154.57 [7678]P144(x76782,x76781,x76783)+E(x76781,f2(a1))+~P1(f328(x76782,f814(x76783,x76781,x76782)))+P1(f328(f328(f242(a1),f812(x76783,x76781,x76782)),f2(a1))) % 154.70/154.57 [7679]P143(x76792,x76791,x76793)+E(x76791,f2(a1))+~P1(f328(x76792,f821(x76793,x76791,x76792)))+P1(f328(f328(f242(a1),f820(x76793,x76791,x76792)),f2(a1))) % 154.70/154.57 [7684]P144(x76843,x76841,x76842)+E(f328(f328(f80(a1),f328(f328(f81(a1),x76841),f814(x76842,x76841,x76843))),f813(x76842,x76841,x76843)),x76842)+~P1(f328(x76843,f2(a1)))+P1(f328(f328(f243(a1),x76841),f2(a1))) % 154.70/154.57 [7740]P143(x77401,x77402,x77403)+~P1(f328(x77401,x77403))+~P1(f328(x77401,f821(x77403,x77402,x77401)))+P1(f328(f328(f242(a1),f820(x77403,x77402,x77401)),f2(a1))) % 154.70/154.57 [7744]P144(x77441,x77442,x77443)+~P1(f328(x77441,f814(x77443,x77442,x77441)))+~P1(f328(x77441,f2(a1)))+P1(f328(f328(f242(a1),f812(x77443,x77442,x77441)),f2(a1))) % 154.70/154.57 [7816]~P62(x78161)+~P1(f328(f328(f243(x78161),f328(f328(f286(x78161),x78163),x78162)),f2(x78161)))+P1(f328(f328(f243(x78161),x78162),f2(x78161)))+P1(f328(f328(f243(x78161),x78163),f2(x78161))) % 154.70/154.57 [7817]~P114(x78171)+~P1(f328(f328(f242(x78171),f328(f328(f81(x78171),x78173),x78172)),f2(x78171)))+P1(f328(f328(f242(x78171),x78172),f2(x78171)))+P1(f328(f328(f242(x78171),x78173),f2(x78171))) % 154.70/154.57 [7818]~P62(x78181)+~P1(f328(f328(f242(x78181),f328(f328(f286(x78181),x78183),x78182)),f2(x78181)))+P1(f328(f328(f242(x78181),x78182),f2(x78181)))+P1(f328(f328(f242(x78181),x78183),f2(x78181))) % 154.70/154.57 [7932]P144(x79323,x79321,x79322)+E(x79321,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x79321),f814(x79322,x79321,x79323))),f813(x79322,x79321,x79323)),x79322)+P1(f328(f328(f243(a1),x79321),f812(x79322,x79321,x79323))) % 154.70/154.57 [7933]P143(x79333,x79331,x79332)+E(x79331,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x79331),f822(x79332,x79331,x79333))),f821(x79332,x79331,x79333)),x79332)+P1(f328(f328(f243(a1),x79331),f820(x79332,x79331,x79333))) % 154.70/154.57 [7945]P144(x79453,x79451,x79452)+E(x79451,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x79451),f819(x79452,x79451,x79453))),f812(x79452,x79451,x79453)),x79452)+P1(f328(f328(f242(a1),f2(a1)),f813(x79452,x79451,x79453))) % 154.70/154.57 [7946]P143(x79463,x79461,x79462)+E(x79461,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x79461),f823(x79462,x79461,x79463))),f820(x79462,x79461,x79463)),x79462)+P1(f328(f328(f242(a1),f2(a1)),f821(x79462,x79461,x79463))) % 154.70/154.57 [7987]P143(x79873,x79871,x79872)+~P1(f328(x79873,x79872))+E(f328(f328(f80(a1),f328(f328(f81(a1),x79871),f822(x79872,x79871,x79873))),f821(x79872,x79871,x79873)),x79872)+P1(f328(f328(f243(a1),x79871),f820(x79872,x79871,x79873))) % 154.70/154.57 [7996]P144(x79963,x79961,x79962)+E(f328(f328(f80(a1),f328(f328(f81(a1),x79961),f814(x79962,x79961,x79963))),f813(x79962,x79961,x79963)),x79962)+P1(f328(f328(f243(a1),x79961),f812(x79962,x79961,x79963)))+~P1(f328(x79963,f2(a1))) % 154.70/154.57 [8002]P143(x80023,x80021,x80022)+~P1(f328(x80023,x80022))+E(f328(f328(f80(a1),f328(f328(f81(a1),x80021),f823(x80022,x80021,x80023))),f820(x80022,x80021,x80023)),x80022)+P1(f328(f328(f242(a1),f2(a1)),f821(x80022,x80021,x80023))) % 154.70/154.57 [8008]P144(x80083,x80081,x80082)+E(f328(f328(f80(a1),f328(f328(f81(a1),x80081),f819(x80082,x80081,x80083))),f812(x80082,x80081,x80083)),x80082)+P1(f328(f328(f242(a1),f2(a1)),f813(x80082,x80081,x80083)))+~P1(f328(x80083,f2(a1))) % 154.70/154.57 [8019]P144(x80193,x80191,x80192)+E(x80191,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x80191),f814(x80192,x80191,x80193))),f813(x80192,x80191,x80193)),x80192)+~P1(f328(x80193,f819(x80192,x80191,x80193))) % 154.70/154.57 [8020]P143(x80203,x80201,x80202)+E(x80201,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x80201),f822(x80202,x80201,x80203))),f821(x80202,x80201,x80203)),x80202)+~P1(f328(x80203,f820(x80202,x80201,x80203))) % 154.70/154.57 [8021]P144(x80213,x80211,x80212)+E(x80211,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x80211),f819(x80212,x80211,x80213))),f812(x80212,x80211,x80213)),x80212)+~P1(f328(x80213,f814(x80212,x80211,x80213))) % 154.70/154.57 [8022]P143(x80223,x80221,x80222)+E(x80221,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x80221),f823(x80222,x80221,x80223))),f820(x80222,x80221,x80223)),x80222)+~P1(f328(x80223,f821(x80222,x80221,x80223))) % 154.70/154.57 [8080]P143(x80803,x80801,x80802)+~P1(f328(x80803,x80802))+E(f328(f328(f80(a1),f328(f328(f81(a1),x80801),f822(x80802,x80801,x80803))),f821(x80802,x80801,x80803)),x80802)+~P1(f328(x80803,f820(x80802,x80801,x80803))) % 154.70/154.57 [8081]P143(x80813,x80811,x80812)+~P1(f328(x80813,x80812))+E(f328(f328(f80(a1),f328(f328(f81(a1),x80811),f823(x80812,x80811,x80813))),f820(x80812,x80811,x80813)),x80812)+~P1(f328(x80813,f821(x80812,x80811,x80813))) % 154.70/154.57 [8092]P144(x80923,x80921,x80922)+E(f328(f328(f80(a1),f328(f328(f81(a1),x80921),f814(x80922,x80921,x80923))),f813(x80922,x80921,x80923)),x80922)+~P1(f328(x80923,f819(x80922,x80921,x80923)))+~P1(f328(x80923,f2(a1))) % 154.70/154.57 [8093]P144(x80933,x80931,x80932)+E(f328(f328(f80(a1),f328(f328(f81(a1),x80931),f819(x80932,x80931,x80933))),f812(x80932,x80931,x80933)),x80932)+~P1(f328(x80933,f814(x80932,x80931,x80933)))+~P1(f328(x80933,f2(a1))) % 154.70/154.57 [8201]P144(x82013,x82011,x82012)+E(x82011,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x82011),f814(x82012,x82011,x82013))),f813(x82012,x82011,x82013)),x82012)+P1(f328(f328(f242(a1),f812(x82012,x82011,x82013)),f2(a1))) % 154.70/154.57 [8202]P143(x82023,x82021,x82022)+E(x82021,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x82021),f822(x82022,x82021,x82023))),f821(x82022,x82021,x82023)),x82022)+P1(f328(f328(f242(a1),f820(x82022,x82021,x82023)),f2(a1))) % 154.70/154.57 [8248]P143(x82483,x82481,x82482)+~P1(f328(x82483,x82482))+E(f328(f328(f80(a1),f328(f328(f81(a1),x82481),f822(x82482,x82481,x82483))),f821(x82482,x82481,x82483)),x82482)+P1(f328(f328(f242(a1),f820(x82482,x82481,x82483)),f2(a1))) % 154.70/154.57 [8253]P144(x82533,x82531,x82532)+E(f328(f328(f80(a1),f328(f328(f81(a1),x82531),f814(x82532,x82531,x82533))),f813(x82532,x82531,x82533)),x82532)+~P1(f328(x82533,f2(a1)))+P1(f328(f328(f242(a1),f812(x82532,x82531,x82533)),f2(a1))) % 154.70/154.57 [8382]P144(x83823,x83821,x83822)+E(x83821,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x83821),f819(x83822,x83821,x83823))),f812(x83822,x83821,x83823)),x83822)+E(f328(f328(f80(a1),f328(f328(f81(a1),x83821),f814(x83822,x83821,x83823))),f813(x83822,x83821,x83823)),x83822) % 154.70/154.57 [8383]P143(x83833,x83831,x83832)+E(x83831,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x83831),f823(x83832,x83831,x83833))),f820(x83832,x83831,x83833)),x83832)+E(f328(f328(f80(a1),f328(f328(f81(a1),x83831),f822(x83832,x83831,x83833))),f821(x83832,x83831,x83833)),x83832) % 154.70/154.57 [8406]P143(x84063,x84061,x84062)+~P1(f328(x84063,x84062))+E(f328(f328(f80(a1),f328(f328(f81(a1),x84061),f823(x84062,x84061,x84063))),f820(x84062,x84061,x84063)),x84062)+E(f328(f328(f80(a1),f328(f328(f81(a1),x84061),f822(x84062,x84061,x84063))),f821(x84062,x84061,x84063)),x84062) % 154.70/154.57 [8418]P144(x84183,x84181,x84182)+E(f328(f328(f80(a1),f328(f328(f81(a1),x84181),f819(x84182,x84181,x84183))),f812(x84182,x84181,x84183)),x84182)+E(f328(f328(f80(a1),f328(f328(f81(a1),x84181),f814(x84182,x84181,x84183))),f813(x84182,x84181,x84183)),x84182)+~P1(f328(x84183,f2(a1))) % 154.70/154.57 [9075]~P114(x90751)+~E(x90753,f2(x90751))+~E(x90752,f2(x90751))+P1(f328(f328(f242(x90751),f328(f328(f80(x90751),f328(f328(f81(x90751),x90752),x90752)),f328(f328(f81(x90751),x90753),x90753))),f2(x90751))) % 154.70/154.57 [10121]~P121(x101211)+~E(x101213,f2(x101211))+~E(x101212,f2(x101211))+P1(f328(f328(f242(x101211),f328(f328(f80(x101211),f328(f328(f253(x101211),x101212),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x101211),x101213),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))),f2(x101211))) % 154.70/154.57 [4801]~E(x48013,x48011)+~P117(x48012)+E(x48011,f2(x48012))+E(f328(f328(f286(x48012),x48013),x48011),f78(x48012)) % 154.70/154.57 [4854]~P3(x48541)+~E(x48543,f192(x48541))+~E(x48542,f192(x48541))+E(f328(f328(f114(x48541),x48542),x48543),f192(x48541)) % 154.70/154.57 [4855]~P97(x48551)+~E(x48553,f251(x48551))+~E(x48552,f251(x48551))+E(f328(f328(f105(x48551),x48552),x48553),f251(x48551)) % 154.70/154.57 [4941]~P117(x49413)+E(x49411,x49412)+E(x49412,f2(x49413))+~E(f328(f328(f286(x49413),x49411),x49412),f78(x49413)) % 154.70/154.57 [4959]~P136(x49592)+E(x49591,f2(x49592))+E(x49593,f2(x49592))+~E(f328(f328(f81(x49592),x49593),x49591),f2(x49592)) % 154.70/154.57 [4961]~P129(x49612)+E(x49611,f2(x49612))+E(x49613,f2(x49612))+~E(f328(f328(f81(x49612),x49613),x49611),f2(x49612)) % 154.70/154.57 [5340]~P116(x53403)+E(x53401,x53402)+E(x53401,f328(f79(x53403),x53402))+~E(f328(f328(f81(x53403),x53401),x53401),f328(f328(f81(x53403),x53402),x53402)) % 154.70/154.57 [5380]~P93(x53801)+E(f328(f79(x53801),x53802),x53803)+~E(f328(f328(f114(x53801),x53802),x53803),f251(x53801))+~E(f328(f328(f105(x53801),x53802),x53803),f192(x53801)) % 154.70/154.57 [5454]~P121(x54543)+E(x54541,x54542)+P1(f328(f328(f243(x54543),x54542),x54541))+P1(f328(f328(f243(x54543),x54541),x54542)) % 154.70/154.57 [5460]~P105(x54603)+E(x54601,x54602)+P1(f328(f328(f243(x54603),x54602),x54601))+P1(f328(f328(f243(x54603),x54601),x54602)) % 154.70/154.57 [5461]~E(x54612,x54613)+~P105(x54611)+P1(f328(f328(f242(x54611),x54612),x54613))+P1(f328(f328(f243(x54611),x54612),x54613)) % 154.70/154.57 [5714]~P107(x57143)+E(x57141,x57142)+~P1(f328(f328(f242(x57143),x57142),x57141))+P1(f328(f328(f243(x57143),x57142),x57141)) % 154.70/154.57 [5716]~P105(x57163)+E(x57161,x57162)+~P1(f328(f328(f242(x57163),x57161),x57162))+P1(f328(f328(f243(x57163),x57161),x57162)) % 154.70/154.57 [5722]~P107(x57223)+E(x57221,x57222)+~P1(f328(f328(f242(x57223),x57221),x57222))+P1(f328(f328(f243(x57223),x57221),x57222)) % 154.70/154.57 [5824]P143(x58241,x58242,x58243)+~P1(f328(x58241,x58243))+P1(f328(f328(f243(a1),x58242),f2(a1)))+P1(f328(f328(f243(a1),f2(a1)),x58242)) % 154.70/154.57 [5871]P144(x58711,x58712,x58713)+~P1(f328(x58711,f2(a1)))+P1(f328(f328(f243(a1),x58712),f2(a1)))+P1(f328(f328(f243(a1),f2(a1)),x58712)) % 154.70/154.57 [5875]~P2(x58751)+E(f328(f328(f114(x58751),x58752),f11(x58751,x58753)),x58752)+~P1(f328(f61(x58751),x58753))+~P1(f328(f328(f330(x58751),x58752),x58753)) % 154.70/154.57 [5876]~P2(x58761)+E(f328(f328(f105(x58761),x58762),f10(x58761,x58763)),x58762)+~P1(f328(f61(x58761),x58763))+~P1(f328(f328(f330(x58761),x58762),x58763)) % 154.70/154.57 [5912]~P2(x59121)+E(f328(f328(f114(x59121),x59122),f10(x59121,x59123)),f10(x59121,x59123))+~P1(f328(f61(x59121),x59123))+~P1(f328(f328(f330(x59121),x59122),x59123)) % 154.70/154.57 [5913]~P2(x59131)+E(f328(f328(f105(x59131),x59132),f11(x59131,x59133)),f11(x59131,x59133))+~P1(f328(f61(x59131),x59133))+~P1(f328(f328(f330(x59131),x59132),x59133)) % 154.70/154.57 [5914]~P105(x59141)+E(f328(f328(f240(x59141),x59142),f14(x59141,x59143)),f14(x59141,x59143))+~P1(f328(f61(x59141),x59143))+~P1(f328(f328(f330(x59141),x59142),x59143)) % 154.70/154.57 [5915]~P105(x59151)+E(f328(f328(f241(x59151),x59152),f15(x59151,x59153)),f15(x59151,x59153))+~P1(f328(f61(x59151),x59153))+~P1(f328(f328(f330(x59151),x59152),x59153)) % 154.70/154.57 [5957]E(x59571,x59572)+~P107(x59573)+~P1(f328(f328(f242(x59573),x59572),x59571))+~P1(f328(f328(f242(x59573),x59571),x59572)) % 154.70/154.57 [6095]~P106(x60951)+P1(f328(f328(f242(x60951),x60953),x60952))+~P1(f328(f328(f242(x60951),x60952),x60953))+P1(f328(f328(f243(x60951),x60952),x60953)) % 154.70/154.57 [6116]~P105(x61161)+~P1(f328(f61(x61161),x61163))+P1(f328(f328(f242(x61161),x61162),f15(x61161,x61163)))+~P1(f328(f328(f330(x61161),x61162),x61163)) % 154.70/154.57 [6171]~P105(x61711)+E(f328(f328(f240(x61711),x61712),f12(x61711,f241(x61711),x61713)),x61712)+~P1(f328(f61(x61711),x61713))+~P1(f328(f328(f330(x61711),x61712),x61713)) % 154.70/154.57 [6172]~P105(x61721)+E(f328(f328(f241(x61721),x61722),f13(x61721,f240(x61721),x61723)),x61722)+~P1(f328(f61(x61721),x61723))+~P1(f328(f328(f330(x61721),x61722),x61723)) % 154.70/154.57 [6311]E(x63111,x63112)+~E(f328(f328(f22(a875),x63111),x63113),f328(f328(f22(a875),x63112),x63113))+~P1(f328(f328(f242(a875),x63113),x63111))+~P1(f328(f328(f242(a875),x63113),x63112)) % 154.70/154.57 [6338]~P105(x63381)+~P1(f328(f61(x63381),x63382))+~P1(f328(f328(f330(x63381),x63383),x63382))+P1(f328(f328(f242(x63381),f14(x63381,x63382)),x63383)) % 154.70/154.57 [6400]P144(x64002,x64001,x64003)+E(x64001,f2(a1))+P1(f328(f328(f243(a1),x64001),f812(x64003,x64001,x64002)))+P1(f328(f328(f243(a1),f2(a1)),x64001)) % 154.70/154.57 [6401]P143(x64012,x64011,x64013)+E(x64011,f2(a1))+P1(f328(f328(f243(a1),x64011),f820(x64013,x64011,x64012)))+P1(f328(f328(f243(a1),f2(a1)),x64011)) % 154.70/154.57 [6402]~P105(x64021)+E(f328(f328(f240(x64021),x64022),f13(x64021,f240(x64021),x64023)),f13(x64021,f240(x64021),x64023))+~P1(f328(f61(x64021),x64023))+~P1(f328(f328(f330(x64021),x64022),x64023)) % 154.70/154.57 [6403]~P105(x64031)+E(f328(f328(f241(x64031),x64032),f12(x64031,f241(x64031),x64033)),f12(x64031,f241(x64031),x64033))+~P1(f328(f61(x64031),x64033))+~P1(f328(f328(f330(x64031),x64032),x64033)) % 154.70/154.57 [6409]~P1(f328(x64091,x64092))+P1(f328(x64091,f515(x64092,x64091,x64093)))+P1(f328(x64091,f2(a875)))+~P1(f328(f328(f243(a875),x64092),x64093)) % 154.70/154.57 [6464]~P1(f328(x64641,x64642))+~P1(f328(f61(x64643),x64642))+P1(f328(x64641,f571(x64641,x64642,x64643)))+P1(f328(x64641,f192(f882(x64643,a870)))) % 154.70/154.57 [6477]~P121(x64771)+~P90(x64771)+P1(f328(f328(f243(x64771),f328(f107(x64771),x64772)),f328(f107(x64771),x64773)))+~P1(f328(f328(f243(a1),x64772),x64773)) % 154.70/154.57 [6478]~P121(x64781)+~P90(x64781)+P1(f328(f328(f242(x64781),f328(f107(x64781),x64782)),f328(f107(x64781),x64783)))+~P1(f328(f328(f242(a1),x64782),x64783)) % 154.70/154.57 [6481]~P1(f328(x64811,x64813))+~P1(f328(f61(x64812),x64813))+P1(f328(f61(x64812),f571(x64811,x64813,x64812)))+P1(f328(x64811,f192(f882(x64812,a870)))) % 154.70/154.57 [6514]P143(x65141,x65142,x65143)+~P1(f328(x65141,x65143))+P1(f328(f328(f243(a1),x65142),f820(x65143,x65142,x65141)))+P1(f328(f328(f243(a1),f2(a1)),x65142)) % 154.70/154.57 [6548]P144(x65481,x65482,x65483)+P1(f328(f328(f243(a1),x65482),f812(x65483,x65482,x65481)))+~P1(f328(x65481,f2(a1)))+P1(f328(f328(f243(a1),f2(a1)),x65482)) % 154.70/154.57 [6579]~P108(x65791)+~P91(x65791)+E(f328(f328(f240(x65791),f328(f107(x65791),x65792)),f328(f107(x65791),x65793)),f328(f107(x65791),x65793))+P1(f328(f328(f242(x65791),f328(f107(x65791),x65792)),f328(f107(x65791),x65793))) % 154.70/154.57 [6580]~P108(x65801)+~P91(x65801)+E(f328(f328(f241(x65801),f328(f107(x65801),x65802)),f328(f107(x65801),x65803)),f328(f107(x65801),x65802))+P1(f328(f328(f242(x65801),f328(f107(x65801),x65802)),f328(f107(x65801),x65803))) % 154.70/154.57 [6639]P144(x66392,x66391,x66393)+E(x66391,f2(a1))+~P1(f328(x66392,f819(x66393,x66391,x66392)))+P1(f328(f328(f243(a1),f2(a1)),x66391)) % 154.70/154.57 [6640]P143(x66402,x66401,x66403)+E(x66401,f2(a1))+~P1(f328(x66402,f820(x66403,x66401,x66402)))+P1(f328(f328(f243(a1),f2(a1)),x66401)) % 154.70/154.57 [6644]P1(f328(x66441,x66442))+~P1(f328(f61(x66443),x66442))+P1(f328(x66441,f824(x66441,x66442,x66443)))+~P1(f328(x66441,f192(f882(x66443,a870)))) % 154.70/154.57 [6663]P1(f328(x66631,x66632))+P1(f328(f61(x66633),f824(x66631,x66632,x66633)))+~P1(f328(f61(x66633),x66632))+~P1(f328(x66631,f192(f882(x66633,a870)))) % 154.70/154.57 [6728]P143(x67281,x67282,x67283)+~P1(f328(x67281,x67283))+~P1(f328(x67281,f820(x67283,x67282,x67281)))+P1(f328(f328(f243(a1),f2(a1)),x67282)) % 154.70/154.57 [6758]P144(x67581,x67582,x67583)+~P1(f328(x67581,f819(x67583,x67582,x67581)))+~P1(f328(x67581,f2(a1)))+P1(f328(f328(f243(a1),f2(a1)),x67582)) % 154.70/154.57 [6867]~P90(x68673)+~P121(x68673)+~P1(f328(f328(f243(x68673),f328(f107(x68673),x68671)),f328(f107(x68673),x68672)))+P1(f328(f328(f243(a1),x68671),x68672)) % 154.70/154.57 [6868]~P90(x68683)+~P121(x68683)+~P1(f328(f328(f242(x68683),f328(f107(x68683),x68681)),f328(f107(x68683),x68682)))+P1(f328(f328(f242(a1),x68681),x68682)) % 154.70/154.57 [6895]~P105(x68951)+~P16(x68951,x68953)+P16(x68951,f328(f328(f148(x68951),x68952),x68953))+~P1(f328(f328(f242(x68951),x68952),f747(x68953,x68952,x68951))) % 154.70/154.57 [6896]~P105(x68961)+~P16(x68961,x68963)+P16(x68961,f328(f328(f148(x68961),x68962),x68963))+~P1(f328(f328(f242(x68961),x68962),f749(x68963,x68962,x68961))) % 154.70/154.57 [6897]~P105(x68971)+~P16(x68971,x68973)+P16(x68971,f328(f328(f148(x68971),x68972),x68973))+~P1(f328(f328(f242(x68971),x68972),f782(x68972,x68973,x68971))) % 154.70/154.57 [6981]P144(x69812,x69811,x69813)+E(x69811,f2(a1))+P1(f328(f328(f243(a1),x69811),f2(a1)))+P1(f328(f328(f243(a1),f813(x69813,x69811,x69812)),x69811)) % 154.70/154.57 [6982]P143(x69822,x69821,x69823)+E(x69821,f2(a1))+P1(f328(f328(f243(a1),x69821),f2(a1)))+P1(f328(f328(f243(a1),f821(x69823,x69821,x69822)),x69821)) % 154.70/154.57 [7021]P144(x70212,x70211,x70213)+E(x70211,f2(a1))+P1(f328(f328(f242(a1),f812(x70213,x70211,x70212)),f2(a1)))+P1(f328(f328(f243(a1),f2(a1)),x70211)) % 154.70/154.57 [7022]P143(x70222,x70221,x70223)+E(x70221,f2(a1))+P1(f328(f328(f242(a1),f820(x70223,x70221,x70222)),f2(a1)))+P1(f328(f328(f243(a1),f2(a1)),x70221)) % 154.70/154.57 [7044]~P105(x70441)+~P16(x70441,x70443)+E(f328(f328(f145(x70441,x70441,f5(x70441)),x70442),f167(x70441,x70442,x70443)),x70443)+~P1(f328(f328(f330(x70441),x70442),f328(f170(x70441),x70443))) % 154.70/154.57 [7091]P143(x70911,x70912,x70913)+~P1(f328(x70911,x70913))+P1(f328(f328(f243(a1),x70912),f2(a1)))+P1(f328(f328(f243(a1),f821(x70913,x70912,x70911)),x70912)) % 154.70/154.57 [7097]~P108(x70971)+~P91(x70971)+E(f328(f328(f240(x70971),f328(f107(x70971),x70972)),f328(f107(x70971),x70973)),f328(f107(x70971),x70972))+~P1(f328(f328(f242(x70971),f328(f107(x70971),x70972)),f328(f107(x70971),x70973))) % 154.70/154.57 [7098]~P108(x70981)+~P91(x70981)+E(f328(f328(f241(x70981),f328(f107(x70981),x70982)),f328(f107(x70981),x70983)),f328(f107(x70981),x70983))+~P1(f328(f328(f242(x70981),f328(f107(x70981),x70982)),f328(f107(x70981),x70983))) % 154.70/154.57 [7112]P144(x71121,x71122,x71123)+~P1(f328(x71121,f2(a1)))+P1(f328(f328(f243(a1),x71122),f2(a1)))+P1(f328(f328(f243(a1),f813(x71123,x71122,x71121)),x71122)) % 154.70/154.57 [7120]P143(x71201,x71202,x71203)+~P1(f328(x71201,x71203))+P1(f328(f328(f242(a1),f820(x71203,x71202,x71201)),f2(a1)))+P1(f328(f328(f243(a1),f2(a1)),x71202)) % 154.70/154.57 [7144]P144(x71441,x71442,x71443)+~P1(f328(x71441,f2(a1)))+P1(f328(f328(f242(a1),f812(x71443,x71442,x71441)),f2(a1)))+P1(f328(f328(f243(a1),f2(a1)),x71442)) % 154.70/154.57 [7174]~P1(f328(x71741,x71742))+P1(f328(x71741,f2(a875)))+~P1(f328(f328(f243(a875),x71742),x71743))+P1(f328(f328(f243(a875),f515(x71742,x71741,x71743)),x71743)) % 154.70/154.57 [7191]~P105(x71911)+~P16(x71911,x71913)+P16(x71911,f328(f328(f148(x71911),x71912),x71913))+P1(f328(f328(f330(x71911),f747(x71913,x71912,x71911)),f328(f170(x71911),x71913))) % 154.70/154.57 [7192]~P105(x71921)+~P16(x71921,x71923)+P16(x71921,f328(f328(f148(x71921),x71922),x71923))+P1(f328(f328(f330(x71921),f749(x71923,x71922,x71921)),f328(f170(x71921),x71923))) % 154.70/154.57 [7193]~P105(x71931)+~P16(x71931,x71933)+P16(x71931,f328(f328(f148(x71931),x71932),x71933))+P1(f328(f328(f330(x71931),f782(x71932,x71933,x71931)),f328(f170(x71931),x71933))) % 154.70/154.57 [7297]~P5(x72971)+~P105(x72971)+~P1(f328(f328(f243(x72971),x72973),f39(x72971,x72972)))+P1(f328(f328(f330(x72971),f853(x72972,x72973,x72971)),x72972)) % 154.70/154.57 [7462]~P5(x74621)+~P105(x74621)+~P1(f328(f328(f243(x74621),f40(x74621,x74623)),x74622))+P1(f328(f328(f330(x74621),f854(x74622,x74623,x74621)),x74623)) % 154.70/154.57 [7463]~P5(x74631)+~P105(x74631)+~P1(f328(f328(f243(x74631),f40(x74631,x74633)),x74632))+P1(f328(f328(f243(x74631),f854(x74632,x74633,x74631)),x74632)) % 154.70/154.57 [7478]P144(x74782,x74781,x74783)+E(x74781,f2(a1))+P1(f328(f328(f243(a1),x74781),f812(x74783,x74781,x74782)))+P1(f328(f328(f243(a1),f813(x74783,x74781,x74782)),x74781)) % 154.70/154.57 [7479]P143(x74792,x74791,x74793)+E(x74791,f2(a1))+P1(f328(f328(f243(a1),x74791),f820(x74793,x74791,x74792)))+P1(f328(f328(f243(a1),f821(x74793,x74791,x74792)),x74791)) % 154.70/154.57 [7569]P144(x75693,x75691,x75692)+E(x75691,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x75691),f819(x75692,x75691,x75693))),f812(x75692,x75691,x75693)),x75692)+P1(f328(f328(f243(a1),f2(a1)),x75691)) % 154.70/154.57 [7570]P143(x75703,x75701,x75702)+E(x75701,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x75701),f823(x75702,x75701,x75703))),f820(x75702,x75701,x75703)),x75702)+P1(f328(f328(f243(a1),f2(a1)),x75701)) % 154.70/154.57 [7574]~P122(x75741)+~P1(f328(f328(f243(x75741),x75743),f2(x75741)))+P1(f328(f328(f243(x75741),f328(f328(f81(x75741),x75742),x75743)),f2(x75741)))+~P1(f328(f328(f243(x75741),f2(x75741)),x75742)) % 154.70/154.57 [7575]~P122(x75751)+~P1(f328(f328(f243(x75751),x75752),f2(x75751)))+P1(f328(f328(f243(x75751),f328(f328(f81(x75751),x75752),x75753)),f2(x75751)))+~P1(f328(f328(f243(x75751),f2(x75751)),x75753)) % 154.70/154.57 [7576]~P63(x75761)+~P1(f328(f328(f243(x75761),x75763),f2(x75761)))+P1(f328(f328(f243(x75761),f328(f328(f286(x75761),x75762),x75763)),f2(x75761)))+~P1(f328(f328(f243(x75761),f2(x75761)),x75762)) % 154.70/154.57 [7577]~P63(x75771)+~P1(f328(f328(f243(x75771),x75772),f2(x75771)))+P1(f328(f328(f243(x75771),f328(f328(f286(x75771),x75772),x75773)),f2(x75771)))+~P1(f328(f328(f243(x75771),f2(x75771)),x75773)) % 154.70/154.57 [7578]~P62(x75781)+~P1(f328(f328(f243(x75781),x75783),f2(x75781)))+P1(f328(f328(f243(x75781),f328(f328(f286(x75781),x75782),x75783)),f2(x75781)))+~P1(f328(f328(f243(x75781),f2(x75781)),x75782)) % 154.70/154.57 [7579]~P62(x75791)+~P1(f328(f328(f243(x75791),x75792),f2(x75791)))+P1(f328(f328(f243(x75791),f328(f328(f286(x75791),x75792),x75793)),f2(x75791)))+~P1(f328(f328(f243(x75791),f2(x75791)),x75793)) % 154.70/154.57 [7581]~P114(x75811)+~P1(f328(f328(f242(x75811),x75813),f2(x75811)))+P1(f328(f328(f242(x75811),f328(f328(f81(x75811),x75812),x75813)),f2(x75811)))+~P1(f328(f328(f242(x75811),f2(x75811)),x75812)) % 154.70/154.57 [7582]~P114(x75821)+~P1(f328(f328(f242(x75821),x75822),f2(x75821)))+P1(f328(f328(f242(x75821),f328(f328(f81(x75821),x75822),x75823)),f2(x75821)))+~P1(f328(f328(f242(x75821),f2(x75821)),x75823)) % 154.70/154.57 [7584]~P130(x75841)+~P1(f328(f328(f242(x75841),x75843),f2(x75841)))+P1(f328(f328(f242(x75841),f328(f328(f81(x75841),x75842),x75843)),f2(x75841)))+~P1(f328(f328(f242(x75841),f2(x75841)),x75842)) % 154.70/154.57 [7586]~P130(x75861)+~P1(f328(f328(f242(x75861),x75862),f2(x75861)))+P1(f328(f328(f242(x75861),f328(f328(f81(x75861),x75862),x75863)),f2(x75861)))+~P1(f328(f328(f242(x75861),f2(x75861)),x75863)) % 154.70/154.57 [7587]~P63(x75871)+~P1(f328(f328(f243(x75871),x75873),f2(x75871)))+P1(f328(f328(f242(x75871),f328(f328(f286(x75871),x75872),x75873)),f2(x75871)))+~P1(f328(f328(f242(x75871),f2(x75871)),x75872)) % 154.70/154.57 [7588]~P63(x75881)+~P1(f328(f328(f242(x75881),x75882),f2(x75881)))+P1(f328(f328(f242(x75881),f328(f328(f286(x75881),x75882),x75883)),f2(x75881)))+~P1(f328(f328(f243(x75881),f2(x75881)),x75883)) % 154.70/154.57 [7589]~P62(x75891)+~P1(f328(f328(f242(x75891),x75893),f2(x75891)))+P1(f328(f328(f242(x75891),f328(f328(f286(x75891),x75892),x75893)),f2(x75891)))+~P1(f328(f328(f242(x75891),f2(x75891)),x75892)) % 154.70/154.57 [7590]~P62(x75901)+~P1(f328(f328(f242(x75901),x75902),f2(x75901)))+P1(f328(f328(f242(x75901),f328(f328(f286(x75901),x75902),x75903)),f2(x75901)))+~P1(f328(f328(f242(x75901),f2(x75901)),x75903)) % 154.70/154.57 [7605]P143(x76051,x76052,x76053)+~P1(f328(x76051,x76053))+P1(f328(f328(f243(a1),x76052),f820(x76053,x76052,x76051)))+P1(f328(f328(f243(a1),f821(x76053,x76052,x76051)),x76052)) % 154.70/154.57 [7618]P144(x76181,x76182,x76183)+P1(f328(f328(f243(a1),x76182),f812(x76183,x76182,x76181)))+~P1(f328(x76181,f2(a1)))+P1(f328(f328(f243(a1),f813(x76183,x76182,x76181)),x76182)) % 154.70/154.57 [7669]P144(x76692,x76691,x76693)+E(x76691,f2(a1))+~P1(f328(x76692,f819(x76693,x76691,x76692)))+P1(f328(f328(f243(a1),f813(x76693,x76691,x76692)),x76691)) % 154.70/154.57 [7670]P143(x76702,x76701,x76703)+E(x76701,f2(a1))+~P1(f328(x76702,f820(x76703,x76701,x76702)))+P1(f328(f328(f243(a1),f821(x76703,x76701,x76702)),x76701)) % 154.70/154.57 [7681]P143(x76813,x76811,x76812)+~P1(f328(x76813,x76812))+E(f328(f328(f80(a1),f328(f328(f81(a1),x76811),f823(x76812,x76811,x76813))),f820(x76812,x76811,x76813)),x76812)+P1(f328(f328(f243(a1),f2(a1)),x76811)) % 154.70/154.57 [7698]P144(x76983,x76981,x76982)+E(f328(f328(f80(a1),f328(f328(f81(a1),x76981),f819(x76982,x76981,x76983))),f812(x76982,x76981,x76983)),x76982)+~P1(f328(x76983,f2(a1)))+P1(f328(f328(f243(a1),f2(a1)),x76981)) % 154.70/154.57 [7724]~P1(f328(x77241,x77243))+~P1(f328(f61(x77242),x77243))+P1(f328(f328(f330(x77242),f563(x77241,x77243,x77242)),f571(x77241,x77243,x77242)))+P1(f328(x77241,f192(f882(x77242,a870)))) % 154.70/154.57 [7735]P143(x77351,x77352,x77353)+~P1(f328(x77351,x77353))+~P1(f328(x77351,f820(x77353,x77352,x77351)))+P1(f328(f328(f243(a1),f821(x77353,x77352,x77351)),x77352)) % 154.70/154.57 [7741]P144(x77411,x77412,x77413)+~P1(f328(x77411,f819(x77413,x77412,x77411)))+~P1(f328(x77411,f2(a1)))+P1(f328(f328(f243(a1),f813(x77413,x77412,x77411)),x77412)) % 154.70/154.57 [7847]~P62(x78471)+~P1(f328(f328(f243(x78471),f328(f328(f286(x78471),x78473),x78472)),f2(x78471)))+P1(f328(f328(f243(x78471),x78472),f2(x78471)))+P1(f328(f328(f243(x78471),f2(x78471)),x78472)) % 154.70/154.57 [7848]~P62(x78481)+~P1(f328(f328(f243(x78481),f328(f328(f286(x78481),x78482),x78483)),f2(x78481)))+P1(f328(f328(f243(x78481),x78482),f2(x78481)))+P1(f328(f328(f243(x78481),f2(x78481)),x78482)) % 154.70/154.57 [7849]~P114(x78491)+~P1(f328(f328(f242(x78491),f328(f328(f81(x78491),x78493),x78492)),f2(x78491)))+P1(f328(f328(f242(x78491),x78492),f2(x78491)))+P1(f328(f328(f242(x78491),f2(x78491)),x78492)) % 154.70/154.57 [7850]~P114(x78501)+~P1(f328(f328(f242(x78501),f328(f328(f81(x78501),x78502),x78503)),f2(x78501)))+P1(f328(f328(f242(x78501),x78502),f2(x78501)))+P1(f328(f328(f242(x78501),f2(x78501)),x78502)) % 154.70/154.57 [7851]~P62(x78511)+~P1(f328(f328(f242(x78511),f328(f328(f286(x78511),x78513),x78512)),f2(x78511)))+P1(f328(f328(f242(x78511),x78512),f2(x78511)))+P1(f328(f328(f242(x78511),f2(x78511)),x78512)) % 154.70/154.57 [7852]~P62(x78521)+~P1(f328(f328(f242(x78521),f328(f328(f286(x78521),x78522),x78523)),f2(x78521)))+P1(f328(f328(f242(x78521),x78522),f2(x78521)))+P1(f328(f328(f242(x78521),f2(x78521)),x78522)) % 154.70/154.57 [7876]~P62(x78761)+~P1(f328(f328(f243(x78761),f328(f328(f286(x78761),x78762),x78763)),f2(x78761)))+P1(f328(f328(f243(x78761),f2(x78761)),x78762))+P1(f328(f328(f243(x78761),f2(x78761)),x78763)) % 154.70/154.57 [7877]~P114(x78771)+~P1(f328(f328(f242(x78771),f328(f328(f81(x78771),x78772),x78773)),f2(x78771)))+P1(f328(f328(f242(x78771),f2(x78771)),x78772))+P1(f328(f328(f242(x78771),f2(x78771)),x78773)) % 154.70/154.57 [7878]~P62(x78781)+~P1(f328(f328(f242(x78781),f328(f328(f286(x78781),x78782),x78783)),f2(x78781)))+P1(f328(f328(f242(x78781),f2(x78781)),x78782))+P1(f328(f328(f242(x78781),f2(x78781)),x78783)) % 154.70/154.57 [7899]P144(x78992,x78991,x78993)+E(x78991,f2(a1))+P1(f328(f328(f242(a1),f812(x78993,x78991,x78992)),f2(a1)))+P1(f328(f328(f243(a1),f813(x78993,x78991,x78992)),x78991)) % 154.70/154.57 [7900]P143(x79002,x79001,x79003)+E(x79001,f2(a1))+P1(f328(f328(f242(a1),f820(x79003,x79001,x79002)),f2(a1)))+P1(f328(f328(f243(a1),f821(x79003,x79001,x79002)),x79001)) % 154.70/154.57 [7907]~P123(x79071)+~P1(f328(f328(f243(x79071),x79072),f78(x79071)))+P1(f328(f328(f243(x79071),f328(f328(f253(x79071),x79072),f328(a116,x79073))),f78(x79071)))+~P1(f328(f328(f243(x79071),f2(x79071)),x79072)) % 154.70/154.57 [7962]~P105(x79621)+~E(x79623,f117(x79621))+~P16(x79621,f328(f166(x79621),x79623))+E(f328(f139(x79621,x79621,f328(f7(x79621,x79621,x79621),f241(x79621)),x79622),f328(f166(x79621),x79623)),x79622) % 154.70/154.57 [7964]P143(x79641,x79642,x79643)+~P1(f328(x79641,x79643))+P1(f328(f328(f242(a1),f820(x79643,x79642,x79641)),f2(a1)))+P1(f328(f328(f243(a1),f821(x79643,x79642,x79641)),x79642)) % 154.70/154.57 [7971]P144(x79711,x79712,x79713)+~P1(f328(x79711,f2(a1)))+P1(f328(f328(f242(a1),f812(x79713,x79712,x79711)),f2(a1)))+P1(f328(f328(f243(a1),f813(x79713,x79712,x79711)),x79712)) % 154.70/154.57 [8196]P144(x81963,x81961,x81962)+E(x81961,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x81961),f819(x81962,x81961,x81963))),f812(x81962,x81961,x81963)),x81962)+P1(f328(f328(f243(a1),f813(x81962,x81961,x81963)),x81961)) % 154.70/154.57 [8197]P143(x81973,x81971,x81972)+E(x81971,f2(a1))+E(f328(f328(f80(a1),f328(f328(f81(a1),x81971),f823(x81972,x81971,x81973))),f820(x81972,x81971,x81973)),x81972)+P1(f328(f328(f243(a1),f821(x81972,x81971,x81973)),x81971)) % 154.70/154.57 [8239]P143(x82393,x82391,x82392)+~P1(f328(x82393,x82392))+E(f328(f328(f80(a1),f328(f328(f81(a1),x82391),f823(x82392,x82391,x82393))),f820(x82392,x82391,x82393)),x82392)+P1(f328(f328(f243(a1),f821(x82392,x82391,x82393)),x82391)) % 154.70/154.57 [8240]~P66(x82401)+~P73(x82401)+~P40(x82403)+E(f328(f328(f6(a875,x82401),f328(f328(f8(a1,x82401,a875),x82402),f104(a1))),f328(f307(a1,a875,a108),x82403)),f328(f328(f6(a1,x82401),x82402),x82403)) % 154.70/154.57 [8241]~P66(x82411)+~P73(x82411)+~P40(x82413)+E(f328(f328(f9(a875,x82411),f328(f328(f8(a1,x82411,a875),x82412),f104(a1))),f328(f307(a1,a875,a108),x82413)),f328(f328(f9(a1,x82411),x82412),x82413)) % 154.70/154.57 [8250]P144(x82503,x82501,x82502)+E(f328(f328(f80(a1),f328(f328(f81(a1),x82501),f819(x82502,x82501,x82503))),f812(x82502,x82501,x82503)),x82502)+~P1(f328(x82503,f2(a1)))+P1(f328(f328(f243(a1),f813(x82502,x82501,x82503)),x82501)) % 154.70/154.57 [8270]~E(x82702,f2(a875))+~E(f328(f262(a875,a875),x82703),f2(a875))+~E(x82701,f328(f328(f80(a875),f328(f328(f81(a875),f328(f262(a875,a875),x82703)),x82702)),f328(f266(a875,a875),x82703)))+P1(f328(f47(x82701,x82702),x82703)) % 154.70/154.57 [8323]P1(f328(x83231,x83232))+~P1(f328(f328(f330(x83233),f828(x83231,x83232,x83233)),f824(x83231,x83232,x83233)))+~P1(f328(f61(x83233),x83232))+~P1(f328(x83231,f192(f882(x83233,a870)))) % 154.70/154.57 [8943]P1(f328(x89431,x89432))+~P1(f328(f61(x89433),x89432))+~P1(f328(x89431,f328(f328(f306(x89433),f828(x89431,x89432,x89433)),f824(x89431,x89432,x89433))))+~P1(f328(x89431,f192(f882(x89433,a870)))) % 154.70/154.57 [9179]P1(f328(f328(f242(a1),x91791),f2(a1)))+~P1(f328(f328(f243(a1),f328(f328(f80(a1),f328(f328(f81(a1),x91792),x91791)),x91793)),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x91792))+~P1(f328(f328(f242(a1),f2(a1)),x91793)) % 154.70/154.57 [5785]~P2(x57852)+E(x57851,f192(f882(x57852,a870)))+~P1(f328(f61(x57852),x57851))+E(f10(x57852,f328(f328(f306(x57852),x57853),x57851)),f328(f328(f114(x57852),x57853),f10(x57852,x57851))) % 154.70/154.57 [5786]~P2(x57862)+E(x57861,f192(f882(x57862,a870)))+~P1(f328(f61(x57862),x57861))+E(f11(x57862,f328(f328(f306(x57862),x57863),x57861)),f328(f328(f105(x57862),x57863),f11(x57862,x57861))) % 154.70/154.57 [5787]~P105(x57872)+E(x57871,f192(f882(x57872,a870)))+~P1(f328(f61(x57872),x57871))+E(f14(x57872,f328(f328(f306(x57872),x57873),x57871)),f328(f328(f240(x57872),x57873),f14(x57872,x57871))) % 154.70/154.57 [5788]~P105(x57882)+E(x57881,f192(f882(x57882,a870)))+~P1(f328(f61(x57882),x57881))+E(f15(x57882,f328(f328(f306(x57882),x57883),x57881)),f328(f328(f241(x57882),x57883),f15(x57882,x57881))) % 154.70/154.57 [6092]~P114(x60921)+~E(x60923,f2(x60921))+~E(x60922,f2(x60921))+E(f328(f328(f80(x60921),f328(f328(f81(x60921),x60922),x60922)),f328(f328(f81(x60921),x60923),x60923)),f2(x60921)) % 154.70/154.57 [6163]~P94(x61632)+E(x61631,f192(f882(x61632,a870)))+~P1(f328(f61(x61632),x61631))+E(f328(f63(x61632,f81(x61632)),f328(f328(f306(x61632),x61633),x61631)),f328(f328(f81(x61632),x61633),f328(f63(x61632,f81(x61632)),x61631))) % 154.70/154.57 [6290]~P105(x62902)+E(x62901,f192(f882(x62902,a870)))+~P1(f328(f61(x62902),x62901))+E(f12(x62902,f241(x62902),f328(f328(f306(x62902),x62903),x62901)),f328(f328(f241(x62902),x62903),f12(x62902,f241(x62902),x62901))) % 154.70/154.57 [6291]~P105(x62912)+E(x62911,f192(f882(x62912,a870)))+~P1(f328(f61(x62912),x62911))+E(f13(x62912,f240(x62912),f328(f328(f306(x62912),x62913),x62911)),f328(f328(f240(x62912),x62913),f13(x62912,f240(x62912),x62911))) % 154.70/154.57 [6793]~P70(x67931)+~P1(f328(f61(x67931),x67933))+E(f328(f63(x67931,f81(x67931)),f328(f328(f306(x67931),x67932),x67933)),f328(f328(f64(x67931,x67931,f81(x67931)),x67932),x67933))+P1(f328(f328(f330(x67931),x67932),x67933)) % 154.70/154.57 [6875]~E(f328(f328(f80(a1),x68752),f328(f328(f81(a1),x68753),x68751)),x68753)+~P1(f328(f328(f243(a1),f2(a1)),x68753))+P1(f328(f328(f242(a1),f78(a1)),x68751))+~P1(f328(f328(f243(a1),x68752),x68753)) % 154.70/154.57 [6902]~E(f328(f328(f80(a1),x69022),f328(f328(f81(a1),x69023),x69021)),x69023)+P1(f328(f328(f242(a1),x69021),f78(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x69023))+~P1(f328(f328(f242(a1),f2(a1)),x69022)) % 154.70/154.57 [6918]E(x69181,f2(a875))+~P1(f328(f47(x69183,x69181),x69182))+~P1(f328(f328(f243(a875),f2(a875)),x69181))+P1(f328(f328(f243(a875),f328(f266(a875,a875),x69182)),x69181)) % 154.70/154.57 [6948]~P133(x69481)+~P1(f328(f328(f242(x69481),x69482),f2(x69481)))+~P1(f328(f328(f242(x69481),x69483),f2(x69481)))+E(f328(f328(f81(x69481),f328(f75(x69481),x69482)),f328(f75(x69481),x69483)),f328(f75(x69481),f328(f328(f81(x69481),x69482),x69483))) % 154.70/154.57 [6998]~P133(x69981)+~P1(f328(f328(f242(x69981),x69982),f2(x69981)))+E(f328(f328(f81(x69981),f328(f75(x69981),x69982)),f328(f75(x69981),x69983)),f328(f75(x69981),f328(f328(f81(x69981),x69982),x69983)))+~P1(f328(f328(f242(x69981),f2(x69981)),x69983)) % 154.70/154.57 [6999]~P133(x69991)+~P1(f328(f328(f242(x69991),x69993),f2(x69991)))+E(f328(f328(f81(x69991),f328(f75(x69991),x69992)),f328(f75(x69991),x69993)),f328(f75(x69991),f328(f328(f81(x69991),x69992),x69993)))+~P1(f328(f328(f242(x69991),f2(x69991)),x69992)) % 154.70/154.57 [7053]~P133(x70531)+E(f328(f328(f81(x70531),f328(f75(x70531),x70532)),f328(f75(x70531),x70533)),f328(f75(x70531),f328(f328(f81(x70531),x70532),x70533)))+~P1(f328(f328(f242(x70531),f2(x70531)),x70532))+~P1(f328(f328(f242(x70531),f2(x70531)),x70533)) % 154.70/154.57 [7069]~P114(x70691)+~P1(f328(f328(f243(x70691),x70693),f2(x70691)))+~P1(f328(f328(f243(x70691),x70692),f2(x70691)))+P1(f328(f328(f243(x70691),f2(x70691)),f328(f328(f81(x70691),x70692),x70693))) % 154.70/154.57 [7070]~P63(x70701)+~P1(f328(f328(f243(x70701),x70703),f2(x70701)))+~P1(f328(f328(f243(x70701),x70702),f2(x70701)))+P1(f328(f328(f243(x70701),f2(x70701)),f328(f328(f286(x70701),x70702),x70703))) % 154.70/154.57 [7071]~P62(x70711)+~P1(f328(f328(f243(x70711),x70713),f2(x70711)))+~P1(f328(f328(f243(x70711),x70712),f2(x70711)))+P1(f328(f328(f243(x70711),f2(x70711)),f328(f328(f286(x70711),x70712),x70713))) % 154.70/154.57 [7072]~P114(x70721)+~P1(f328(f328(f242(x70721),x70723),f2(x70721)))+~P1(f328(f328(f242(x70721),x70722),f2(x70721)))+P1(f328(f328(f242(x70721),f2(x70721)),f328(f328(f81(x70721),x70722),x70723))) % 154.70/154.57 [7074]~P127(x70741)+~P1(f328(f328(f242(x70741),x70743),f2(x70741)))+~P1(f328(f328(f242(x70741),x70742),f2(x70741)))+P1(f328(f328(f242(x70741),f2(x70741)),f328(f328(f81(x70741),x70742),x70743))) % 154.70/154.57 [7075]~P63(x70751)+~P1(f328(f328(f243(x70751),x70753),f2(x70751)))+~P1(f328(f328(f242(x70751),x70752),f2(x70751)))+P1(f328(f328(f242(x70751),f2(x70751)),f328(f328(f286(x70751),x70752),x70753))) % 154.70/154.57 [7076]~P62(x70761)+~P1(f328(f328(f242(x70761),x70763),f2(x70761)))+~P1(f328(f328(f242(x70761),x70762),f2(x70761)))+P1(f328(f328(f242(x70761),f2(x70761)),f328(f328(f286(x70761),x70762),x70763))) % 154.70/154.57 [7077]~P123(x70771)+~P1(f328(f328(f243(a875),f2(a875)),x70773))+~P1(f328(f328(f243(x70771),f78(x70771)),x70772))+P1(f328(f328(f243(x70771),f78(x70771)),f328(f328(f253(x70771),x70772),x70773))) % 154.70/154.57 [7175]~P85(x71751)+~P1(f328(f328(f243(x71751),f2(x71751)),x71753))+~P1(f328(f328(f243(x71751),f2(x71751)),x71752))+P1(f328(f328(f243(x71751),f2(x71751)),f328(f328(f80(x71751),x71752),x71753))) % 154.70/154.57 [7178]~P122(x71781)+~P1(f328(f328(f243(x71781),f2(x71781)),x71783))+~P1(f328(f328(f243(x71781),f2(x71781)),x71782))+P1(f328(f328(f243(x71781),f2(x71781)),f328(f328(f81(x71781),x71782),x71783))) % 154.70/154.57 [7179]~P63(x71791)+~P1(f328(f328(f243(x71791),f2(x71791)),x71793))+~P1(f328(f328(f243(x71791),f2(x71791)),x71792))+P1(f328(f328(f243(x71791),f2(x71791)),f328(f328(f286(x71791),x71792),x71793))) % 154.70/154.57 [7180]~P62(x71801)+~P1(f328(f328(f243(x71801),f2(x71801)),x71803))+~P1(f328(f328(f243(x71801),f2(x71801)),x71802))+P1(f328(f328(f243(x71801),f2(x71801)),f328(f328(f286(x71801),x71802),x71803))) % 154.70/154.57 [7181]~P123(x71811)+~P1(f328(f328(f243(x71811),f78(x71811)),x71813))+~P1(f328(f328(f243(x71811),f78(x71811)),x71812))+P1(f328(f328(f243(x71811),f78(x71811)),f328(f328(f81(x71811),x71812),x71813))) % 154.70/154.57 [7183]~P114(x71831)+~P1(f328(f328(f242(x71831),f2(x71831)),x71833))+~P1(f328(f328(f242(x71831),f2(x71831)),x71832))+P1(f328(f328(f242(x71831),f2(x71831)),f328(f328(f81(x71831),x71832),x71833))) % 154.70/154.57 [7184]~P127(x71841)+~P1(f328(f328(f242(x71841),f2(x71841)),x71843))+~P1(f328(f328(f242(x71841),f2(x71841)),x71842))+P1(f328(f328(f242(x71841),f2(x71841)),f328(f328(f81(x71841),x71842),x71843))) % 154.70/154.57 [7185]~P130(x71851)+~P1(f328(f328(f242(x71851),f2(x71851)),x71853))+~P1(f328(f328(f242(x71851),f2(x71851)),x71852))+P1(f328(f328(f242(x71851),f2(x71851)),f328(f328(f81(x71851),x71852),x71853))) % 154.70/154.57 [7186]~P63(x71861)+~P1(f328(f328(f243(x71861),f2(x71861)),x71863))+~P1(f328(f328(f242(x71861),f2(x71861)),x71862))+P1(f328(f328(f242(x71861),f2(x71861)),f328(f328(f286(x71861),x71862),x71863))) % 154.70/154.57 [7187]~P62(x71871)+~P1(f328(f328(f242(x71871),f2(x71871)),x71873))+~P1(f328(f328(f242(x71871),f2(x71871)),x71872))+P1(f328(f328(f242(x71871),f2(x71871)),f328(f328(f286(x71871),x71872),x71873))) % 154.70/154.57 [7258]~P2(x72581)+~P1(f328(f61(x72581),x72583))+E(f10(x72581,f328(f328(f306(x72581),x72582),x72583)),x72582)+~E(f328(f328(f22(f882(x72581,a870)),x72583),f328(f328(f306(x72581),x72582),f192(f882(x72581,a870)))),f192(f882(x72581,a870))) % 154.70/154.57 [7259]~P2(x72591)+~P1(f328(f61(x72591),x72593))+E(f11(x72591,f328(f328(f306(x72591),x72592),x72593)),x72592)+~E(f328(f328(f22(f882(x72591,a870)),x72593),f328(f328(f306(x72591),x72592),f192(f882(x72591,a870)))),f192(f882(x72591,a870))) % 154.70/154.57 [7260]~P105(x72601)+~P1(f328(f61(x72601),x72603))+E(f14(x72601,f328(f328(f306(x72601),x72602),x72603)),x72602)+~E(f328(f328(f22(f882(x72601,a870)),x72603),f328(f328(f306(x72601),x72602),f192(f882(x72601,a870)))),f192(f882(x72601,a870))) % 154.70/154.57 [7261]~P105(x72611)+~P1(f328(f61(x72611),x72613))+E(f15(x72611,f328(f328(f306(x72611),x72612),x72613)),x72612)+~E(f328(f328(f22(f882(x72611,a870)),x72613),f328(f328(f306(x72611),x72612),f192(f882(x72611,a870)))),f192(f882(x72611,a870))) % 154.70/154.57 [7262]~P62(x72621)+P1(f328(f328(f243(x72621),x72622),f2(x72621)))+P1(f328(f328(f243(x72621),f2(x72621)),x72623))+~P1(f328(f328(f243(x72621),f2(x72621)),f328(f328(f286(x72621),x72623),x72622))) % 154.70/154.57 [7263]~P62(x72631)+P1(f328(f328(f243(x72631),x72632),f2(x72631)))+P1(f328(f328(f243(x72631),f2(x72631)),x72633))+~P1(f328(f328(f243(x72631),f2(x72631)),f328(f328(f286(x72631),x72632),x72633))) % 154.70/154.57 [7264]~P62(x72641)+P1(f328(f328(f243(x72641),x72642),f2(x72641)))+P1(f328(f328(f243(x72641),f2(x72641)),x72642))+~P1(f328(f328(f243(x72641),f2(x72641)),f328(f328(f286(x72641),x72643),x72642))) % 154.70/154.57 [7265]~P62(x72651)+P1(f328(f328(f243(x72651),x72652),f2(x72651)))+P1(f328(f328(f243(x72651),f2(x72651)),x72652))+~P1(f328(f328(f243(x72651),f2(x72651)),f328(f328(f286(x72651),x72652),x72653))) % 154.70/154.57 [7266]~P114(x72661)+P1(f328(f328(f242(x72661),x72662),f2(x72661)))+P1(f328(f328(f242(x72661),f2(x72661)),x72663))+~P1(f328(f328(f242(x72661),f2(x72661)),f328(f328(f81(x72661),x72663),x72662))) % 154.70/154.57 [7267]~P114(x72671)+P1(f328(f328(f242(x72671),x72672),f2(x72671)))+P1(f328(f328(f242(x72671),f2(x72671)),x72673))+~P1(f328(f328(f242(x72671),f2(x72671)),f328(f328(f81(x72671),x72672),x72673))) % 154.70/154.57 [7268]~P62(x72681)+P1(f328(f328(f242(x72681),x72682),f2(x72681)))+P1(f328(f328(f242(x72681),f2(x72681)),x72683))+~P1(f328(f328(f242(x72681),f2(x72681)),f328(f328(f286(x72681),x72683),x72682))) % 154.70/154.57 [7269]~P62(x72691)+P1(f328(f328(f242(x72691),x72692),f2(x72691)))+P1(f328(f328(f242(x72691),f2(x72691)),x72693))+~P1(f328(f328(f242(x72691),f2(x72691)),f328(f328(f286(x72691),x72692),x72693))) % 154.70/154.57 [7270]~P114(x72701)+P1(f328(f328(f242(x72701),x72702),f2(x72701)))+P1(f328(f328(f242(x72701),f2(x72701)),x72702))+~P1(f328(f328(f242(x72701),f2(x72701)),f328(f328(f81(x72701),x72703),x72702))) % 154.70/154.57 [7271]~P114(x72711)+P1(f328(f328(f242(x72711),x72712),f2(x72711)))+P1(f328(f328(f242(x72711),f2(x72711)),x72712))+~P1(f328(f328(f242(x72711),f2(x72711)),f328(f328(f81(x72711),x72712),x72713))) % 154.70/154.57 [7272]~P62(x72721)+P1(f328(f328(f242(x72721),x72722),f2(x72721)))+P1(f328(f328(f242(x72721),f2(x72721)),x72722))+~P1(f328(f328(f242(x72721),f2(x72721)),f328(f328(f286(x72721),x72723),x72722))) % 154.70/154.57 [7273]~P62(x72731)+P1(f328(f328(f242(x72731),x72732),f2(x72731)))+P1(f328(f328(f242(x72731),f2(x72731)),x72732))+~P1(f328(f328(f242(x72731),f2(x72731)),f328(f328(f286(x72731),x72732),x72733))) % 154.70/154.57 [7363]~E(f328(f328(f105(f882(x73631,a870)),f328(f170(x73631),x73632)),f328(f170(x73631),x73633)),f192(f882(x73631,a870)))+~P1(f328(f134(x73631),x73633))+~P1(f328(f134(x73631),x73632))+P1(f328(f134(x73631),f328(f328(f125(x73631),x73632),x73633))) % 154.70/154.57 [7364]~P105(x73641)+~P1(f328(f61(x73641),x73643))+E(f12(x73641,f241(x73641),f328(f328(f306(x73641),x73642),x73643)),x73642)+~E(f328(f328(f22(f882(x73641,a870)),x73643),f328(f328(f306(x73641),x73642),f192(f882(x73641,a870)))),f192(f882(x73641,a870))) % 154.70/154.57 [7365]~P105(x73651)+~P1(f328(f61(x73651),x73653))+E(f13(x73651,f240(x73651),f328(f328(f306(x73651),x73652),x73653)),x73652)+~E(f328(f328(f22(f882(x73651,a870)),x73653),f328(f328(f306(x73651),x73652),f192(f882(x73651,a870)))),f192(f882(x73651,a870))) % 154.70/154.57 [7380]~P121(x73801)+~P1(f328(f328(f243(x73801),x73802),x73803))+~P1(f328(f328(f243(x73801),f328(f79(x73801),x73802)),x73803))+P1(f328(f328(f243(x73801),f328(f75(x73801),x73802)),x73803)) % 154.70/154.57 [7382]~P83(x73821)+~P1(f328(f328(f242(x73821),x73822),x73823))+~P1(f328(f328(f242(x73821),f328(f79(x73821),x73822)),x73823))+P1(f328(f328(f242(x73821),f328(f75(x73821),x73822)),x73823)) % 154.70/154.57 [7452]~P122(x74521)+P1(f328(f328(f243(x74521),f2(x74521)),x74522))+~P1(f328(f328(f243(x74521),f2(x74521)),x74523))+~P1(f328(f328(f243(x74521),f2(x74521)),f328(f328(f81(x74521),x74523),x74522))) % 154.70/154.57 [7453]~P122(x74531)+P1(f328(f328(f243(x74531),f2(x74531)),x74532))+~P1(f328(f328(f243(x74531),f2(x74531)),x74533))+~P1(f328(f328(f243(x74531),f2(x74531)),f328(f328(f81(x74531),x74532),x74533))) % 154.70/154.57 [7757]E(x77571,x77572)+~P1(f328(f61(x77573),x77571))+~P1(f328(f328(f242(a875),f328(f37(x77573),x77571)),f328(f37(x77573),x77572)))+~P1(f328(f328(f242(f882(x77573,a870)),x77572),x77571)) % 154.70/154.57 [7903]~P1(f328(f328(f243(a1),x79031),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x79032))+~P1(f328(f328(f242(a1),x79032),x79033))+P1(f328(f328(f242(a1),f328(f328(f38(a1),x79031),x79032)),f328(f328(f38(a1),x79031),x79033))) % 154.70/154.57 [7915]~P1(f328(f328(f243(a1),f2(a1)),x79153))+~P1(f328(f328(f242(a1),f2(a1)),x79151))+~P1(f328(f328(f242(a1),x79153),x79152))+P1(f328(f328(f242(a1),f328(f328(f38(a1),x79151),x79152)),f328(f328(f38(a1),x79151),x79153))) % 154.70/154.57 [8047]E(f328(x80471,f448(x80472,x80471,x80473)),x80472)+~P1(f328(f328(f242(a1),x80472),f328(x80471,x80473)))+P1(f328(f328(f243(a875),f440(x80472,x80471,x80473)),x80473))+~P1(f328(f328(f242(a1),f328(x80471,f2(a875))),x80472)) % 154.70/154.57 [8048]E(f328(x80481,f449(x80482,x80481,x80483)),x80482)+~P1(f328(f328(f242(a1),x80482),f328(x80481,x80483)))+P1(f328(f328(f243(a875),f450(x80482,x80481,x80483)),x80483))+~P1(f328(f328(f242(a1),f328(x80481,f2(a875))),x80482)) % 154.70/154.57 [8153]~P1(f328(f61(x81531),x81533))+~P1(f328(f328(f243(a875),f328(f37(x81531),x81532)),f328(f37(x81531),x81533)))+~P1(f328(f328(f242(f882(x81531,a870)),x81532),x81533))+P1(f328(f328(f243(f882(x81531,a870)),x81532),x81533)) % 154.70/154.57 [8185]E(f328(f328(f80(a1),f394(x81853,x81851,x81852)),f395(x81853,x81851,x81852)),x81851)+E(f328(f328(f22(a1),x81851),x81852),x81851)+~P1(f328(f328(f243(a1),f2(a1)),x81852))+~P1(f328(f328(f330(a1),f328(f328(f22(a1),x81851),f78(a1))),x81853)) % 154.70/154.57 [8186]E(f328(f328(f22(a1),f405(x81863,x81861,x81862)),f406(x81863,x81861,x81862)),x81861)+E(f328(f328(f80(a1),x81861),x81862),x81861)+~P1(f328(f328(f243(a1),f2(a1)),x81862))+~P1(f328(f328(f330(a1),f328(f328(f80(a1),x81861),f78(a1))),x81863)) % 154.70/154.57 [8245]~P1(f328(f328(f242(a875),x82453),x82451))+P1(f328(f328(f243(a875),x82451),x82452))+~P1(f328(f328(f242(a875),x82453),x82452))+~P1(f328(f328(f243(a875),f328(f328(f22(a875),x82451),x82453)),f328(f328(f22(a875),x82452),x82453))) % 154.70/154.57 [8246]~P1(f328(f328(f242(a875),x82463),x82461))+P1(f328(f328(f242(a875),x82461),x82462))+~P1(f328(f328(f242(a875),x82463),x82462))+~P1(f328(f328(f242(a875),f328(f328(f22(a875),x82461),x82463)),f328(f328(f22(a875),x82462),x82463))) % 154.70/154.57 [8262]~P105(x82622)+E(x82621,f117(x82622))+~P16(x82622,f328(f166(x82622),x82621))+E(f328(f139(x82622,x82622,f328(f7(x82622,x82622,x82622),f241(x82622)),x82623),f328(f166(x82622),x82621)),f328(f328(f241(x82622),f328(f328(f162(x82622),x82621),f2(a875))),x82623)) % 154.70/154.57 [8328]E(f328(f328(f22(a1),x83281),x83282),x83281)+~P1(f328(f328(f243(a1),f2(a1)),x83282))+P1(f328(f328(f330(a1),f394(x83283,x83281,x83282)),x83283))+~P1(f328(f328(f330(a1),f328(f328(f22(a1),x83281),f78(a1))),x83283)) % 154.70/154.57 [8329]E(f328(f328(f80(a1),x83291),x83292),x83291)+~P1(f328(f328(f243(a1),f2(a1)),x83292))+P1(f328(f328(f330(a1),f405(x83293,x83291,x83292)),x83293))+~P1(f328(f328(f330(a1),f328(f328(f80(a1),x83291),f78(a1))),x83293)) % 154.70/154.57 [8404]~P1(f328(f328(f242(a1),x84041),f328(x84042,x84043)))+P1(f328(f328(f242(a875),f448(x84041,x84042,x84043)),x84043))+P1(f328(f328(f243(a875),f440(x84041,x84042,x84043)),x84043))+~P1(f328(f328(f242(a1),f328(x84042,f2(a875))),x84041)) % 154.70/154.57 [8405]~P1(f328(f328(f242(a1),x84051),f328(x84052,x84053)))+P1(f328(f328(f242(a875),f449(x84051,x84052,x84053)),x84053))+P1(f328(f328(f243(a875),f450(x84051,x84052,x84053)),x84053))+~P1(f328(f328(f242(a1),f328(x84052,f2(a875))),x84051)) % 154.70/154.57 [8478]E(f328(f328(f22(a1),x84781),x84782),x84781)+~P1(f328(f328(f243(a1),f2(a1)),x84782))+P1(f328(f328(f330(a1),f395(x84783,x84781,x84782)),f299(a1,f78(a1),x84782)))+~P1(f328(f328(f330(a1),f328(f328(f22(a1),x84781),f78(a1))),x84783)) % 154.70/154.57 [8479]E(f328(f328(f80(a1),x84791),x84792),x84791)+~P1(f328(f328(f243(a1),f2(a1)),x84792))+P1(f328(f328(f330(a1),f406(x84793,x84791,x84792)),f299(a1,f78(a1),x84792)))+~P1(f328(f328(f330(a1),f328(f328(f80(a1),x84791),f78(a1))),x84793)) % 154.70/154.57 [8615]~P123(x86151)+~P1(f328(f328(f243(x86151),x86152),f78(x86151)))+~P1(f328(f328(f243(x86151),f2(x86151)),x86152))+P1(f328(f328(f243(x86151),f328(f328(f81(x86151),x86152),f328(f328(f253(x86151),x86152),x86153))),f328(f328(f253(x86151),x86152),x86153))) % 154.70/154.57 [8701]~P1(f328(x87011,x87012))+P1(f328(x87011,f2(a875)))+~P1(f328(f328(f243(a875),x87012),x87013))+~P1(f328(x87011,f44(a875,f328(a116,f515(x87012,x87011,x87013)),x87013))) % 154.70/154.57 [8839]E(f543(x88391,x88392,x88393),f2(a875))+P1(f328(f328(x88391,x88393),x88392))+P1(f328(f328(x88391,f543(x88391,x88392,x88393)),f44(a875,f542(x88391,x88392,x88393),f543(x88391,x88392,x88393))))+~P1(f328(f316(f881(a875,a875),a226),f328(f328(f263(a875,a875),x88393),x88392))) % 154.70/154.57 [8877]~P27(x88771,x88771,x88772,x88773)+E(f328(f307(x88771,x88771,x88772),x88773),x88773)+~P1(f328(f61(x88771),x88773))+~P1(f328(f328(f242(f882(x88771,a870)),f328(f307(x88771,x88771,x88772),x88773)),x88773)) % 154.70/154.57 [9120]P1(f328(f328(x91201,x91202),x91203))+~P1(f328(f328(f243(a1),f541(x91201,x91203,x91202)),f2(a1)))+P1(f328(f328(x91201,f328(f79(a1),f540(x91201,x91203,x91202))),f328(f79(a1),f541(x91201,x91203,x91202))))+~P1(f328(f316(f881(a1,a1),a231),f328(f328(f263(a1,a1),x91202),x91203))) % 154.70/154.57 [9307]P1(f328(f328(x93071,x93072),x93073))+P1(f328(f328(x93071,f328(f328(f80(a1),f692(x93071,x93073,x93072)),f78(a1))),f694(x93071,x93073,x93072)))+~P1(f328(f328(f242(a1),f692(x93071,x93073,x93072)),f694(x93071,x93073,x93072)))+~P1(f328(f316(f881(a1,a1),a181),f328(f328(f263(a1,a1),x93072),x93073))) % 154.70/154.57 [9733]~P59(x97332)+~P59(x97331)+~P1(f328(f58(f881(x97331,x97332)),x97333))+P1(f328(f58(x97331),f328(f328(f8(f882(x97332,a870),a870,x97331),f58(x97332)),f328(f328(f8(f882(x97332,f881(x97331,x97332)),f882(x97332,a870),x97331),f328(f8(f881(x97331,x97332),a870,x97332),x97333)),f263(x97331,x97332))))) % 154.70/154.57 [9734]~P59(x97342)+~P59(x97341)+~P1(f328(f57(f881(x97341,x97342)),x97343))+P1(f328(f57(x97341),f328(f328(f8(f882(x97342,a870),a870,x97341),f57(x97342)),f328(f328(f8(f882(x97342,f881(x97341,x97342)),f882(x97342,a870),x97341),f328(f8(f881(x97341,x97342),a870,x97342),x97343)),f263(x97341,x97342))))) % 154.70/154.57 [9836]~P59(x98362)+~P59(x98361)+P1(f328(f58(f881(x98361,x98362)),x98363))+~P1(f328(f58(x98361),f328(f328(f8(f882(x98362,a870),a870,x98361),f58(x98362)),f328(f328(f8(f882(x98362,f881(x98361,x98362)),f882(x98362,a870),x98361),f328(f8(f881(x98361,x98362),a870,x98362),x98363)),f263(x98361,x98362))))) % 154.70/154.57 [9837]~P59(x98372)+~P59(x98371)+P1(f328(f57(f881(x98371,x98372)),x98373))+~P1(f328(f57(x98371),f328(f328(f8(f882(x98372,a870),a870,x98371),f57(x98372)),f328(f328(f8(f882(x98372,f881(x98371,x98372)),f882(x98372,a870),x98371),f328(f8(f881(x98371,x98372),a870,x98372),x98373)),f263(x98371,x98372))))) % 154.70/154.57 [10006]E(f328(x100061,f448(x100062,x100061,x100063)),x100062)+~P1(f328(f328(f242(a1),x100062),f328(x100061,x100063)))+~P1(f328(f328(f242(a1),f328(f75(a1),f328(f328(f22(a1),f328(x100061,f328(f328(f80(a875),f440(x100062,x100061,x100063)),f78(a875)))),f328(x100061,f440(x100062,x100061,x100063))))),f78(a1)))+~P1(f328(f328(f242(a1),f328(x100061,f2(a875))),x100062)) % 154.70/154.57 [10007]E(f328(x100071,f449(x100072,x100071,x100073)),x100072)+~P1(f328(f328(f242(a1),x100072),f328(x100071,x100073)))+~P1(f328(f328(f242(a1),f328(f75(a1),f328(f328(f22(a1),f328(x100071,f328(f328(f80(a875),f450(x100072,x100071,x100073)),f78(a875)))),f328(x100071,f450(x100072,x100071,x100073))))),f78(a1)))+~P1(f328(f328(f242(a1),f328(x100071,f2(a875))),x100072)) % 154.70/154.57 [10011]~P1(f328(f328(f242(a1),x100111),f328(x100112,x100113)))+~P1(f328(f328(f242(a1),f328(f75(a1),f328(f328(f22(a1),f328(x100112,f328(f328(f80(a875),f440(x100111,x100112,x100113)),f78(a875)))),f328(x100112,f440(x100111,x100112,x100113))))),f78(a1)))+P1(f328(f328(f242(a875),f448(x100111,x100112,x100113)),x100113))+~P1(f328(f328(f242(a1),f328(x100112,f2(a875))),x100111)) % 154.70/154.57 [10012]~P1(f328(f328(f242(a1),x100121),f328(x100122,x100123)))+~P1(f328(f328(f242(a1),f328(f75(a1),f328(f328(f22(a1),f328(x100122,f328(f328(f80(a875),f450(x100121,x100122,x100123)),f78(a875)))),f328(x100122,f450(x100121,x100122,x100123))))),f78(a1)))+P1(f328(f328(f242(a875),f449(x100121,x100122,x100123)),x100123))+~P1(f328(f328(f242(a1),f328(x100122,f2(a875))),x100121)) % 154.70/154.57 [10067]E(x100671,x100672)+~E(f328(f139(f876(x100673),f876(x100673),f125(x100673),f117(x100673)),x100671),f328(f139(f876(x100673),f876(x100673),f125(x100673),f117(x100673)),x100672))+~E(f328(f193(f876(f876(x100673))),x100671),f328(f193(f876(f876(x100673))),x100672))+~P1(f328(f328(f267(f876(x100673),f876(x100673),a870),f328(f328(f7(f876(x100673),f882(f876(x100673),a875),f882(f876(x100673),a870)),f328(f328(f8(f882(a875,a870),f882(f882(f876(x100673),a875),f882(f876(x100673),a870)),f876(x100673)),f8(a875,a870,f876(x100673))),f328(f328(f8(a875,f882(a875,a870),f876(x100673)),a325),f193(f876(x100673))))),f193(f876(x100673)))),f741(x100672,x100671,x100673))) % 154.70/154.57 [10068]E(x100681,x100682)+~E(f328(f139(f876(x100683),f876(x100683),f125(x100683),f117(x100683)),x100681),f328(f139(f876(x100683),f876(x100683),f125(x100683),f117(x100683)),x100682))+~E(f328(f193(f876(f876(x100683))),x100681),f328(f193(f876(f876(x100683))),x100682))+~P1(f328(f328(f267(f876(x100683),f876(x100683),a870),f328(f328(f7(f876(x100683),f882(f876(x100683),a875),f882(f876(x100683),a870)),f328(f328(f8(f882(a875,a870),f882(f882(f876(x100683),a875),f882(f876(x100683),a870)),f876(x100683)),f8(a875,a870,f876(x100683))),f328(f328(f8(a875,f882(a875,a870),f876(x100683)),a325),f193(f876(x100683))))),f193(f876(x100683)))),f742(x100681,x100682,x100683))) % 154.70/154.57 [6780]~E(f78(a875),f2(a875))+~P1(f328(f61(x67801),x67803))+~P1(f328(f61(x67801),x67802))+E(f328(f328(f80(a875),f328(f37(x67801),x67802)),f328(f37(x67801),x67803)),f328(f37(x67801),f328(f328(f114(f882(x67801,a870)),x67802),x67803))) % 154.70/154.57 [7194]~P100(x71941)+~P1(f328(f61(x71941),x71942))+~P1(f328(f328(f330(x71941),x71943),x71942))+P1(f328(f328(f242(x71941),f328(f63(x71941,f105(x71941)),x71942)),x71943)) % 154.70/154.57 [7195]~P105(x71951)+~P1(f328(f61(x71951),x71952))+~P1(f328(f328(f330(x71951),x71953),x71952))+P1(f328(f328(f242(x71951),f328(f63(x71951,f240(x71951)),x71952)),x71953)) % 154.70/154.57 [7446]~P1(f328(f61(x74461),x74463))+~P1(f328(f61(x74461),x74462))+~E(f328(f328(f105(f882(x74461,a870)),x74462),x74463),f192(f882(x74461,a870)))+E(f328(f328(f80(a875),f328(f37(x74461),x74462)),f328(f37(x74461),x74463)),f328(f37(x74461),f328(f328(f114(f882(x74461,a870)),x74462),x74463))) % 154.70/154.57 [8251]~P39(x82511,x82513)+~P39(x82511,x82512)+~E(f328(f328(f105(f882(x82511,a870)),f328(f261(x82511,x82511),x82512)),f328(f259(x82511,x82511),x82513)),f192(f882(x82511,a870)))+P39(x82511,f328(f328(f114(f882(f881(x82511,x82511),a870)),x82512),x82513)) % 154.70/154.57 [8343]E(x83431,f328(f328(f38(a875),x83432),x83433))+~P1(f328(f328(f243(a875),f2(a875)),x83433))+~P1(f328(f328(f243(a875),x83432),f328(f328(f81(a875),x83433),f328(a116,x83431))))+~P1(f328(f328(f242(a875),f328(f328(f81(a875),x83433),x83431)),x83432)) % 154.70/154.57 [8476]~P1(f328(f61(x84761),x84762))+~P1(f328(f61(x84761),x84763))+E(f328(f328(f80(a875),f328(f37(x84761),x84762)),f328(f37(x84761),x84763)),f328(f37(x84761),f328(f328(f114(f882(x84761,a870)),x84762),x84763)))+P1(f328(f328(f330(x84761),f843(x84763,x84762,x84761)),f328(f328(f105(f882(x84761,a870)),x84762),x84763))) % 154.70/154.57 [8851]~P114(x88512)+~E(x88511,f2(x88512))+~E(x88513,f2(x88512))+~P1(f328(f328(f243(x88512),f2(x88512)),f328(f328(f80(x88512),f328(f328(f81(x88512),x88513),x88513)),f328(f328(f81(x88512),x88511),x88511)))) % 154.70/154.57 [9386]~P39(x93861,x93863)+~P39(x93861,x93862)+P39(x93861,f328(f328(f114(f882(f881(x93861,x93861),a870)),x93862),x93863))+~P1(f328(f328(f242(f882(f881(x93861,x93861),a870)),f328(f328(f285(x93861,x93861,x93861),x93862),x93863)),x93862)) % 154.70/154.57 [9512]~P1(f328(x95121,x95123))+~P1(f328(f61(x95122),x95123))+P1(f328(x95121,f192(f882(x95122,a870))))+~P1(f328(x95121,f328(f328(f22(f882(x95122,a870)),f571(x95121,x95123,x95122)),f328(f328(f306(x95122),f563(x95121,x95123,x95122)),f192(f882(x95122,a870)))))) % 154.70/154.57 [9763]~P59(x97631)+~P59(x97632)+P13(x97631,f328(f328(f8(f882(x97632,x97631),a870,f876(x97631)),x97633),f328(f328(f8(f882(x97632,f879(x97631)),f882(x97632,x97631),f876(x97631)),f73(f879(x97631),x97631,x97632,f239(x97631))),f328(f328(f8(f876(f881(x97632,x97631)),f882(x97632,f879(x97631)),f876(x97631)),f176(x97632,x97631)),f328(f180(x97632,x97631),f55(x97632))))),f328(f193(f876(x97632)),f55(x97632)))+~P1(f328(f58(f882(x97632,x97631)),x97633)) % 154.70/154.57 [9764]~P59(x97641)+~P59(x97642)+P12(x97641,f328(f328(f8(f882(x97642,x97641),a870,f876(x97641)),x97643),f328(f328(f8(f882(x97642,f879(x97641)),f882(x97642,x97641),f876(x97641)),f73(f879(x97641),x97641,x97642,f239(x97641))),f328(f328(f8(f876(f881(x97642,x97641)),f882(x97642,f879(x97641)),f876(x97641)),f176(x97642,x97641)),f328(f180(x97642,x97641),f55(x97642))))),f328(f193(f876(x97642)),f55(x97642)))+~P1(f328(f57(f882(x97642,x97641)),x97643)) % 154.70/154.57 [9860]~P59(x98601)+~P59(x98602)+~P13(x98602,f328(f328(f8(f882(x98601,x98602),a870,f876(x98602)),x98603),f328(f328(f8(f882(x98601,f879(x98602)),f882(x98601,x98602),f876(x98602)),f73(f879(x98602),x98602,x98601,f239(x98602))),f328(f328(f8(f876(f881(x98601,x98602)),f882(x98601,f879(x98602)),f876(x98602)),f176(x98601,x98602)),f328(f180(x98601,x98602),f55(x98601))))),f328(f193(f876(x98601)),f55(x98601)))+P1(f328(f58(f882(x98601,x98602)),x98603)) % 154.70/154.57 [9861]~P59(x98611)+~P59(x98612)+~P12(x98612,f328(f328(f8(f882(x98611,x98612),a870,f876(x98612)),x98613),f328(f328(f8(f882(x98611,f879(x98612)),f882(x98611,x98612),f876(x98612)),f73(f879(x98612),x98612,x98611,f239(x98612))),f328(f328(f8(f876(f881(x98611,x98612)),f882(x98611,f879(x98612)),f876(x98612)),f176(x98611,x98612)),f328(f180(x98611,x98612),f55(x98611))))),f328(f193(f876(x98611)),f55(x98611)))+P1(f328(f57(f882(x98611,x98612)),x98613)) % 154.70/154.57 [8653]~P1(f328(f328(f243(a1),f2(a1)),x86533))+P1(f328(f328(f242(a1),f2(a1)),x86531))+~P1(f328(f328(f243(a1),x86532),x86533))+~P1(f328(f328(f242(a1),f2(a1)),f328(f328(f80(a1),f328(f328(f81(a1),x86533),x86531)),x86532))) % 154.70/154.57 [8675]~P2(x86751)+~P1(f328(f61(x86751),x86752))+E(f328(f328(f22(f882(x86751,a870)),x86752),f328(f328(f306(x86751),x86753),f192(f882(x86751,a870)))),f192(f882(x86751,a870)))+E(f328(f328(f114(x86751),x86753),f10(x86751,f328(f328(f22(f882(x86751,a870)),x86752),f328(f328(f306(x86751),x86753),f192(f882(x86751,a870)))))),f10(x86751,f328(f328(f306(x86751),x86753),x86752))) % 154.70/154.57 [8676]~P2(x86761)+~P1(f328(f61(x86761),x86762))+E(f328(f328(f22(f882(x86761,a870)),x86762),f328(f328(f306(x86761),x86763),f192(f882(x86761,a870)))),f192(f882(x86761,a870)))+E(f328(f328(f105(x86761),x86763),f11(x86761,f328(f328(f22(f882(x86761,a870)),x86762),f328(f328(f306(x86761),x86763),f192(f882(x86761,a870)))))),f11(x86761,f328(f328(f306(x86761),x86763),x86762))) % 154.70/154.57 [8677]~P105(x86771)+~P1(f328(f61(x86771),x86772))+E(f328(f328(f22(f882(x86771,a870)),x86772),f328(f328(f306(x86771),x86773),f192(f882(x86771,a870)))),f192(f882(x86771,a870)))+E(f328(f328(f240(x86771),x86773),f14(x86771,f328(f328(f22(f882(x86771,a870)),x86772),f328(f328(f306(x86771),x86773),f192(f882(x86771,a870)))))),f14(x86771,f328(f328(f306(x86771),x86773),x86772))) % 154.70/154.57 [8678]~P105(x86781)+~P1(f328(f61(x86781),x86782))+E(f328(f328(f22(f882(x86781,a870)),x86782),f328(f328(f306(x86781),x86783),f192(f882(x86781,a870)))),f192(f882(x86781,a870)))+E(f328(f328(f241(x86781),x86783),f15(x86781,f328(f328(f22(f882(x86781,a870)),x86782),f328(f328(f306(x86781),x86783),f192(f882(x86781,a870)))))),f15(x86781,f328(f328(f306(x86781),x86783),x86782))) % 154.70/154.57 [8742]~P105(x87421)+~P1(f328(f61(x87421),x87422))+E(f328(f328(f22(f882(x87421,a870)),x87422),f328(f328(f306(x87421),x87423),f192(f882(x87421,a870)))),f192(f882(x87421,a870)))+E(f328(f328(f241(x87421),x87423),f12(x87421,f241(x87421),f328(f328(f22(f882(x87421,a870)),x87422),f328(f328(f306(x87421),x87423),f192(f882(x87421,a870)))))),f12(x87421,f241(x87421),f328(f328(f306(x87421),x87423),x87422))) % 154.70/154.57 [8743]~P105(x87431)+~P1(f328(f61(x87431),x87432))+E(f328(f328(f22(f882(x87431,a870)),x87432),f328(f328(f306(x87431),x87433),f192(f882(x87431,a870)))),f192(f882(x87431,a870)))+E(f328(f328(f240(x87431),x87433),f13(x87431,f240(x87431),f328(f328(f22(f882(x87431,a870)),x87432),f328(f328(f306(x87431),x87433),f192(f882(x87431,a870)))))),f13(x87431,f240(x87431),f328(f328(f306(x87431),x87433),x87432))) % 154.70/154.57 [9327]E(x93271,x93272)+~E(f328(f139(f876(x93273),f876(x93273),f125(x93273),f117(x93273)),x93271),f328(f139(f876(x93273),f876(x93273),f125(x93273),f117(x93273)),x93272))+~E(f328(f193(f876(f876(x93273))),x93271),f328(f193(f876(f876(x93273))),x93272))+P1(f328(f328(f330(f881(f876(x93273),f876(x93273))),f741(x93272,x93271,x93273)),f328(f170(f881(f876(x93273),f876(x93273))),f328(f328(f180(f876(x93273),f876(x93273)),x93271),x93272)))) % 154.70/154.57 [9328]E(x93281,x93282)+~E(f328(f139(f876(x93283),f876(x93283),f125(x93283),f117(x93283)),x93281),f328(f139(f876(x93283),f876(x93283),f125(x93283),f117(x93283)),x93282))+~E(f328(f193(f876(f876(x93283))),x93281),f328(f193(f876(f876(x93283))),x93282))+P1(f328(f328(f330(f881(f876(x93283),f876(x93283))),f742(x93281,x93282,x93283)),f328(f170(f881(f876(x93283),f876(x93283))),f328(f328(f180(f876(x93283),f876(x93283)),x93282),x93281)))) % 154.70/154.57 [10154]~P96(x101542)+E(x101541,f192(f882(x101542,a870)))+~P1(f328(f61(x101542),x101541))+E(f11(x101542,f328(f248(x101542),f328(f328(f8(f882(x101542,a870),a870,x101542),f87(x101542)),f328(f328(f7(x101542,f882(x101542,a870),f882(x101542,a870)),f328(f328(f8(f882(x101542,f882(a870,a870)),f882(f882(x101542,a870),f882(x101542,a870)),x101542),f18(x101542,a870,a870)),f328(f328(f8(f882(x101542,a870),f882(x101542,f882(a870,a870)),x101542),f328(f8(a870,f882(a870,a870),x101542),a326)),f328(f328(f7(x101542,f882(x101542,x101542),f882(x101542,a870)),f328(f328(f8(f882(x101542,a870),f882(f882(x101542,x101542),f882(x101542,a870)),x101542),f8(x101542,a870,x101542)),a325)),f328(f114(x101542),x101543))))),f328(f328(f7(x101542,f882(x101542,a870),a870),f330(x101542)),x101541))))),f328(f328(f114(x101542),x101543),f11(x101542,x101541))) % 154.70/154.57 [10155]~P96(x101552)+E(x101551,f192(f882(x101552,a870)))+~P1(f328(f61(x101552),x101551))+E(f10(x101552,f328(f248(x101552),f328(f328(f8(f882(x101552,a870),a870,x101552),f87(x101552)),f328(f328(f7(x101552,f882(x101552,a870),f882(x101552,a870)),f328(f328(f8(f882(x101552,f882(a870,a870)),f882(f882(x101552,a870),f882(x101552,a870)),x101552),f18(x101552,a870,a870)),f328(f328(f8(f882(x101552,a870),f882(x101552,f882(a870,a870)),x101552),f328(f8(a870,f882(a870,a870),x101552),a326)),f328(f328(f7(x101552,f882(x101552,x101552),f882(x101552,a870)),f328(f328(f8(f882(x101552,a870),f882(f882(x101552,x101552),f882(x101552,a870)),x101552),f8(x101552,a870,x101552)),a325)),f328(f105(x101552),x101553))))),f328(f328(f7(x101552,f882(x101552,a870),a870),f330(x101552)),x101551))))),f328(f328(f105(x101552),x101553),f10(x101552,x101551))) % 154.70/154.57 [10156]~P75(x101562)+E(x101561,f192(f882(x101562,a870)))+~P1(f328(f61(x101562),x101561))+E(f14(x101562,f328(f248(x101562),f328(f328(f8(f882(x101562,a870),a870,x101562),f87(x101562)),f328(f328(f7(x101562,f882(x101562,a870),f882(x101562,a870)),f328(f328(f8(f882(x101562,f882(a870,a870)),f882(f882(x101562,a870),f882(x101562,a870)),x101562),f18(x101562,a870,a870)),f328(f328(f8(f882(x101562,a870),f882(x101562,f882(a870,a870)),x101562),f328(f8(a870,f882(a870,a870),x101562),a326)),f328(f328(f7(x101562,f882(x101562,x101562),f882(x101562,a870)),f328(f328(f8(f882(x101562,a870),f882(f882(x101562,x101562),f882(x101562,a870)),x101562),f8(x101562,a870,x101562)),a325)),f328(f80(x101562),x101563))))),f328(f328(f7(x101562,f882(x101562,a870),a870),f330(x101562)),x101561))))),f328(f328(f80(x101562),x101563),f14(x101562,x101561))) % 154.70/154.57 [10157]~P75(x101572)+E(x101571,f192(f882(x101572,a870)))+~P1(f328(f61(x101572),x101571))+E(f15(x101572,f328(f248(x101572),f328(f328(f8(f882(x101572,a870),a870,x101572),f87(x101572)),f328(f328(f7(x101572,f882(x101572,a870),f882(x101572,a870)),f328(f328(f8(f882(x101572,f882(a870,a870)),f882(f882(x101572,a870),f882(x101572,a870)),x101572),f18(x101572,a870,a870)),f328(f328(f8(f882(x101572,a870),f882(x101572,f882(a870,a870)),x101572),f328(f8(a870,f882(a870,a870),x101572),a326)),f328(f328(f7(x101572,f882(x101572,x101572),f882(x101572,a870)),f328(f328(f8(f882(x101572,a870),f882(f882(x101572,x101572),f882(x101572,a870)),x101572),f8(x101572,a870,x101572)),a325)),f328(f80(x101572),x101573))))),f328(f328(f7(x101572,f882(x101572,a870),a870),f330(x101572)),x101571))))),f328(f328(f80(x101572),x101573),f15(x101572,x101571))) % 154.70/154.57 [10158]~P105(x101582)+E(x101581,f192(f882(x101582,a870)))+~P1(f328(f61(x101582),x101581))+E(f12(x101582,f241(x101582),f328(f248(x101582),f328(f328(f8(f882(x101582,a870),a870,x101582),f87(x101582)),f328(f328(f7(x101582,f882(x101582,a870),f882(x101582,a870)),f328(f328(f8(f882(x101582,f882(a870,a870)),f882(f882(x101582,a870),f882(x101582,a870)),x101582),f18(x101582,a870,a870)),f328(f328(f8(f882(x101582,a870),f882(x101582,f882(a870,a870)),x101582),f328(f8(a870,f882(a870,a870),x101582),a326)),f328(f328(f7(x101582,f882(x101582,x101582),f882(x101582,a870)),f328(f328(f8(f882(x101582,a870),f882(f882(x101582,x101582),f882(x101582,a870)),x101582),f8(x101582,a870,x101582)),a325)),f328(f240(x101582),x101583))))),f328(f328(f7(x101582,f882(x101582,a870),a870),f330(x101582)),x101581))))),f328(f328(f240(x101582),x101583),f12(x101582,f241(x101582),x101581))) % 154.70/154.57 [10159]~P105(x101592)+E(x101591,f192(f882(x101592,a870)))+~P1(f328(f61(x101592),x101591))+E(f13(x101592,f240(x101592),f328(f248(x101592),f328(f328(f8(f882(x101592,a870),a870,x101592),f87(x101592)),f328(f328(f7(x101592,f882(x101592,a870),f882(x101592,a870)),f328(f328(f8(f882(x101592,f882(a870,a870)),f882(f882(x101592,a870),f882(x101592,a870)),x101592),f18(x101592,a870,a870)),f328(f328(f8(f882(x101592,a870),f882(x101592,f882(a870,a870)),x101592),f328(f8(a870,f882(a870,a870),x101592),a326)),f328(f328(f7(x101592,f882(x101592,x101592),f882(x101592,a870)),f328(f328(f8(f882(x101592,a870),f882(f882(x101592,x101592),f882(x101592,a870)),x101592),f8(x101592,a870,x101592)),a325)),f328(f241(x101592),x101593))))),f328(f328(f7(x101592,f882(x101592,a870),a870),f330(x101592)),x101591))))),f328(f328(f241(x101592),x101593),f13(x101592,f240(x101592),x101591))) % 154.70/154.57 [9910]~P121(x99101)+~E(x99103,f2(x99101))+~E(x99102,f2(x99101))+E(f328(f328(f80(x99101),f328(f328(f253(x99101),x99102),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x99101),x99103),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f2(x99101)) % 154.70/154.57 [10052]~P123(x100521)+~P1(f328(f328(f242(x100521),f2(x100521)),x100523))+P1(f328(f328(f242(x100521),x100522),x100523))+~P1(f328(f328(f242(x100521),f328(f328(f253(x100521),x100522),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x100521),x100523),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))))) % 154.70/154.57 [10098]~P121(x100982)+~E(x100981,f2(x100982))+~E(x100983,f2(x100982))+~P1(f328(f328(f243(x100982),f2(x100982)),f328(f328(f80(x100982),f328(f328(f253(x100982),x100983),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))),f328(f328(f253(x100982),x100981),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))))) % 154.70/154.57 [9289]E(x92891,x92892)+~E(f674(x92891,x92892,x92894,x92893),f675(x92891,x92892,x92894,x92893))+P1(f328(f328(f330(f881(f876(x92893),f876(x92893))),f328(f328(f263(f876(x92893),f876(x92893)),x92892),x92891)),f144(x92893,x92894)))+P1(f328(f328(f330(f881(f876(x92893),f876(x92893))),f328(f328(f263(f876(x92893),f876(x92893)),x92891),x92892)),f144(x92893,x92894))) % 154.70/154.57 [4840]~P60(x48402)+~E(x48404,f2(x48402))+~E(x48401,f2(x48402))+E(x48401,f328(f328(f286(x48402),x48403),x48404)) % 154.70/154.57 [4841]~P60(x48411)+~E(x48413,f2(x48411))+~E(x48414,f2(x48411))+E(f328(f328(f286(x48411),x48412),x48413),x48414) % 154.70/154.57 [4950]~P60(x49502)+E(x49501,f2(x49502))+~E(x49503,f2(x49502))+~E(x49501,f328(f328(f286(x49502),x49504),x49503)) % 154.70/154.57 [4951]~P60(x49512)+E(x49511,f2(x49512))+~E(x49513,f2(x49512))+~E(f328(f328(f286(x49512),x49514),x49513),x49511) % 154.70/154.57 [5129]~P117(x51292)+E(x51291,f2(x51292))+~E(f328(f328(f286(x51292),x51293),x51291),x51294)+E(x51293,f328(f328(f81(x51292),x51294),x51291)) % 154.70/154.57 [5131]~P117(x51312)+E(x51311,f2(x51312))+~E(f328(f328(f81(x51312),x51313),x51311),x51314)+E(x51313,f328(f328(f286(x51312),x51314),x51311)) % 154.70/154.57 [5132]~P60(x51322)+E(x51321,f2(x51322))+~E(f328(f328(f286(x51322),x51323),x51321),x51324)+E(x51323,f328(f328(f81(x51322),x51324),x51321)) % 154.70/154.57 [5133]~P60(x51332)+E(x51331,f2(x51332))+~E(f328(f328(f81(x51332),x51333),x51331),x51334)+E(x51333,f328(f328(f286(x51332),x51334),x51331)) % 154.70/154.57 [5134]~P117(x51342)+E(x51341,f2(x51342))+~E(x51343,f328(f328(f286(x51342),x51344),x51341))+E(f328(f328(f81(x51342),x51343),x51341),x51344) % 154.70/154.57 [5136]~P117(x51362)+E(x51361,f2(x51362))+~E(x51363,f328(f328(f81(x51362),x51364),x51361))+E(f328(f328(f286(x51362),x51363),x51361),x51364) % 154.70/154.57 [5137]~P60(x51372)+E(x51371,f2(x51372))+~E(x51373,f328(f328(f286(x51372),x51374),x51371))+E(f328(f328(f81(x51372),x51373),x51371),x51374) % 154.70/154.57 [5138]~P60(x51382)+E(x51381,f2(x51382))+~E(x51383,f328(f328(f81(x51382),x51384),x51381))+E(f328(f328(f286(x51382),x51383),x51381),x51384) % 154.70/154.57 [5170]~P60(x51702)+~E(x51701,f2(x51702))+~E(f328(f328(f81(x51702),x51701),x51704),x51703)+E(x51701,f328(f328(f286(x51702),x51703),x51704)) % 154.70/154.57 [5171]~P60(x51711)+~E(x51714,f2(x51711))+~E(x51712,f328(f328(f81(x51711),x51714),x51713))+E(f328(f328(f286(x51711),x51712),x51713),x51714) % 154.70/154.57 [5244]~E(x52443,x52444)+~E(x52442,x52443)+~P107(x52441)+E(f299(x52441,x52442,x52443),f328(f328(f306(x52441),x52444),f192(f882(x52441,a870)))) % 154.70/154.57 [5449]~E(f118(x54492,x54491),x54493)+~E(f141(x54492,x54491),x54494)+E(x54491,f117(x54492))+E(f328(f328(f125(x54492),x54493),f328(f328(f148(x54492),x54494),f117(x54492))),x54491) % 154.70/154.57 [6060]~P123(x60603)+E(x60601,x60602)+~E(f328(f328(f253(x60603),x60604),x60601),f328(f328(f253(x60603),x60604),x60602))+~P1(f328(f328(f243(x60603),f78(x60603)),x60604)) % 154.70/154.57 [6061]E(x60611,x60612)+~E(f328(f328(f306(x60613),x60614),x60611),f328(f328(f306(x60613),x60614),x60612))+P1(f328(f328(f330(x60613),x60614),x60612))+P1(f328(f328(f330(x60613),x60614),x60611)) % 154.70/154.57 [6099]E(f328(x60991,x60992),f2(a875))+~E(f328(f328(f6(x60993,a875),x60991),x60994),f2(a875))+~P1(f328(f61(x60993),x60994))+~P1(f328(f328(f330(x60993),x60992),x60994)) % 154.70/154.57 [6100]E(f328(x61001,x61002),f78(a875))+~E(f328(f328(f9(x61003,a875),x61001),x61004),f78(a875))+~P1(f328(f61(x61003),x61004))+~P1(f328(f328(f330(x61003),x61002),x61004)) % 154.70/154.57 [6323]~P107(x63231)+~P1(f328(f328(f243(x63231),x63234),x63233))+P1(f328(f328(f243(x63231),x63232),x63233))+~P1(f328(f328(f243(x63231),x63232),x63234)) % 154.70/154.57 [6324]~P107(x63241)+~P1(f328(f328(f242(x63241),x63244),x63243))+P1(f328(f328(f243(x63241),x63242),x63243))+~P1(f328(f328(f243(x63241),x63242),x63244)) % 154.70/154.57 [6325]~P107(x63251)+~P1(f328(f328(f242(x63251),x63252),x63254))+P1(f328(f328(f243(x63251),x63252),x63253))+~P1(f328(f328(f243(x63251),x63254),x63253)) % 154.70/154.57 [6326]~P106(x63261)+~P1(f328(f328(f243(x63261),x63262),x63264))+P1(f328(f328(f243(x63261),x63262),x63263))+~P1(f328(f328(f243(x63261),x63264),x63263)) % 154.70/154.57 [6327]~P106(x63271)+~P1(f328(f328(f242(x63271),x63272),x63274))+P1(f328(f328(f243(x63271),x63272),x63273))+~P1(f328(f328(f243(x63271),x63274),x63273)) % 154.70/154.57 [6328]~P106(x63281)+~P1(f328(f328(f242(x63281),x63284),x63283))+P1(f328(f328(f243(x63281),x63282),x63283))+~P1(f328(f328(f243(x63281),x63282),x63284)) % 154.70/154.57 [6329]~P107(x63291)+~P1(f328(f328(f242(x63291),x63294),x63293))+P1(f328(f328(f242(x63291),x63292),x63293))+~P1(f328(f328(f242(x63291),x63292),x63294)) % 154.70/154.57 [6330]~P106(x63301)+~P1(f328(f328(f242(x63301),x63302),x63304))+P1(f328(f328(f242(x63301),x63302),x63303))+~P1(f328(f328(f242(x63301),x63304),x63303)) % 154.70/154.57 [6410]~P37(x64104,x64103,x64102)+E(x64101,f810(x64102,x64103,x64104))+~P1(f328(x64103,x64101))+~P1(f328(f328(f330(x64104),x64101),f328(f170(x64104),x64102))) % 154.70/154.57 [6554]~P5(x65541)+~P1(f328(f328(f242(x65541),x65542),f40(x65541,x65544)))+P1(f328(f328(f242(x65541),x65542),x65543))+~P1(f328(f328(f330(x65541),x65543),x65544)) % 154.70/154.57 [6701]~P105(x67011)+~P16(x67011,f328(f328(f148(x67011),x67012),x67014))+~P1(f328(f328(f330(x67011),x67013),f328(f170(x67011),x67014)))+P1(f328(f328(f242(x67011),x67012),x67013)) % 154.70/154.57 [6791]~P5(x67911)+~P1(f328(f328(f242(x67911),f39(x67911,x67914)),x67913))+P1(f328(f328(f242(x67911),x67912),x67913))+~P1(f328(f328(f330(x67911),x67912),x67914)) % 154.70/154.57 [7197]~P105(x71971)+E(f328(f328(f114(f882(x71971,a870)),f328(f298(x71971,x71972),x71973)),f328(f298(x71971,x71973),x71974)),f328(f298(x71971,x71972),x71974))+~P1(f328(f328(f242(x71971),x71973),x71974))+~P1(f328(f328(f242(x71971),x71972),x71973)) % 154.70/154.57 [7234]P37(x72341,x72342,x72343)+~E(f815(x72343,x72342,x72341,x72344),x72344)+~P1(f328(x72342,x72344))+~P1(f328(f328(f330(x72341),x72344),f328(f170(x72341),x72343))) % 154.70/154.57 [7308]~P105(x73081)+E(f328(f328(f114(f882(x73081,a870)),f328(f298(x73081,x73082),x73083)),f299(x73081,x73083,x73084)),f299(x73081,x73082,x73084))+~P1(f328(f328(f242(x73081),x73083),x73084))+~P1(f328(f328(f242(x73081),x73082),x73083)) % 154.70/154.57 [7374]~P105(x73741)+E(f328(f328(f114(f882(x73741,a870)),f302(x73741,x73742,x73743)),f328(f298(x73741,x73743),x73744)),f302(x73741,x73742,x73744))+~P1(f328(f328(f243(x73741),x73742),x73743))+~P1(f328(f328(f242(x73741),x73743),x73744)) % 154.70/154.57 [7394]~P105(x73941)+E(f328(f328(f114(f882(x73941,a870)),f299(x73941,x73942,x73943)),f302(x73941,x73943,x73944)),f328(f298(x73941,x73942),x73944))+~P1(f328(f328(f243(x73941),x73943),x73944))+~P1(f328(f328(f242(x73941),x73942),x73943)) % 154.70/154.57 [7426]~P105(x74261)+E(f328(f328(f114(f882(x74261,a870)),f302(x74261,x74262,x74263)),f299(x74261,x74263,x74264)),f301(x74261,x74262,x74264))+~P1(f328(f328(f243(x74261),x74262),x74263))+~P1(f328(f328(f242(x74261),x74263),x74264)) % 154.70/154.57 [7427]~P105(x74271)+E(f328(f328(f114(f882(x74271,a870)),f301(x74271,x74272,x74273)),f302(x74271,x74273,x74274)),f302(x74271,x74272,x74274))+~P1(f328(f328(f243(x74271),x74273),x74274))+~P1(f328(f328(f242(x74271),x74272),x74273)) % 154.70/154.57 [7428]~P105(x74281)+E(f328(f328(f114(f882(x74281,a870)),f301(x74281,x74282,x74283)),f301(x74281,x74283,x74284)),f301(x74281,x74282,x74284))+~P1(f328(f328(f242(x74281),x74283),x74284))+~P1(f328(f328(f242(x74281),x74282),x74283)) % 154.70/154.57 [7429]~P105(x74291)+E(f328(f328(f114(f882(x74291,a870)),f299(x74291,x74292,x74293)),f301(x74291,x74293,x74294)),f299(x74291,x74292,x74294))+~P1(f328(f328(f242(x74291),x74293),x74294))+~P1(f328(f328(f242(x74291),x74292),x74293)) % 154.70/154.57 [8235]P27(x82351,x82352,f442(x82353,x82352,x82354,x82351),x82354)+~P1(f328(f61(x82352),x82353))+~P1(f328(f61(x82351),x82354))+~P1(f328(f328(f242(a875),f328(f37(x82351),x82354)),f328(f37(x82352),x82353))) % 154.70/154.57 [8256]P37(x82561,x82562,x82563)+~P1(f328(x82562,x82564))+P1(f328(x82562,f815(x82563,x82562,x82561,x82564)))+~P1(f328(f328(f330(x82561),x82564),f328(f170(x82561),x82563))) % 154.70/154.57 [8307]~P73(x83071)+~E(f328(x83073,f509(x83073,x83074,x83072,x83071)),f78(x83071))+E(f328(f328(f328(f65(x83071,x83072,f81(x83071)),x83073),f78(x83071)),x83074),f78(x83071))+~P1(f328(f61(x83072),x83074)) % 154.70/154.57 [8582]~P123(x85821)+~P1(f328(f328(f242(x85821),f2(x85821)),x85823))+P1(f328(f328(f242(x85821),x85822),x85823))+~P1(f328(f328(f242(x85821),f328(f328(f253(x85821),x85822),f328(a116,x85824))),f328(f328(f253(x85821),x85823),f328(a116,x85824)))) % 154.70/154.57 [8878]P37(x88781,x88782,x88783)+~P1(f328(x88782,x88784))+~P1(f328(f328(f330(x88781),x88784),f328(f170(x88781),x88783)))+P1(f328(f328(f330(x88781),f815(x88783,x88782,x88781,x88784)),f328(f170(x88781),x88783))) % 154.70/154.57 [8964]~P73(x89641)+E(f328(f328(f328(f65(x89641,x89642,f81(x89641)),x89643),f78(x89641)),x89644),f78(x89641))+~P1(f328(f61(x89642),x89644))+P1(f328(f328(f330(x89642),f509(x89643,x89644,x89642,x89641)),x89644)) % 154.70/154.57 [9453]~P1(f328(f328(f242(a1),x94534),f2(a1)))+P1(f328(f328(f242(a1),f328(f328(f80(a1),f328(f328(f81(a1),x94531),f44(a1,x94532,x94533))),x94534)),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x94533))+~P1(f328(f328(f243(a1),x94531),x94534)) % 154.70/154.57 [9903]~P1(f328(f61(x99031),x99032))+~P1(f328(f328(f330(x99031),x99034),x99032))+~P1(f328(f328(f330(x99031),x99033),x99032))+P1(f328(f328(f243(a875),f328(f37(x99031),f328(f328(f22(f882(x99031,a870)),f328(f328(f22(f882(x99031,a870)),x99032),f328(f328(f306(x99031),x99033),f192(f882(x99031,a870))))),f328(f328(f306(x99031),x99034),f192(f882(x99031,a870)))))),f328(f37(x99031),x99032))) % 154.70/154.57 [6905]~P105(x69051)+~P1(f328(f328(f243(x69051),x69052),x69054))+~P1(f328(f328(f243(x69051),x69052),x69053))+P1(f328(f328(f243(x69051),x69052),f328(f328(f240(x69051),x69053),x69054))) % 154.70/154.57 [6908]~P100(x69081)+~P1(f328(f328(f242(x69081),x69082),x69084))+~P1(f328(f328(f242(x69081),x69082),x69083))+P1(f328(f328(f242(x69081),x69082),f328(f328(f105(x69081),x69083),x69084))) % 154.70/154.57 [6911]~P105(x69111)+~P1(f328(f328(f242(x69111),x69112),x69114))+~P1(f328(f328(f242(x69111),x69112),x69113))+P1(f328(f328(f242(x69111),x69112),f328(f328(f240(x69111),x69113),x69114))) % 154.70/154.57 [6930]~P61(x69302)+E(x69301,f2(x69302))+E(f328(f328(f286(x69302),f328(f328(f253(x69302),x69301),x69303)),f328(f328(f253(x69302),x69301),x69304)),f328(f328(f253(x69302),x69301),f328(f328(f22(a875),x69303),x69304)))+~P1(f328(f328(f242(a875),x69304),x69303)) % 154.70/154.57 [6975]~P105(x69751)+~P16(x69751,f328(f328(f148(x69751),x69753),x69754))+P16(x69751,f328(f328(f148(x69751),x69752),f328(f328(f148(x69751),x69753),x69754)))+~P1(f328(f328(f242(x69751),x69752),x69753)) % 154.70/154.57 [7014]~P123(x70141)+~P1(f328(f328(f243(x70141),f2(x70141)),x70143))+~P1(f328(f328(f243(x70141),x70142),x70144))+P1(f328(f328(f243(x70141),x70142),f328(f328(f80(x70141),x70143),x70144))) % 154.70/154.57 [7015]~P85(x70151)+~P1(f328(f328(f242(x70151),f2(x70151)),x70153))+~P1(f328(f328(f243(x70151),x70152),x70154))+P1(f328(f328(f243(x70151),x70152),f328(f328(f80(x70151),x70153),x70154))) % 154.70/154.57 [7016]~P85(x70161)+~P1(f328(f328(f242(x70161),x70162),x70164))+~P1(f328(f328(f243(x70161),f2(x70161)),x70163))+P1(f328(f328(f243(x70161),x70162),f328(f328(f80(x70161),x70163),x70164))) % 154.70/154.57 [7017]~P85(x70171)+~P1(f328(f328(f242(x70171),f2(x70171)),x70174))+~P1(f328(f328(f242(x70171),x70172),x70173))+P1(f328(f328(f242(x70171),x70172),f328(f328(f80(x70171),x70173),x70174))) % 154.70/154.57 [7018]~P85(x70181)+~P1(f328(f328(f242(x70181),f2(x70181)),x70183))+~P1(f328(f328(f242(x70181),x70182),x70184))+P1(f328(f328(f242(x70181),x70182),f328(f328(f80(x70181),x70183),x70184))) % 154.70/154.57 [7057]~P105(x70571)+P1(f328(f328(f243(x70571),x70572),x70573))+P1(f328(f328(f243(x70571),x70572),x70574))+~P1(f328(f328(f243(x70571),x70572),f328(f328(f241(x70571),x70574),x70573))) % 154.70/154.57 [7058]~P105(x70581)+P1(f328(f328(f242(x70581),x70582),x70583))+P1(f328(f328(f242(x70581),x70582),x70584))+~P1(f328(f328(f242(x70581),x70582),f328(f328(f241(x70581),x70584),x70583))) % 154.70/154.57 [7347]~P107(x73472)+~P59(x73471)+~P1(f328(f328(f243(f882(x73471,x73472)),x73473),x73474))+P1(f328(f328(f242(f882(x73471,x73472)),x73473),x73474)) % 154.70/154.57 [7717]~P63(x77171)+~P1(f328(f328(f243(x77171),x77174),f2(x77171)))+~P1(f328(f328(f243(x77171),x77173),f328(f328(f286(x77171),x77172),x77174)))+P1(f328(f328(f243(x77171),x77172),f328(f328(f81(x77171),x77173),x77174))) % 154.70/154.57 [7718]~P63(x77181)+~P1(f328(f328(f243(x77181),x77184),f2(x77181)))+~P1(f328(f328(f243(x77181),x77183),f328(f328(f81(x77181),x77182),x77184)))+P1(f328(f328(f243(x77181),x77182),f328(f328(f286(x77181),x77183),x77184))) % 154.70/154.57 [7719]~P63(x77191)+~P1(f328(f328(f243(x77191),x77194),f2(x77191)))+~P1(f328(f328(f242(x77191),x77193),f328(f328(f286(x77191),x77192),x77194)))+P1(f328(f328(f242(x77191),x77192),f328(f328(f81(x77191),x77193),x77194))) % 154.70/154.57 [7720]~P63(x77201)+~P1(f328(f328(f243(x77201),x77204),f2(x77201)))+~P1(f328(f328(f242(x77201),x77203),f328(f328(f81(x77201),x77202),x77204)))+P1(f328(f328(f242(x77201),x77202),f328(f328(f286(x77201),x77203),x77204))) % 154.70/154.57 [7833]~P114(x78331)+~P1(f328(f328(f243(x78331),x78333),f2(x78331)))+~P1(f328(f328(f243(x78331),x78334),x78332))+P1(f328(f328(f243(x78331),f328(f328(f81(x78331),x78332),x78333)),f328(f328(f81(x78331),x78334),x78333))) % 154.70/154.57 [7834]~P114(x78341)+~P1(f328(f328(f243(x78341),x78342),f2(x78341)))+~P1(f328(f328(f243(x78341),x78344),x78343))+P1(f328(f328(f243(x78341),f328(f328(f81(x78341),x78342),x78343)),f328(f328(f81(x78341),x78342),x78344))) % 154.70/154.57 [7835]~P63(x78351)+~P1(f328(f328(f243(x78351),x78353),f2(x78351)))+~P1(f328(f328(f243(x78351),x78354),x78352))+P1(f328(f328(f243(x78351),f328(f328(f286(x78351),x78352),x78353)),f328(f328(f286(x78351),x78354),x78353))) % 154.70/154.57 [7836]~P114(x78361)+~P1(f328(f328(f243(x78361),x78362),f2(x78361)))+~P1(f328(f328(f242(x78361),x78364),x78363))+P1(f328(f328(f242(x78361),f328(f328(f81(x78361),x78362),x78363)),f328(f328(f81(x78361),x78362),x78364))) % 154.70/154.57 [7837]~P127(x78371)+~P1(f328(f328(f242(x78371),x78372),f2(x78371)))+~P1(f328(f328(f242(x78371),x78374),x78373))+P1(f328(f328(f242(x78371),f328(f328(f81(x78371),x78372),x78373)),f328(f328(f81(x78371),x78372),x78374))) % 154.70/154.57 [7838]~P127(x78381)+~P1(f328(f328(f242(x78381),x78383),f2(x78381)))+~P1(f328(f328(f242(x78381),x78384),x78382))+P1(f328(f328(f242(x78381),f328(f328(f81(x78381),x78382),x78383)),f328(f328(f81(x78381),x78384),x78383))) % 154.70/154.57 [7839]~P62(x78391)+~P1(f328(f328(f242(x78391),x78393),f2(x78391)))+~P1(f328(f328(f242(x78391),x78394),x78392))+P1(f328(f328(f242(x78391),f328(f328(f286(x78391),x78392),x78393)),f328(f328(f286(x78391),x78394),x78393))) % 154.70/154.57 [7841]~P123(x78411)+~P1(f328(f328(f243(x78411),f78(x78411)),x78412))+~P1(f328(f328(f243(a875),x78413),x78414))+P1(f328(f328(f243(x78411),f328(f328(f253(x78411),x78412),x78413)),f328(f328(f253(x78411),x78412),x78414))) % 154.70/154.57 [7842]~P123(x78421)+~P1(f328(f328(f243(x78421),f78(x78421)),x78422))+~P1(f328(f328(f242(a875),x78423),x78424))+P1(f328(f328(f242(x78421),f328(f328(f253(x78421),x78422),x78423)),f328(f328(f253(x78421),x78422),x78424))) % 154.70/154.57 [7843]~P123(x78431)+~P1(f328(f328(f242(x78431),f78(x78431)),x78432))+~P1(f328(f328(f242(a875),x78433),x78434))+P1(f328(f328(f242(x78431),f328(f328(f253(x78431),x78432),x78433)),f328(f328(f253(x78431),x78432),x78434))) % 154.70/154.57 [7870]P1(f328(f328(f243(a875),f2(a875)),f328(x78701,x78702)))+~P1(f328(f61(x78703),x78704))+~P1(f328(f328(f330(x78703),x78702),x78704))+~P1(f328(f328(f243(a875),f2(a875)),f328(f328(f9(x78703,a875),x78701),x78704))) % 154.70/154.57 [7880]~P115(x78801)+~P1(f328(f328(f243(x78801),x78803),x78804))+~P1(f328(f328(f243(x78801),f2(x78801)),x78802))+P1(f328(f328(f243(x78801),f328(f328(f81(x78801),x78802),x78803)),f328(f328(f81(x78801),x78802),x78804))) % 154.70/154.57 [7881]~P122(x78811)+~P1(f328(f328(f243(x78811),x78813),x78814))+~P1(f328(f328(f243(x78811),f2(x78811)),x78812))+P1(f328(f328(f243(x78811),f328(f328(f81(x78811),x78812),x78813)),f328(f328(f81(x78811),x78812),x78814))) % 154.70/154.57 [7882]~P114(x78821)+~P1(f328(f328(f243(x78821),x78822),x78824))+~P1(f328(f328(f243(x78821),f2(x78821)),x78823))+P1(f328(f328(f243(x78821),f328(f328(f81(x78821),x78822),x78823)),f328(f328(f81(x78821),x78824),x78823))) % 154.70/154.57 [7883]~P122(x78831)+~P1(f328(f328(f243(x78831),x78832),x78834))+~P1(f328(f328(f243(x78831),f2(x78831)),x78833))+P1(f328(f328(f243(x78831),f328(f328(f81(x78831),x78832),x78833)),f328(f328(f81(x78831),x78834),x78833))) % 154.70/154.57 [7884]~P114(x78841)+~P1(f328(f328(f243(x78841),x78843),x78844))+~P1(f328(f328(f243(x78841),f2(x78841)),x78842))+P1(f328(f328(f243(x78841),f328(f328(f81(x78841),x78842),x78843)),f328(f328(f81(x78841),x78842),x78844))) % 154.70/154.57 [7885]~P63(x78851)+~P1(f328(f328(f243(x78851),x78852),x78854))+~P1(f328(f328(f243(x78851),f2(x78851)),x78853))+P1(f328(f328(f243(x78851),f328(f328(f286(x78851),x78852),x78853)),f328(f328(f286(x78851),x78854),x78853))) % 154.70/154.57 [7886]~P114(x78861)+~P1(f328(f328(f243(x78861),f2(x78861)),x78862))+~P1(f328(f328(f242(x78861),x78863),x78864))+P1(f328(f328(f242(x78861),f328(f328(f81(x78861),x78862),x78863)),f328(f328(f81(x78861),x78862),x78864))) % 154.70/154.57 [7887]~P132(x78871)+~P1(f328(f328(f242(x78871),x78873),x78874))+~P1(f328(f328(f242(x78871),f2(x78871)),x78872))+P1(f328(f328(f242(x78871),f328(f328(f81(x78871),x78872),x78873)),f328(f328(f81(x78871),x78872),x78874))) % 154.70/154.57 [7888]~P131(x78881)+~P1(f328(f328(f242(x78881),x78883),x78884))+~P1(f328(f328(f242(x78881),f2(x78881)),x78882))+P1(f328(f328(f242(x78881),f328(f328(f81(x78881),x78882),x78883)),f328(f328(f81(x78881),x78882),x78884))) % 154.70/154.57 [7889]~P132(x78891)+~P1(f328(f328(f242(x78891),x78892),x78894))+~P1(f328(f328(f242(x78891),f2(x78891)),x78893))+P1(f328(f328(f242(x78891),f328(f328(f81(x78891),x78892),x78893)),f328(f328(f81(x78891),x78894),x78893))) % 154.70/154.57 [7890]~P123(x78901)+~P1(f328(f328(f242(x78901),x78902),x78904))+~P1(f328(f328(f242(x78901),f2(x78901)),x78902))+P1(f328(f328(f242(x78901),f328(f328(f253(x78901),x78902),x78903)),f328(f328(f253(x78901),x78904),x78903))) % 154.70/154.57 [7891]~P62(x78911)+~P1(f328(f328(f242(x78911),x78912),x78914))+~P1(f328(f328(f242(x78911),f2(x78911)),x78913))+P1(f328(f328(f242(x78911),f328(f328(f286(x78911),x78912),x78913)),f328(f328(f286(x78911),x78914),x78913))) % 154.70/154.57 [7934]~P108(x79342)+P1(f328(f328(f242(f882(x79341,x79342)),x79344),x79343))+~P1(f328(f328(f242(f882(x79341,x79342)),x79343),x79344))+P1(f328(f328(f243(f882(x79341,x79342)),x79343),x79344)) % 154.70/154.57 [7973]P1(f328(f328(f330(x79731),x79732),x79733))+P1(f328(f328(f330(x79731),x79732),x79734))+~P1(f328(f328(f242(f882(x79731,a870)),x79734),x79733))+P1(f328(f328(f243(f882(x79731,a870)),x79734),f328(f328(f306(x79731),x79732),x79733))) % 154.70/154.57 [8130]P1(f328(f328(f330(x81301),x81302),x81303))+P1(f328(f328(f330(x81301),x81302),x81304))+~P1(f328(f328(f243(f882(x81301,a870)),x81304),f328(f328(f306(x81301),x81302),x81303)))+P1(f328(f328(f242(f882(x81301,a870)),x81304),x81303)) % 154.70/154.57 [8138]~P59(x81381)+P12(x81381,x81382,x81383)+~P1(f328(x81382,x81384))+~P1(f328(f328(f330(f876(x81381)),x81384),f328(f170(f876(x81381)),f54(x81381,x81383,f55(x81381))))) % 154.70/154.57 [8150]~P13(x81503,x81501,x81504)+~P59(x81503)+P1(f328(x81501,x81502))+~P1(f328(f328(f330(f876(x81503)),x81502),f328(f170(f876(x81503)),f54(x81503,x81504,f55(x81503))))) % 154.70/154.57 [8209]~P114(x82091)+P1(f328(f328(f243(x82091),x82093),x82092))+P1(f328(f328(f243(x82091),x82092),x82093))+~P1(f328(f328(f243(x82091),f328(f328(f81(x82091),x82094),x82092)),f328(f328(f81(x82091),x82094),x82093))) % 154.70/154.57 [8210]~P114(x82101)+P1(f328(f328(f243(x82101),x82103),x82102))+P1(f328(f328(f243(x82101),x82102),x82103))+~P1(f328(f328(f243(x82101),f328(f328(f81(x82101),x82102),x82104)),f328(f328(f81(x82101),x82103),x82104))) % 154.70/154.57 [8223]~P114(x82231)+P1(f328(f328(f243(x82231),x82234),f2(x82231)))+P1(f328(f328(f243(x82231),x82232),x82233))+~P1(f328(f328(f243(x82231),f328(f328(f81(x82231),x82232),x82234)),f328(f328(f81(x82231),x82233),x82234))) % 154.70/154.57 [8224]~P114(x82241)+P1(f328(f328(f243(x82241),x82244),f2(x82241)))+P1(f328(f328(f243(x82241),x82242),x82243))+~P1(f328(f328(f243(x82241),f328(f328(f81(x82241),x82244),x82242)),f328(f328(f81(x82241),x82244),x82243))) % 154.70/154.57 [8229]~P114(x82291)+P1(f328(f328(f243(x82291),x82292),x82293))+P1(f328(f328(f243(x82291),f2(x82291)),x82294))+~P1(f328(f328(f243(x82291),f328(f328(f81(x82291),x82294),x82293)),f328(f328(f81(x82291),x82294),x82292))) % 154.70/154.57 [8230]~P114(x82301)+P1(f328(f328(f243(x82301),x82302),x82303))+P1(f328(f328(f243(x82301),f2(x82301)),x82304))+~P1(f328(f328(f243(x82301),f328(f328(f81(x82301),x82303),x82304)),f328(f328(f81(x82301),x82302),x82304))) % 154.70/154.57 [8243]~P114(x82431)+P1(f328(f328(f243(x82431),x82432),f2(x82431)))+P1(f328(f328(f243(x82431),f2(x82431)),x82432))+~P1(f328(f328(f243(x82431),f328(f328(f81(x82431),x82433),x82432)),f328(f328(f81(x82431),x82434),x82432))) % 154.70/154.57 [8244]~P114(x82441)+P1(f328(f328(f243(x82441),x82442),f2(x82441)))+P1(f328(f328(f243(x82441),f2(x82441)),x82442))+~P1(f328(f328(f243(x82441),f328(f328(f81(x82441),x82442),x82443)),f328(f328(f81(x82441),x82442),x82444))) % 154.70/154.57 [8271]~P114(x82711)+~P1(f328(f328(f243(x82711),x82714),f2(x82711)))+P1(f328(f328(f243(x82711),x82712),x82713))+~P1(f328(f328(f243(x82711),f328(f328(f81(x82711),x82714),x82713)),f328(f328(f81(x82711),x82714),x82712))) % 154.70/154.57 [8272]~P114(x82721)+~P1(f328(f328(f243(x82721),x82724),f2(x82721)))+P1(f328(f328(f242(x82721),x82722),x82723))+~P1(f328(f328(f242(x82721),f328(f328(f81(x82721),x82724),x82723)),f328(f328(f81(x82721),x82724),x82722))) % 154.70/154.57 [8282]~P123(x82823)+~P1(f328(f328(f243(x82823),f78(x82823)),x82824))+P1(f328(f328(f243(a875),x82821),x82822))+~P1(f328(f328(f243(x82823),f328(f328(f253(x82823),x82824),x82821)),f328(f328(f253(x82823),x82824),x82822))) % 154.70/154.57 [8284]~P123(x82843)+~P1(f328(f328(f243(x82843),f78(x82843)),x82844))+P1(f328(f328(f242(a875),x82841),x82842))+~P1(f328(f328(f242(x82843),f328(f328(f253(x82843),x82844),x82841)),f328(f328(f253(x82843),x82844),x82842))) % 154.70/154.57 [8294]~P114(x82941)+P1(f328(f328(f243(x82941),x82942),x82943))+~P1(f328(f328(f243(x82941),f2(x82941)),x82944))+~P1(f328(f328(f243(x82941),f328(f328(f81(x82941),x82944),x82942)),f328(f328(f81(x82941),x82944),x82943))) % 154.70/154.57 [8295]~P122(x82951)+P1(f328(f328(f243(x82951),x82952),x82953))+~P1(f328(f328(f242(x82951),f2(x82951)),x82954))+~P1(f328(f328(f243(x82951),f328(f328(f81(x82951),x82954),x82952)),f328(f328(f81(x82951),x82954),x82953))) % 154.70/154.57 [8296]~P124(x82961)+P1(f328(f328(f243(x82961),x82962),x82963))+~P1(f328(f328(f242(x82961),f2(x82961)),x82964))+~P1(f328(f328(f243(x82961),f328(f328(f81(x82961),x82964),x82962)),f328(f328(f81(x82961),x82964),x82963))) % 154.70/154.57 [8297]~P122(x82971)+P1(f328(f328(f243(x82971),x82972),x82973))+~P1(f328(f328(f242(x82971),f2(x82971)),x82974))+~P1(f328(f328(f243(x82971),f328(f328(f81(x82971),x82972),x82974)),f328(f328(f81(x82971),x82973),x82974))) % 154.70/154.57 [8298]~P123(x82981)+~P1(f328(f328(f242(x82981),f2(x82981)),x82983))+P1(f328(f328(f243(x82981),x82982),x82983))+~P1(f328(f328(f243(x82981),f328(f328(f253(x82981),x82982),x82984)),f328(f328(f253(x82981),x82983),x82984))) % 154.70/154.57 [8299]~P124(x82991)+P1(f328(f328(f243(x82991),x82992),x82993))+~P1(f328(f328(f242(x82991),f2(x82991)),x82994))+~P1(f328(f328(f243(x82991),f328(f328(f81(x82991),x82992),x82994)),f328(f328(f81(x82991),x82993),x82994))) % 154.70/154.57 [8300]~P114(x83001)+P1(f328(f328(f242(x83001),x83002),x83003))+~P1(f328(f328(f243(x83001),f2(x83001)),x83004))+~P1(f328(f328(f242(x83001),f328(f328(f81(x83001),x83004),x83002)),f328(f328(f81(x83001),x83004),x83003))) % 154.70/154.57 [8301]~P122(x83011)+P1(f328(f328(f242(x83011),x83012),x83013))+~P1(f328(f328(f243(x83011),f2(x83011)),x83014))+~P1(f328(f328(f242(x83011),f328(f328(f81(x83011),x83014),x83012)),f328(f328(f81(x83011),x83014),x83013))) % 154.70/154.57 [8302]~P122(x83021)+P1(f328(f328(f242(x83021),x83022),x83023))+~P1(f328(f328(f243(x83021),f2(x83021)),x83024))+~P1(f328(f328(f242(x83021),f328(f328(f81(x83021),x83022),x83024)),f328(f328(f81(x83021),x83023),x83024))) % 154.70/154.57 [8346]P1(f328(f328(f330(x83461),x83462),x83463))+~P1(f328(f328(f242(f882(x83461,a870)),x83463),x83464))+~P1(f328(f328(f243(f882(x83461,a870)),x83463),x83464))+P1(f328(f328(f243(f882(x83461,a870)),x83463),f328(f328(f306(x83461),x83462),x83464))) % 154.70/154.57 [8605]~P59(x86051)+~P92(x86052)+~E(f328(x86053,f805(x86054,x86053,x86051,x86052)),f328(x86054,f805(x86054,x86053,x86051,x86052)))+P1(f328(f328(f91(f882(x86051,x86052)),x86053),x86054)) % 154.70/154.57 [8722]E(f328(f328(f22(a1),f414(x87221,x87222,x87223,x87224)),f415(x87221,x87222,x87223,x87224)),x87224)+~P1(f328(f328(f243(a1),f2(a1)),x87223))+~P1(f328(f328(f242(a1),x87221),x87224))+P1(f328(f328(f242(a1),x87221),f328(f328(f80(a1),x87224),x87223))) % 154.70/154.57 [8723]E(f328(f328(f22(a1),f424(x87231,x87232,x87233,x87234)),f425(x87231,x87232,x87233,x87234)),x87234)+~P1(f328(f328(f243(a1),f2(a1)),x87233))+~P1(f328(f328(f243(a1),x87231),x87234))+P1(f328(f328(f243(a1),x87231),f328(f328(f80(a1),x87234),x87233))) % 154.70/154.57 [8858]~E(f328(f328(f162(x88581),x88583),f693(x88584,x88583,x88581,x88582)),f328(f328(f162(x88581),x88584),f693(x88584,x88583,x88581,x88582)))+E(f328(f328(f173(x88581),x88582),x88583),f328(f328(f173(x88581),x88582),x88584))+~P1(f328(f328(f242(a875),x88582),f328(f193(f876(x88581)),x88583)))+~P1(f328(f328(f242(a875),x88582),f328(f193(f876(x88581)),x88584))) % 154.70/154.57 [8930]~P1(f328(f328(f243(a1),f2(a1)),x89303))+~P1(f328(f328(f242(a1),x89301),x89304))+P1(f328(f328(f330(a1),f414(x89301,x89302,x89303,x89304)),x89302))+P1(f328(f328(f242(a1),x89301),f328(f328(f80(a1),x89304),x89303))) % 154.70/154.57 [8931]~P1(f328(f328(f243(a1),f2(a1)),x89313))+~P1(f328(f328(f243(a1),x89311),x89314))+P1(f328(f328(f330(a1),f424(x89311,x89312,x89313,x89314)),x89312))+P1(f328(f328(f243(a1),x89311),f328(f328(f80(a1),x89314),x89313))) % 154.70/154.57 [8975]~P100(x89751)+~P1(f328(f61(x89751),x89753))+~P1(f328(f328(f330(x89751),x89754),x89753))+P1(f328(f328(f242(x89751),f328(f328(f64(x89751,x89751,f105(x89751)),x89752),x89753)),f328(f328(f105(x89751),x89754),x89752))) % 154.70/154.57 [8976]~P105(x89761)+~P1(f328(f61(x89761),x89763))+~P1(f328(f328(f330(x89761),x89764),x89763))+P1(f328(f328(f242(x89761),f328(f328(f64(x89761,x89761,f240(x89761)),x89762),x89763)),f328(f328(f240(x89761),x89764),x89762))) % 154.70/154.57 [9020]E(f328(f328(f173(x90201),x90202),x90203),f328(f328(f173(x90201),x90202),x90204))+P1(f328(f328(f243(a875),f693(x90203,x90204,x90201,x90202)),x90202))+~P1(f328(f328(f242(a875),x90202),f328(f193(f876(x90201)),x90203)))+~P1(f328(f328(f242(a875),x90202),f328(f193(f876(x90201)),x90204))) % 154.70/154.57 [9025]~P1(f328(f328(f243(a1),f2(a1)),x90253))+~P1(f328(f328(f243(a1),x90251),x90252))+P1(f328(f328(f330(a1),f425(x90251,x90254,x90253,x90252)),f299(a1,f78(a1),x90253)))+P1(f328(f328(f243(a1),x90251),f328(f328(f80(a1),x90252),x90253))) % 154.70/154.57 [9026]~P1(f328(f328(f243(a1),f2(a1)),x90263))+~P1(f328(f328(f242(a1),x90261),x90262))+P1(f328(f328(f330(a1),f415(x90261,x90264,x90263,x90262)),f299(a1,f78(a1),x90263)))+P1(f328(f328(f242(a1),x90261),f328(f328(f80(a1),x90262),x90263))) % 154.70/154.57 [9192]~E(f328(f176(x91921,x91922),x91923),f328(f176(x91921,x91922),x91924))+E(f328(f170(f881(x91921,x91922)),x91923),f328(f170(f881(x91921,x91922)),x91924))+~P1(f328(f134(x91921),f328(f328(f151(f881(x91921,x91922),x91921),f262(x91921,x91922)),x91924)))+~P1(f328(f134(x91921),f328(f328(f151(f881(x91921,x91922),x91921),f262(x91921,x91922)),x91923))) % 154.70/154.57 [9204]E(f328(f176(x92041,x92042),x92043),f328(f176(x92041,x92042),x92044))+~E(f328(f170(f881(x92041,x92042)),x92043),f328(f170(f881(x92041,x92042)),x92044))+~P1(f328(f134(x92041),f328(f328(f151(f881(x92041,x92042),x92041),f262(x92041,x92042)),x92044)))+~P1(f328(f134(x92041),f328(f328(f151(f881(x92041,x92042),x92041),f262(x92041,x92042)),x92043))) % 154.70/154.57 [9347]~P105(x93471)+~P1(f328(f61(x93471),x93474))+P1(f328(f328(f330(x93471),f519(x93472,x93473,x93474,x93471)),x93474))+P1(f328(f328(f242(x93471),f328(f328(f64(x93471,x93471,f241(x93471)),x93472),x93474)),f328(f328(f241(x93471),x93473),x93472))) % 154.70/154.57 [9348]~P99(x93481)+~P1(f328(f61(x93481),x93484))+P1(f328(f328(f330(x93481),f528(x93482,x93483,x93484,x93481)),x93484))+P1(f328(f328(f242(x93481),f328(f328(f64(x93481,x93481,f114(x93481)),x93482),x93484)),f328(f328(f114(x93481),x93483),x93482))) % 154.70/154.57 [9471]~P99(x94711)+~P1(f328(f61(x94711),x94713))+~P1(f328(f328(f242(x94711),f528(x94712,x94714,x94713,x94711)),x94714))+P1(f328(f328(f242(x94711),f328(f328(f64(x94711,x94711,f114(x94711)),x94712),x94713)),f328(f328(f114(x94711),x94714),x94712))) % 154.70/154.57 [9472]~P105(x94721)+~P1(f328(f61(x94721),x94723))+~P1(f328(f328(f242(x94721),f519(x94722,x94724,x94723,x94721)),x94724))+P1(f328(f328(f242(x94721),f328(f328(f64(x94721,x94721,f241(x94721)),x94722),x94723)),f328(f328(f241(x94721),x94724),x94722))) % 154.70/154.57 [9475]~P1(f328(f328(f243(a1),f2(a1)),x94753))+~P1(f328(f328(f242(a1),f2(a1)),x94754))+~P1(f328(f328(f243(a1),x94754),x94751))+P1(f328(f328(f243(a1),f328(f328(f80(a1),f328(f328(f81(a1),x94751),f44(a1,x94752,x94753))),x94754)),f328(f328(f81(a1),x94751),x94753))) % 154.70/154.57 [9872]E(x98721,x98722)+P1(f328(f328(f330(f881(f876(x98723),f876(x98723))),f328(f328(f263(f876(x98723),f876(x98723)),x98722),x98721)),f144(x98723,x98724)))+P1(f328(f328(f330(f881(f876(x98723),f876(x98723))),f328(f328(f263(f876(x98723),f876(x98723)),x98721),x98722)),f144(x98723,x98724)))+~P1(f328(f328(f330(f881(x98723,x98723)),f328(f328(f263(x98723,x98723),f674(x98721,x98722,x98724,x98723)),f675(x98721,x98722,x98724,x98723))),x98724)) % 154.70/154.57 [9873]E(x98731,x98732)+P1(f328(f328(f330(f881(f876(x98733),f876(x98733))),f328(f328(f263(f876(x98733),f876(x98733)),x98732),x98731)),f144(x98733,x98734)))+P1(f328(f328(f330(f881(f876(x98733),f876(x98733))),f328(f328(f263(f876(x98733),f876(x98733)),x98731),x98732)),f144(x98733,x98734)))+~P1(f328(f328(f330(f881(x98733,x98733)),f328(f328(f263(x98733,x98733),f675(x98731,x98732,x98734,x98733)),f674(x98731,x98732,x98734,x98733))),x98734)) % 154.70/154.57 [7414]~P105(x74141)+~P1(f328(f328(f243(x74141),x74143),x74144))+~P1(f328(f328(f243(x74141),x74142),x74144))+P1(f328(f328(f243(x74141),f328(f328(f241(x74141),x74142),x74143)),x74144)) % 154.70/154.57 [7417]~P99(x74171)+~P1(f328(f328(f242(x74171),x74173),x74174))+~P1(f328(f328(f242(x74171),x74172),x74174))+P1(f328(f328(f242(x74171),f328(f328(f114(x74171),x74172),x74173)),x74174)) % 154.70/154.57 [7420]~P105(x74201)+~P1(f328(f328(f242(x74201),x74203),x74204))+~P1(f328(f328(f242(x74201),x74202),x74204))+P1(f328(f328(f242(x74201),f328(f328(f241(x74201),x74202),x74203)),x74204)) % 154.70/154.57 [7742]~E(x77421,x77423)+E(f136(a875,f328(f298(a875,x77421),x77422)),f328(f328(f148(a875),x77423),x77424))+~E(f136(a875,f328(f298(a875,f328(f328(f80(a875),x77421),f78(a875))),x77422)),x77424)+~P1(f328(f328(f243(a875),x77421),x77422)) % 154.70/154.57 [7751]~P105(x77511)+P1(f328(f328(f243(x77511),x77512),x77513))+P1(f328(f328(f243(x77511),x77514),x77513))+~P1(f328(f328(f243(x77511),f328(f328(f240(x77511),x77514),x77512)),x77513)) % 154.70/154.57 [7752]~P105(x77521)+P1(f328(f328(f242(x77521),x77522),x77523))+P1(f328(f328(f242(x77521),x77524),x77523))+~P1(f328(f328(f242(x77521),f328(f328(f240(x77521),x77524),x77522)),x77523)) % 154.70/154.57 [8029]~P62(x80291)+~P1(f328(f328(f243(x80291),f2(x80291)),x80293))+~P1(f328(f328(f243(x80291),x80292),f328(f328(f286(x80291),x80294),x80293)))+P1(f328(f328(f243(x80291),f328(f328(f81(x80291),x80292),x80293)),x80294)) % 154.70/154.57 [8030]~P63(x80301)+~P1(f328(f328(f243(x80301),f2(x80301)),x80303))+~P1(f328(f328(f243(x80301),x80302),f328(f328(f286(x80301),x80304),x80303)))+P1(f328(f328(f243(x80301),f328(f328(f81(x80301),x80302),x80303)),x80304)) % 154.70/154.57 [8032]~P62(x80321)+~P1(f328(f328(f243(x80321),f2(x80321)),x80323))+~P1(f328(f328(f243(x80321),x80322),f328(f328(f81(x80321),x80324),x80323)))+P1(f328(f328(f243(x80321),f328(f328(f286(x80321),x80322),x80323)),x80324)) % 154.70/154.57 [8033]~P63(x80331)+~P1(f328(f328(f243(x80331),f2(x80331)),x80333))+~P1(f328(f328(f243(x80331),x80332),f328(f328(f81(x80331),x80334),x80333)))+P1(f328(f328(f243(x80331),f328(f328(f286(x80331),x80332),x80333)),x80334)) % 154.70/154.57 [8034]~P62(x80341)+~P1(f328(f328(f243(x80341),f2(x80341)),x80343))+~P1(f328(f328(f242(x80341),x80342),f328(f328(f286(x80341),x80344),x80343)))+P1(f328(f328(f242(x80341),f328(f328(f81(x80341),x80342),x80343)),x80344)) % 154.70/154.57 [8035]~P63(x80351)+~P1(f328(f328(f243(x80351),f2(x80351)),x80353))+~P1(f328(f328(f242(x80351),x80352),f328(f328(f286(x80351),x80354),x80353)))+P1(f328(f328(f242(x80351),f328(f328(f81(x80351),x80352),x80353)),x80354)) % 154.70/154.57 [8037]~P62(x80371)+~P1(f328(f328(f243(x80371),f2(x80371)),x80373))+~P1(f328(f328(f242(x80371),x80372),f328(f328(f81(x80371),x80374),x80373)))+P1(f328(f328(f242(x80371),f328(f328(f286(x80371),x80372),x80373)),x80374)) % 154.70/154.57 [8038]~P63(x80381)+~P1(f328(f328(f243(x80381),f2(x80381)),x80383))+~P1(f328(f328(f242(x80381),x80382),f328(f328(f81(x80381),x80384),x80383)))+P1(f328(f328(f242(x80381),f328(f328(f286(x80381),x80382),x80383)),x80384)) % 154.70/154.57 [8175]~P62(x81751)+~P1(f328(f328(f243(x81751),f2(x81751)),x81754))+P1(f328(f328(f243(x81751),x81752),f328(f328(f81(x81751),x81753),x81754)))+~P1(f328(f328(f243(x81751),f328(f328(f286(x81751),x81752),x81754)),x81753)) % 154.70/154.57 [8177]~P62(x81771)+~P1(f328(f328(f243(x81771),f2(x81771)),x81774))+P1(f328(f328(f243(x81771),x81772),f328(f328(f286(x81771),x81773),x81774)))+~P1(f328(f328(f243(x81771),f328(f328(f81(x81771),x81772),x81774)),x81773)) % 154.70/154.57 [8178]~P63(x81781)+~P1(f328(f328(f243(x81781),f2(x81781)),x81784))+P1(f328(f328(f243(x81781),x81782),f328(f328(f81(x81781),x81783),x81784)))+~P1(f328(f328(f243(x81781),f328(f328(f286(x81781),x81782),x81784)),x81783)) % 154.70/154.57 [8179]~P63(x81791)+~P1(f328(f328(f243(x81791),f2(x81791)),x81794))+P1(f328(f328(f243(x81791),x81792),f328(f328(f286(x81791),x81793),x81794)))+~P1(f328(f328(f243(x81791),f328(f328(f81(x81791),x81792),x81794)),x81793)) % 154.70/154.57 [8180]~P62(x81801)+~P1(f328(f328(f243(x81801),f2(x81801)),x81804))+P1(f328(f328(f242(x81801),x81802),f328(f328(f81(x81801),x81803),x81804)))+~P1(f328(f328(f242(x81801),f328(f328(f286(x81801),x81802),x81804)),x81803)) % 154.70/154.57 [8182]~P62(x81821)+~P1(f328(f328(f243(x81821),f2(x81821)),x81824))+P1(f328(f328(f242(x81821),x81822),f328(f328(f286(x81821),x81823),x81824)))+~P1(f328(f328(f242(x81821),f328(f328(f81(x81821),x81822),x81824)),x81823)) % 154.70/154.57 [8183]~P63(x81831)+~P1(f328(f328(f243(x81831),f2(x81831)),x81834))+P1(f328(f328(f242(x81831),x81832),f328(f328(f81(x81831),x81833),x81834)))+~P1(f328(f328(f242(x81831),f328(f328(f286(x81831),x81832),x81834)),x81833)) % 154.70/154.57 [8184]~P63(x81841)+~P1(f328(f328(f243(x81841),f2(x81841)),x81844))+P1(f328(f328(f242(x81841),x81842),f328(f328(f286(x81841),x81843),x81844)))+~P1(f328(f328(f242(x81841),f328(f328(f81(x81841),x81842),x81844)),x81843)) % 154.70/154.57 [8350]~P63(x83501)+~P1(f328(f328(f243(x83501),x83503),f2(x83501)))+~P1(f328(f328(f243(x83501),f328(f328(f286(x83501),x83504),x83503)),x83502))+P1(f328(f328(f243(x83501),f328(f328(f81(x83501),x83502),x83503)),x83504)) % 154.70/154.57 [8351]~P63(x83511)+~P1(f328(f328(f243(x83511),x83513),f2(x83511)))+~P1(f328(f328(f243(x83511),f328(f328(f81(x83511),x83514),x83513)),x83512))+P1(f328(f328(f243(x83511),f328(f328(f286(x83511),x83512),x83513)),x83514)) % 154.70/154.57 [8352]~P63(x83521)+~P1(f328(f328(f243(x83521),x83523),f2(x83521)))+~P1(f328(f328(f242(x83521),f328(f328(f286(x83521),x83524),x83523)),x83522))+P1(f328(f328(f242(x83521),f328(f328(f81(x83521),x83522),x83523)),x83524)) % 154.70/154.57 [8353]~P63(x83531)+~P1(f328(f328(f243(x83531),x83533),f2(x83531)))+~P1(f328(f328(f242(x83531),f328(f328(f81(x83531),x83534),x83533)),x83532))+P1(f328(f328(f242(x83531),f328(f328(f286(x83531),x83532),x83533)),x83534)) % 154.70/154.57 [8363]~P1(f328(x83631,x83634))+~P1(f328(f328(f243(a875),x83632),f328(f328(f81(a875),x83633),f328(a116,x83634))))+P1(f328(x83631,f328(f328(f38(a875),x83632),x83633)))+~P1(f328(f328(f242(a875),f328(f328(f81(a875),x83633),x83634)),x83632)) % 154.70/154.57 [8579]~P99(x85791)+~P1(f328(f61(x85791),x85794))+~P1(f328(f328(f330(x85791),x85792),x85794))+P1(f328(f328(f242(x85791),f328(f328(f114(x85791),x85792),x85793)),f328(f328(f64(x85791,x85791,f114(x85791)),x85793),x85794))) % 154.70/154.57 [8580]~P105(x85801)+~P1(f328(f61(x85801),x85804))+~P1(f328(f328(f330(x85801),x85802),x85804))+P1(f328(f328(f242(x85801),f328(f328(f241(x85801),x85802),x85803)),f328(f328(f64(x85801,x85801,f241(x85801)),x85803),x85804))) % 154.70/154.57 [8724]~P1(f328(f61(x87241),x87242))+E(f328(f37(x87241),f328(f328(f22(f882(x87241,a870)),x87242),f328(f328(f306(x87241),x87243),x87244))),f328(f328(f22(a875),f328(f37(x87241),f328(f328(f22(f882(x87241,a870)),x87242),x87244))),f78(a875)))+P1(f328(f328(f330(x87241),x87243),x87244))+~P1(f328(f328(f330(x87241),x87243),x87242)) % 154.70/154.57 [8794]E(f328(f328(f80(a1),f419(x87941,x87942,x87943,x87944)),f420(x87941,x87942,x87943,x87944)),x87944)+~P1(f328(f328(f243(a1),f2(a1)),x87943))+~P1(f328(f328(f242(a1),x87944),x87941))+P1(f328(f328(f242(a1),f328(f328(f22(a1),x87944),x87943)),x87941)) % 154.70/154.57 [8795]E(f328(f328(f80(a1),f427(x87951,x87952,x87953,x87954)),f428(x87951,x87952,x87953,x87954)),x87954)+~P1(f328(f328(f243(a1),f2(a1)),x87953))+~P1(f328(f328(f243(a1),x87954),x87951))+P1(f328(f328(f243(a1),f328(f328(f22(a1),x87954),x87953)),x87951)) % 154.70/154.57 [9005]~P1(f328(f328(f243(a1),f2(a1)),x90053))+~P1(f328(f328(f242(a1),x90054),x90051))+P1(f328(f328(f330(a1),f419(x90051,x90052,x90053,x90054)),x90052))+P1(f328(f328(f242(a1),f328(f328(f22(a1),x90054),x90053)),x90051)) % 154.70/154.57 [9006]~P1(f328(f328(f243(a1),f2(a1)),x90063))+~P1(f328(f328(f243(a1),x90064),x90061))+P1(f328(f328(f330(a1),f427(x90061,x90062,x90063,x90064)),x90062))+P1(f328(f328(f243(a1),f328(f328(f22(a1),x90064),x90063)),x90061)) % 154.70/154.57 [9094]~P1(f328(f328(f243(a1),f2(a1)),x90942))+~P1(f328(f328(f243(a1),x90941),x90943))+P1(f328(f328(f330(a1),f428(x90943,x90944,x90942,x90941)),f299(a1,f78(a1),x90942)))+P1(f328(f328(f243(a1),f328(f328(f22(a1),x90941),x90942)),x90943)) % 154.70/154.57 [9095]~P1(f328(f328(f243(a1),f2(a1)),x90952))+~P1(f328(f328(f242(a1),x90951),x90953))+P1(f328(f328(f330(a1),f420(x90953,x90954,x90952,x90951)),f299(a1,f78(a1),x90952)))+P1(f328(f328(f242(a1),f328(f328(f22(a1),x90951),x90952)),x90953)) % 154.70/154.57 [9111]~P1(f328(f328(f243(a1),f2(a1)),x91113))+~P1(f328(f328(f242(a1),f2(a1)),x91114))+~P1(f328(f328(f243(a1),x91114),x91111))+P1(f328(f328(f242(a1),f2(a1)),f328(f328(f80(a1),f328(f328(f81(a1),x91111),f44(a1,x91112,x91113))),x91114))) % 154.70/154.57 [9175]~P100(x91751)+~P1(f328(f61(x91751),x91754))+~P1(f328(f328(f242(x91751),x91752),f527(x91753,x91752,x91754,x91751)))+P1(f328(f328(f242(x91751),f328(f328(f105(x91751),x91752),x91753)),f328(f328(f64(x91751,x91751,f105(x91751)),x91753),x91754))) % 154.70/154.57 [9176]~P105(x91761)+~P1(f328(f61(x91761),x91764))+~P1(f328(f328(f242(x91761),x91762),f518(x91763,x91762,x91764,x91761)))+P1(f328(f328(f242(x91761),f328(f328(f240(x91761),x91762),x91763)),f328(f328(f64(x91761,x91761,f240(x91761)),x91763),x91764))) % 154.70/154.57 [9191]~P1(f328(f328(f242(a1),x91914),f2(a1)))+~P1(f328(f328(f243(a1),f2(a1)),x91912))+~P1(f328(f328(f243(a1),x91911),x91914))+P1(f328(f328(f243(a1),f328(f328(f81(a1),x91911),x91912)),f328(f328(f80(a1),f328(f328(f81(a1),x91911),f44(a1,x91913,x91912))),x91914))) % 154.70/154.57 [9213]P1(f328(f61(x92131),x92132))+~P1(f328(f61(x92131),x92133))+~P1(f328(f328(f330(f882(x92131,a870)),x92132),f328(f328(f60(x92131),x92133),x92134)))+~P1(f328(f328(f242(f882(f881(x92131,x92131),a870)),x92134),f328(f328(f265(x92131,x92131),x92133),f328(f16(f882(x92131,a870),x92131),x92133)))) % 154.70/154.57 [9241]~P105(x92411)+~P1(f328(f61(x92411),x92414))+P1(f328(f328(f330(x92411),f518(x92412,x92413,x92414,x92411)),x92414))+P1(f328(f328(f242(x92411),f328(f328(f240(x92411),x92413),x92412)),f328(f328(f64(x92411,x92411,f240(x92411)),x92412),x92414))) % 154.70/154.57 [9242]~P100(x92421)+~P1(f328(f61(x92421),x92424))+P1(f328(f328(f330(x92421),f527(x92422,x92423,x92424,x92421)),x92424))+P1(f328(f328(f242(x92421),f328(f328(f105(x92421),x92423),x92422)),f328(f328(f64(x92421,x92421,f105(x92421)),x92422),x92424))) % 154.70/154.57 [9638]~P1(f328(f61(x96382),x96384))+~P1(f328(f61(x96381),x96383))+~P1(f328(f328(f242(a875),f328(f37(x96382),x96384)),f328(f37(x96381),x96383)))+P1(f328(f328(f242(f882(x96381,a870)),f328(f307(x96382,x96381,f442(x96383,x96381,x96384,x96382)),x96384)),x96383)) % 154.70/154.57 [9288]~P1(f328(f328(f330(x92881),x92882),x92884))+P1(f328(f328(f330(x92881),x92882),x92883))+~P1(f328(f328(f243(f882(x92881,a870)),x92884),f328(f328(f306(x92881),x92882),x92883)))+P1(f328(f328(f243(f882(x92881,a870)),f328(f328(f22(f882(x92881,a870)),x92884),f328(f328(f306(x92881),x92882),f192(f882(x92881,a870))))),x92883)) % 154.70/154.57 [9449]~P1(f328(f328(f330(x94491),x94492),x94494))+P1(f328(f328(f330(x94491),x94492),x94493))+P1(f328(f328(f243(f882(x94491,a870)),x94494),f328(f328(f306(x94491),x94492),x94493)))+~P1(f328(f328(f243(f882(x94491,a870)),f328(f328(f22(f882(x94491,a870)),x94494),f328(f328(f306(x94491),x94492),f192(f882(x94491,a870))))),x94493)) % 154.70/154.57 [9478]P1(f328(f328(f330(x94781),x94782),x94783))+~P1(f328(f328(f242(f882(x94781,a870)),x94784),x94783))+P1(f328(f328(f243(f882(x94781,a870)),x94784),f328(f328(f306(x94781),x94782),x94783)))+~P1(f328(f328(f243(f882(x94781,a870)),f328(f328(f22(f882(x94781,a870)),x94784),f328(f328(f306(x94781),x94782),f192(f882(x94781,a870))))),x94783)) % 154.70/154.57 [9483]~P1(f328(f328(f330(x94831),x94833),x94832))+~P1(f328(f328(f243(f882(x94831,a870)),x94832),x94834))+P1(f328(f328(f243(f882(x94831,a870)),x94832),f328(f328(f306(x94831),x94833),x94834)))+~P1(f328(f328(f243(f882(x94831,a870)),f328(f328(f22(f882(x94831,a870)),x94832),f328(f328(f306(x94831),x94833),f192(f882(x94831,a870))))),x94834)) % 154.70/154.57 [9496]~P1(f328(f328(f242(f882(x94961,a870)),x94962),x94964))+~P1(f328(f328(f243(f882(x94961,a870)),x94962),x94964))+P1(f328(f328(f243(f882(x94961,a870)),x94962),f328(f328(f306(x94961),x94963),x94964)))+~P1(f328(f328(f243(f882(x94961,a870)),f328(f328(f22(f882(x94961,a870)),x94962),f328(f328(f306(x94961),x94963),f192(f882(x94961,a870))))),x94964)) % 154.70/154.57 [9541]~P107(x95412)+~P59(x95411)+~P1(f328(f328(f242(f882(x95411,x95412)),x95413),x95414))+P1(f328(f58(x95411),f328(f328(f18(x95411,x95412,a870),f328(f328(f8(x95412,f882(x95412,a870),x95411),f242(x95412)),x95413)),x95414))) % 154.70/154.57 [9686]~P107(x96862)+~P59(x96861)+P1(f328(f328(f242(f882(x96861,x96862)),x96863),x96864))+~P1(f328(f58(x96861),f328(f328(f18(x96861,x96862,a870),f328(f328(f8(x96862,f882(x96862,a870),x96861),f242(x96862)),x96863)),x96864))) % 154.70/154.57 [9856]E(f328(f328(f162(x98561),f328(f328(f162(f876(x98561)),f178(x98561,x98562)),x98563)),x98564),f328(f328(f162(x98561),f328(f328(f162(f876(x98561)),x98562),x98564)),x98563))+~P1(f328(f328(f243(a875),x98563),f328(f193(f876(f876(x98561))),f178(x98561,x98562))))+~P16(a875,f328(f166(a875),f328(f328(f151(f876(x98561),a875),f193(f876(x98561))),x98562)))+~P1(f328(f328(f243(a875),x98564),f328(f193(f876(f876(x98561))),f328(f133(f876(x98561),f328(f328(f8(a875,a870,f876(x98561)),f328(f243(a875),x98563)),f193(f876(x98561)))),x98562)))) % 154.70/154.57 [9885]~P1(f328(f328(f330(f881(a875,a875)),x98854),x98851))+~P1(f328(f328(f330(f881(f881(a875,a875),f881(a875,a875))),f328(f328(f263(f881(a875,a875),f881(a875,a875)),x98854),x98852)),a35))+~P1(f328(f328(f330(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f328(f328(f263(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),x98851),x98853)),a68))+P1(f328(f328(f330(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f328(f328(f263(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),x98851),f328(f328(f306(f881(a875,a875)),x98852),x98853))),a68)) % 154.70/154.57 [9886]~P1(f328(f328(f330(f881(a875,a875)),x98864),x98861))+~P1(f328(f328(f330(f881(f881(a875,a875),f881(a875,a875))),f328(f328(f263(f881(a875,a875),f881(a875,a875)),x98864),x98862)),a70))+~P1(f328(f328(f330(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f328(f328(f263(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),x98861),x98863)),a71))+P1(f328(f328(f330(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f328(f328(f263(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),x98861),f328(f328(f306(f881(a875,a875)),x98862),x98863))),a71)) % 154.70/154.57 [9770]~P107(x97702)+~P59(x97701)+~P1(f328(f328(f243(f882(x97701,x97702)),x97703),x97704))+P1(f328(f57(x97701),f328(f328(f8(a870,a870,x97701),a323),f328(f328(f18(x97701,x97702,a870),f328(f328(f8(x97702,f882(x97702,a870),x97701),a325),x97703)),x97704)))) % 154.70/154.57 [9899]~P1(f328(f328(f330(f881(a875,a875)),x98994),x98993))+~P1(f328(f328(f330(f881(f881(a875,a875),f881(a875,a875))),f328(f328(f263(f881(a875,a875),f881(a875,a875)),x98991),x98994)),a35))+~P1(f328(f328(f330(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f328(f328(f263(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),x98992),x98993)),a36))+P1(f328(f328(f330(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f328(f328(f263(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),f328(f328(f306(f881(a875,a875)),x98991),x98992)),x98993)),a36)) % 154.70/154.57 [9900]~P1(f328(f328(f330(f881(a875,a875)),x99004),x99003))+~P1(f328(f328(f330(f881(f881(a875,a875),f881(a875,a875))),f328(f328(f263(f881(a875,a875),f881(a875,a875)),x99001),x99004)),a70))+~P1(f328(f328(f330(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f328(f328(f263(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),x99002),x99003)),a69))+P1(f328(f328(f330(f881(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870))),f328(f328(f263(f882(f881(a875,a875),a870),f882(f881(a875,a875),a870)),f328(f328(f306(f881(a875,a875)),x99001),x99002)),x99003)),a69)) % 154.70/154.57 [6009]~P7(x60094,x60091)+~P1(f328(f328(x60091,x60092),x60095))+P1(f328(f328(x60091,x60092),x60093))+~P1(f328(f328(x60091,x60095),x60093)) % 154.70/154.57 [5276]~P65(x52765)+E(x52761,x52762)+~E(x52763,x52764)+~E(f328(f328(f22(x52765),x52763),x52764),f328(f328(f22(x52765),x52761),x52762)) % 154.70/154.57 [6117]~P19(x61175,x61171,x61173)+E(f328(f328(x61171,x61172),f328(x61173,x61174)),f328(x61173,x61174))+~P1(f328(f61(x61175),x61174))+~P1(f328(f328(f330(x61175),x61172),x61174)) % 154.70/154.57 [6314]~P81(x63141)+~E(f328(f328(f22(x63141),x63144),x63145),f328(f328(f22(x63141),x63142),x63143))+~P1(f328(f328(f243(x63141),x63144),x63145))+P1(f328(f328(f243(x63141),x63142),x63143)) % 154.70/154.57 [6316]~P81(x63161)+~E(f328(f328(f22(x63161),x63164),x63165),f328(f328(f22(x63161),x63162),x63163))+~P1(f328(f328(f242(x63161),x63164),x63165))+P1(f328(f328(f242(x63161),x63162),x63163)) % 154.70/154.57 [7275]~E(x72752,f328(f328(f148(x72751),x72754),x72755))+P1(f328(f328(f330(f876(x72751)),x72752),f158(x72751,x72753)))+~P1(f328(f328(f330(f876(x72751)),x72755),f158(x72751,x72753)))+~P1(f328(f328(f330(x72751),x72754),x72753)) % 154.70/154.57 [7693]~E(f328(f193(f876(x76931)),x76933),f328(f193(f876(x76932)),x76934))+~E(f328(f328(f151(f881(x76931,x76932),x76932),f266(x76931,x76932)),x76935),x76934)+~E(f328(f328(f151(f881(x76931,x76932),x76931),f262(x76931,x76932)),x76935),x76933)+E(f328(f328(f180(x76931,x76932),x76933),x76934),x76935) % 154.70/154.57 [8026]~P107(x80261)+P1(f328(f328(f243(f882(x80261,a870)),f299(x80261,x80262,x80263)),f299(x80261,x80264,x80265)))+~P1(f328(f328(f242(x80261),x80264),x80265))+P1(f328(f328(f242(x80261),x80262),x80263)) % 154.70/154.57 [8123]~P107(x81231)+P1(f328(f328(f242(f882(x81231,a870)),f299(x81231,x81232,x81233)),f299(x81231,x81234,x81235)))+~P1(f328(f328(f242(x81231),x81233),x81235))+~P1(f328(f328(f242(x81231),x81234),x81232)) % 154.70/154.57 [8258]~P105(x82581)+P1(f328(f328(f242(x82581),x82582),x82583))+P1(f328(f328(f242(x82581),x82584),x82583))+~P1(f328(f328(f242(f882(x82581,a870)),f328(f298(x82581,x82583),x82582)),f328(f298(x82581,x82584),x82585))) % 154.70/154.57 [8259]~P105(x82591)+P1(f328(f328(f242(x82591),x82592),x82593))+P1(f328(f328(f242(x82591),x82592),x82594))+~P1(f328(f328(f242(f882(x82591,a870)),f328(f298(x82591,x82593),x82592)),f328(f298(x82591,x82595),x82594))) % 154.70/154.57 [8490]~P107(x84901)+~P1(f328(f328(f243(f882(x84901,a870)),f299(x84901,x84904,x84902)),f299(x84901,x84905,x84903)))+P1(f328(f328(f242(x84901),x84902),x84903))+~P1(f328(f328(f242(x84901),x84904),x84902)) % 154.70/154.57 [8491]~P107(x84911)+~P1(f328(f328(f242(f882(x84911,a870)),f299(x84911,x84914,x84912)),f299(x84911,x84915,x84913)))+P1(f328(f328(f242(x84911),x84912),x84913))+~P1(f328(f328(f242(x84911),x84914),x84912)) % 154.70/154.57 [8492]~P107(x84921)+~P1(f328(f328(f243(f882(x84921,a870)),f299(x84921,x84923,x84924)),f299(x84921,x84922,x84925)))+P1(f328(f328(f242(x84921),x84922),x84923))+~P1(f328(f328(f242(x84921),x84923),x84924)) % 154.70/154.57 [8493]~P107(x84931)+~P1(f328(f328(f242(f882(x84931,a870)),f299(x84931,x84933,x84934)),f299(x84931,x84932,x84935)))+P1(f328(f328(f242(x84931),x84932),x84933))+~P1(f328(f328(f242(x84931),x84933),x84934)) % 154.70/154.57 [6008]~P19(x60082,x60085,x60083)+E(x60081,f192(f882(x60082,a870)))+~P1(f328(f61(x60082),x60081))+E(f328(x60083,f328(f328(f306(x60082),x60084),x60081)),f328(f328(x60085,x60084),f328(x60083,x60081))) % 154.70/154.57 [6778]~E(x67781,x67782)+~E(f328(f328(f105(f882(x67783,a870)),x67784),x67785),f192(f882(x67783,a870)))+~P1(f328(f328(f330(x67783),x67782),x67785))+~P1(f328(f328(f330(x67783),x67781),x67784)) % 154.70/154.57 [6860]~P20(x68602,x68605,x68601)+~P1(f328(f61(x68602),x68604))+E(f328(x68601,f328(f328(f306(x68602),x68603),x68604)),f328(f328(f64(x68602,x68602,x68605),x68603),x68604))+P1(f328(f328(f330(x68602),x68603),x68604)) % 154.70/154.57 [6926]~P66(x69262)+~P1(f328(f61(x69261),x69265))+E(f328(f328(f6(x69261,x69262),x69263),f328(f328(f306(x69261),x69264),x69265)),f328(f328(f80(x69262),f328(x69263,x69264)),f328(f328(f6(x69261,x69262),x69263),x69265)))+P1(f328(f328(f330(x69261),x69264),x69265)) % 154.70/154.57 [6928]~P73(x69282)+~P1(f328(f61(x69281),x69285))+E(f328(f328(f9(x69281,x69282),x69283),f328(f328(f306(x69281),x69284),x69285)),f328(f328(f81(x69282),f328(x69283,x69284)),f328(f328(f9(x69281,x69282),x69283),x69285)))+P1(f328(f328(f330(x69281),x69284),x69285)) % 154.70/154.57 [7431]~P20(x74312,x74315,x74311)+~P1(f328(f61(x74312),x74314))+E(f328(x74311,f328(f328(f306(x74312),x74313),x74314)),x74313)+~E(f328(f328(f22(f882(x74312,a870)),x74314),f328(f328(f306(x74312),x74313),f192(f882(x74312,a870)))),f192(f882(x74312,a870))) % 154.70/154.57 [7799]~P84(x77991)+~P1(f328(f328(f243(x77991),x77993),x77995))+~P1(f328(f328(f243(x77991),x77992),x77994))+P1(f328(f328(f243(x77991),f328(f328(f80(x77991),x77992),x77993)),f328(f328(f80(x77991),x77994),x77995))) % 154.70/154.57 [7800]~P84(x78001)+~P1(f328(f328(f242(x78001),x78002),x78004))+~P1(f328(f328(f243(x78001),x78003),x78005))+P1(f328(f328(f243(x78001),f328(f328(f80(x78001),x78002),x78003)),f328(f328(f80(x78001),x78004),x78005))) % 154.70/154.57 [7801]~P84(x78011)+~P1(f328(f328(f242(x78011),x78013),x78015))+~P1(f328(f328(f243(x78011),x78012),x78014))+P1(f328(f328(f243(x78011),f328(f328(f80(x78011),x78012),x78013)),f328(f328(f80(x78011),x78014),x78015))) % 154.70/154.57 [7802]~P99(x78021)+~P1(f328(f328(f242(x78021),x78023),x78025))+~P1(f328(f328(f242(x78021),x78022),x78024))+P1(f328(f328(f242(x78021),f328(f328(f114(x78021),x78022),x78023)),f328(f328(f114(x78021),x78024),x78025))) % 154.70/154.57 [7803]~P100(x78031)+~P1(f328(f328(f242(x78031),x78033),x78035))+~P1(f328(f328(f242(x78031),x78032),x78034))+P1(f328(f328(f242(x78031),f328(f328(f105(x78031),x78032),x78033)),f328(f328(f105(x78031),x78034),x78035))) % 154.70/154.57 [7804]~P82(x78041)+~P1(f328(f328(f242(x78041),x78043),x78045))+~P1(f328(f328(f242(x78041),x78042),x78044))+P1(f328(f328(f242(x78041),f328(f328(f80(x78041),x78042),x78043)),f328(f328(f80(x78041),x78044),x78045))) % 154.70/154.57 [7805]~P105(x78051)+~P1(f328(f328(f242(x78051),x78053),x78055))+~P1(f328(f328(f242(x78051),x78052),x78054))+P1(f328(f328(f242(x78051),f328(f328(f240(x78051),x78052),x78053)),f328(f328(f240(x78051),x78054),x78055))) % 154.70/154.57 [7806]~P105(x78061)+~P1(f328(f328(f242(x78061),x78063),x78065))+~P1(f328(f328(f242(x78061),x78062),x78064))+P1(f328(f328(f242(x78061),f328(f328(f241(x78061),x78062),x78063)),f328(f328(f241(x78061),x78064),x78065))) % 154.70/154.57 [7944]~P141(x79445)+E(x79441,x79442)+E(x79443,x79444)+~E(f328(f328(f80(x79445),f328(f328(f81(x79445),x79443),x79441)),f328(f328(f81(x79445),x79444),x79442)),f328(f328(f80(x79445),f328(f328(f81(x79445),x79443),x79442)),f328(f328(f81(x79445),x79444),x79441))) % 154.70/154.57 [8077]P29(x80771,x80772,x80773)+~P30(x80771,x80774,x80775)+~P29(x80771,x80772,f605(x80775,x80774,x80771,x80772))+~P1(f328(f328(f330(f874(x80771)),x80773),x80775)) % 154.70/154.57 [8140]~P1(f328(x81401,x81403))+~P1(f328(f328(f328(a198,x81402),x81403),x81405))+~P1(f328(f328(f328(a198,f32(x81401,x81402)),x81405),x81404))+P1(f328(f328(f328(a198,f32(x81401,x81402)),x81403),x81404)) % 154.70/154.57 [8147]~P105(x81474)+~P1(f328(f134(x81471),x81473))+P1(f328(f328(f330(x81471),x81472),f328(f170(x81471),x81473)))+P1(f328(f134(x81471),f328(f328(f145(x81471,x81474,x81475),x81472),x81473))) % 154.70/154.57 [8303]~P65(x83031)+E(f328(f328(f22(x83031),f328(f328(f6(a875,x83031),x83032),f328(f298(a875,x83033),x83034))),f328(f328(f6(a875,x83031),x83032),f328(f298(a875,x83033),x83035))),f328(f328(f6(a875,x83031),x83032),f328(f298(a875,x83035),x83034)))+~P1(f328(f328(f242(a875),x83035),x83034))+~P1(f328(f328(f242(a875),x83033),x83035)) % 154.70/154.57 [8304]~P66(x83041)+E(f328(f328(f80(x83041),f328(f328(f6(a875,x83041),x83042),f328(f298(a875,x83043),x83044))),f328(f328(f6(a875,x83041),x83042),f328(f298(a875,x83044),x83045))),f328(f328(f6(a875,x83041),x83042),f328(f298(a875,x83043),x83045)))+~P1(f328(f328(f242(a875),x83044),x83045))+~P1(f328(f328(f242(a875),x83043),x83044)) % 154.70/154.57 [8636]~P61(x86362)+E(x86361,f2(x86362))+E(x86363,f2(x86362))+E(f328(f328(f286(x86362),f328(f328(f22(x86362),f328(f328(f81(x86362),x86364),x86361)),f328(f328(f81(x86362),x86365),x86363))),f328(f328(f81(x86362),x86363),x86361)),f328(f328(f22(x86362),f328(f328(f286(x86362),x86364),x86363)),f328(f328(f286(x86362),x86365),x86361))) % 154.70/154.57 [8637]~P61(x86372)+E(x86371,f2(x86372))+E(x86373,f2(x86372))+E(f328(f328(f286(x86372),f328(f328(f80(x86372),f328(f328(f81(x86372),x86374),x86371)),f328(f328(f81(x86372),x86375),x86373))),f328(f328(f81(x86372),x86373),x86371)),f328(f328(f80(x86372),f328(f328(f286(x86372),x86374),x86373)),f328(f328(f286(x86372),x86375),x86371))) % 154.70/154.57 [8649]~E(x86492,f328(x86493,x86491))+E(x86491,f437(x86492,x86493,x86494,x86495))+~P27(x86495,x86494,x86493,f251(f882(x86495,a870)))+~P1(f328(f328(f330(x86494),x86492),f328(f307(x86495,x86494,x86493),f251(f882(x86495,a870))))) % 154.70/154.57 [8843]~P121(x88431)+~P1(f328(f328(f243(x88431),f328(f75(x88431),x88432)),x88434))+P1(f328(f328(f243(x88431),f328(f328(f81(x88431),f328(f75(x88431),x88432)),f328(f75(x88431),x88433))),f328(f328(f81(x88431),x88434),x88435)))+~P1(f328(f328(f243(x88431),f328(f75(x88431),x88433)),x88435)) % 154.70/154.57 [8860]~P30(x88601,x88605,x88604)+P29(x88601,x88602,x88603)+P1(f328(f328(f330(f874(x88601)),f605(x88604,x88605,x88601,x88602)),x88605))+~P1(f328(f328(f330(f874(x88601)),x88603),x88604)) % 154.70/154.57 [8965]~P27(x89651,x89653,x89655,x89652)+~P1(f328(f61(x89653),x89654))+P1(f328(f328(f242(a875),f328(f37(x89651),x89652)),f328(f37(x89653),x89654)))+~P1(f328(f328(f242(f882(x89653,a870)),f328(f307(x89651,x89653,x89655),x89652)),x89654)) % 154.70/154.57 [9034]~P66(x90342)+~P27(x90341,x90341,x90344,x90345)+~P1(f328(f61(x90341),x90345))+E(f328(f328(f6(x90341,x90342),f328(f73(x90341,x90342,x90341,x90343),x90344)),x90345),f328(f328(f6(x90341,x90342),x90343),f328(f307(x90341,x90341,x90344),x90345))) % 154.70/154.57 [9035]~P73(x90352)+~P27(x90351,x90351,x90354,x90355)+~P1(f328(f61(x90351),x90355))+E(f328(f328(f9(x90351,x90352),f328(f73(x90351,x90352,x90351,x90353),x90354)),x90355),f328(f328(f9(x90351,x90352),x90353),f328(f307(x90351,x90351,x90354),x90355))) % 154.70/154.57 [9152]~P39(x91521,x91522)+~P1(f328(f328(f330(x91521),x91523),x91524))+~P1(f328(f328(f330(x91521),x91525),x91524))+~P1(f328(f328(f330(f881(x91521,x91521)),f328(f328(f263(x91521,x91521),x91525),f633(x91522,x91521,x91524))),x91522)) % 154.70/154.57 [9190]~P27(x91902,x91903,x91905,x91901)+E(x91901,f192(f882(x91902,a870)))+E(f328(f307(x91903,x91902,f439(x91904,x91903,x91902,x91901)),x91904),x91901)+~P1(f328(f328(f242(f882(x91903,a870)),f328(f307(x91902,x91903,x91905),x91901)),x91904)) % 154.70/154.57 [9667]~P5(x96675)+~P105(x96675)+P1(f328(f328(f330(x96671),f855(x96672,x96673,x96671,x96674,x96675)),x96673))+~P1(f328(f328(f243(x96675),x96674),f328(f328(f41(x96671,x96675),x96673),x96672))) % 154.70/154.57 [9672]~P5(x96721)+~P105(x96721)+P1(f328(f328(f243(x96721),x96722),f328(x96723,f855(x96723,x96724,x96725,x96722,x96721))))+~P1(f328(f328(f243(x96721),x96722),f328(f328(f41(x96725,x96721),x96724),x96723))) % 154.70/154.57 [9750]~P70(x97501)+~P1(f328(f66(x97501,x97501,f81(x97501),x97502,x97503),x97505))+P1(f328(f328(f330(x97501),x97502),x97503))+P1(f328(f66(x97501,x97501,f81(x97501),x97504,f328(f328(f306(x97501),x97502),x97503)),f328(f328(f81(x97501),x97504),x97505))) % 154.70/154.57 [9967]~P66(x99672)+~P1(f328(f61(x99671),x99675))+E(f328(f328(f6(x99671,x99672),f328(f328(f7(x99671,x99672,x99672),f328(f328(f18(x99671,x99672,f882(x99672,x99672)),f328(f328(f8(a870,f882(x99672,f882(x99672,x99672)),x99671),f100(x99672)),f328(a325,x99673))),x99674)),f2(x99672))),x99675),f2(x99672))+P1(f328(f328(f330(x99671),x99673),x99675)) % 154.70/154.57 [9968]~P73(x99682)+~P1(f328(f61(x99681),x99685))+E(f328(f328(f9(x99681,x99682),f328(f328(f7(x99681,x99682,x99682),f328(f328(f18(x99681,x99682,f882(x99682,x99682)),f328(f328(f8(a870,f882(x99682,f882(x99682,x99682)),x99681),f100(x99682)),f328(a325,x99683))),x99684)),f78(x99682))),x99685),f78(x99682))+P1(f328(f328(f330(x99681),x99683),x99685)) % 154.70/154.57 [9969]~P66(x99692)+~P1(f328(f61(x99691),x99695))+E(f328(f328(f6(x99691,x99692),f328(f328(f7(x99691,x99692,x99692),f328(f328(f18(x99691,x99692,f882(x99692,x99692)),f328(f328(f8(a870,f882(x99692,f882(x99692,x99692)),x99691),f100(x99692)),f328(a325,x99693))),x99694)),f2(x99692))),x99695),f328(x99694,x99693))+~P1(f328(f328(f330(x99691),x99693),x99695)) % 154.70/154.57 [9970]~P73(x99702)+~P1(f328(f61(x99701),x99705))+E(f328(f328(f9(x99701,x99702),f328(f328(f7(x99701,x99702,x99702),f328(f328(f18(x99701,x99702,f882(x99702,x99702)),f328(f328(f8(a870,f882(x99702,f882(x99702,x99702)),x99701),f100(x99702)),f328(a325,x99703))),x99704)),f78(x99702))),x99705),f328(x99704,x99703))+~P1(f328(f328(f330(x99701),x99703),x99705)) % 154.70/154.57 [10025]~P66(x100252)+~P1(f328(f61(x100251),x100255))+E(f328(f328(f6(x100251,x100252),f328(f328(f7(x100251,x100252,x100252),f328(f328(f18(x100251,x100252,f882(x100252,x100252)),f328(f328(f8(a870,f882(x100252,f882(x100252,x100252)),x100251),f100(x100252)),f328(f328(f7(x100251,x100251,a870),a325),x100253))),x100254)),f2(x100252))),x100255),f2(x100252))+P1(f328(f328(f330(x100251),x100253),x100255)) % 154.70/154.57 [10026]~P73(x100262)+~P1(f328(f61(x100261),x100265))+E(f328(f328(f9(x100261,x100262),f328(f328(f7(x100261,x100262,x100262),f328(f328(f18(x100261,x100262,f882(x100262,x100262)),f328(f328(f8(a870,f882(x100262,f882(x100262,x100262)),x100261),f100(x100262)),f328(f328(f7(x100261,x100261,a870),a325),x100263))),x100264)),f78(x100262))),x100265),f78(x100262))+P1(f328(f328(f330(x100261),x100263),x100265)) % 154.70/154.57 [10028]~P66(x100282)+~P1(f328(f61(x100281),x100285))+E(f328(f328(f6(x100281,x100282),f328(f328(f7(x100281,x100282,x100282),f328(f328(f18(x100281,x100282,f882(x100282,x100282)),f328(f328(f8(a870,f882(x100282,f882(x100282,x100282)),x100281),f100(x100282)),f328(f328(f7(x100281,x100281,a870),a325),x100283))),x100284)),f2(x100282))),x100285),f328(x100284,x100283))+~P1(f328(f328(f330(x100281),x100283),x100285)) % 154.70/154.57 [10029]~P73(x100292)+~P1(f328(f61(x100291),x100295))+E(f328(f328(f9(x100291,x100292),f328(f328(f7(x100291,x100292,x100292),f328(f328(f18(x100291,x100292,f882(x100292,x100292)),f328(f328(f8(a870,f882(x100292,f882(x100292,x100292)),x100291),f100(x100292)),f328(f328(f7(x100291,x100291,a870),a325),x100293))),x100294)),f78(x100292))),x100295),f328(x100294,x100293))+~P1(f328(f328(f330(x100291),x100293),x100295)) % 154.70/154.57 [7798]~P65(x77982)+~P1(f328(f61(x77981),x77984))+E(f328(f328(f6(x77981,x77982),x77983),f328(f328(f22(f882(x77981,a870)),x77984),f328(f328(f306(x77981),x77985),f192(f882(x77981,a870))))),f328(f328(f6(x77981,x77982),x77983),x77984))+P1(f328(f328(f330(x77981),x77985),x77984)) % 154.70/154.57 [8310]~P103(x83102)+~P1(f328(f61(x83101),x83104))+E(f328(f328(f6(x83101,x83102),x83103),f328(f328(f22(f882(x83101,a870)),x83104),f328(f328(f306(x83101),x83105),f192(f882(x83101,a870))))),f328(f328(f22(x83102),f328(f328(f6(x83101,x83102),x83103),x83104)),f328(x83103,x83105)))+~P1(f328(f328(f330(x83101),x83105),x83104)) % 154.70/154.57 [8311]~P65(x83112)+~P1(f328(f61(x83111),x83114))+E(f328(f328(f6(x83111,x83112),x83113),f328(f328(f22(f882(x83111,a870)),x83114),f328(f328(f306(x83111),x83115),f192(f882(x83111,a870))))),f328(f328(f22(x83112),f328(f328(f6(x83111,x83112),x83113),x83114)),f328(x83113,x83115)))+~P1(f328(f328(f330(x83111),x83115),x83114)) % 154.70/154.57 [8342]~P65(x83421)+~P1(f328(f61(x83422),x83424))+E(f328(f328(f22(x83421),f328(f328(f6(x83422,x83421),x83423),x83424)),f328(f328(f6(x83422,x83421),x83423),x83425)),f328(f328(f6(x83422,x83421),x83423),f328(f328(f22(f882(x83422,a870)),x83424),x83425)))+~P1(f328(f328(f242(f882(x83422,a870)),x83425),x83424)) % 154.70/154.57 [8362]P1(f328(f61(x83621),f328(x83622,x83623)))+~P1(f328(f61(x83624),x83625))+~P1(f328(f328(f330(x83624),x83623),x83625))+~P1(f328(f61(x83621),f328(f328(f41(x83624,f882(x83621,a870)),x83625),x83622))) % 154.70/154.57 [8806]~P8(x88061,x88065,x88064)+~E(f328(f282(x88061,x88061,x88064),f328(f328(f306(x88061),x88062),f192(f882(x88061,a870)))),f328(f282(x88061,x88061,x88064),f328(f328(f306(x88061),x88063),f192(f882(x88061,a870)))))+~P1(f328(f328(f330(x88061),x88063),x88065))+P1(f328(f328(f330(f881(x88061,x88061)),f328(f328(f263(x88061,x88061),x88062),x88063)),x88064)) % 154.70/154.57 [9109]~P1(f328(x91091,x91095))+P1(f328(x91091,f869(x91091,x91092,x91093,x91094)))+P1(f328(x91091,f860(x91091,x91092,x91093,x91094)))+~P1(f328(f328(f330(x91094),x91095),f328(f328(f114(f882(x91094,a870)),x91093),x91092))) % 154.70/154.57 [9293]~P1(f328(x92931,x92935))+P1(f328(x92931,f860(x92931,x92932,x92933,x92934)))+P1(f328(f328(f330(x92934),f869(x92931,x92932,x92933,x92934)),x92932))+~P1(f328(f328(f330(x92934),x92935),f328(f328(f114(f882(x92934,a870)),x92933),x92932))) % 154.70/154.57 [9294]~P1(f328(x92941,x92945))+P1(f328(x92941,f869(x92941,x92942,x92943,x92944)))+P1(f328(f328(f330(x92944),f860(x92941,x92942,x92943,x92944)),x92943))+~P1(f328(f328(f330(x92944),x92945),f328(f328(f114(f882(x92944,a870)),x92943),x92942))) % 154.70/154.57 [9300]P1(f328(x93001,x93002))+~P1(f328(x93001,f850(x93001,x93003,x93004,x93005)))+~P1(f328(x93001,f836(x93001,x93003,x93004,x93005)))+~P1(f328(f328(f330(x93005),x93002),f328(f328(f114(f882(x93005,a870)),x93004),x93003))) % 154.70/154.57 [9342]E(x93421,x93422)+~P1(f328(f328(f330(f881(x93423,x93423)),f328(f328(f263(x93423,x93423),x93421),x93422)),f304(x93423,x93425)))+P1(f328(f328(f330(x93423),x93421),x93424))+~P1(f328(f328(f242(f882(f881(x93423,x93423),a870)),x93425),f328(f328(f265(x93423,x93423),x93424),f328(f16(f882(x93423,a870),x93423),x93424)))) % 154.70/154.57 [9361]P1(f328(x93611,x93612))+~P1(f328(x93611,f836(x93611,x93614,x93615,x93613)))+P1(f328(f328(f330(x93613),f850(x93611,x93614,x93615,x93613)),x93614))+~P1(f328(f328(f330(x93613),x93612),f328(f328(f114(f882(x93613,a870)),x93615),x93614))) % 154.70/154.57 [9362]P1(f328(x93621,x93622))+~P1(f328(x93621,f850(x93621,x93624,x93625,x93623)))+P1(f328(f328(f330(x93623),f836(x93621,x93624,x93625,x93623)),x93625))+~P1(f328(f328(f330(x93623),x93622),f328(f328(f114(f882(x93623,a870)),x93625),x93624))) % 154.70/154.57 [9423]P1(f328(x94231,x94232))+P1(f328(f328(f330(x94233),f850(x94231,x94234,x94235,x94233)),x94234))+P1(f328(f328(f330(x94233),f836(x94231,x94234,x94235,x94233)),x94235))+~P1(f328(f328(f330(x94233),x94232),f328(f328(f114(f882(x94233,a870)),x94235),x94234))) % 154.70/154.57 [9425]~P1(f328(x94252,x94255))+P1(f328(f328(f330(x94251),f869(x94252,x94253,x94254,x94251)),x94253))+P1(f328(f328(f330(x94251),f860(x94252,x94253,x94254,x94251)),x94254))+~P1(f328(f328(f330(x94251),x94255),f328(f328(f114(f882(x94251,a870)),x94254),x94253))) % 154.70/154.57 [9574]~P8(x95741,x95745,x95744)+~P1(f328(f328(f330(x95741),x95743),x95745))+P1(f328(f328(f330(f881(x95741,x95741)),f328(f328(f263(x95741,x95741),x95742),x95743)),x95744))+~P1(f328(f328(f242(f882(x95741,a870)),f328(f282(x95741,x95741,x95744),f328(f328(f306(x95741),x95743),f192(f882(x95741,a870))))),f328(f282(x95741,x95741,x95744),f328(f328(f306(x95741),x95742),f192(f882(x95741,a870)))))) % 154.70/154.57 [9698]~P5(x96985)+~P105(x96985)+P1(f328(f328(f330(x96981),f856(x96982,x96983,x96984,x96981,x96985)),x96984))+~P1(f328(f328(f243(x96985),f328(f328(f42(x96981,x96985),x96984),x96983)),x96982)) % 154.70/154.57 [9730]~P77(x97305)+~P82(x97305)+P1(f328(f328(f330(x97301),f715(x97302,x97303,x97304,x97301,x97305)),f328(f170(x97301),x97304)))+P1(f328(f328(f242(x97305),f328(f163(x97305),f328(f328(f151(x97301,x97305),x97303),x97304))),f328(f163(x97305),f328(f328(f151(x97301,x97305),x97302),x97304)))) % 154.70/154.57 [9845]~P5(x98451)+~P105(x98451)+P1(f328(f328(f243(x98451),f328(x98452,f856(x98453,x98452,x98454,x98455,x98451))),x98453))+~P1(f328(f328(f243(x98451),f328(f328(f42(x98455,x98451),x98454),x98452)),x98453)) % 154.70/154.57 [9985]~P77(x99851)+~P82(x99851)+~P1(f328(f328(f242(x99851),f328(x99853,f715(x99855,x99853,x99854,x99852,x99851))),f328(x99855,f715(x99855,x99853,x99854,x99852,x99851))))+P1(f328(f328(f242(x99851),f328(f163(x99851),f328(f328(f151(x99852,x99851),x99853),x99854))),f328(f163(x99851),f328(f328(f151(x99852,x99851),x99855),x99854)))) % 154.70/154.57 [8657]~P66(x86571)+~P1(f328(f61(x86574),x86575))+~P1(f328(f328(f330(x86574),x86573),x86575))+E(f328(f328(f80(x86571),f328(x86572,x86573)),f328(f328(f6(x86574,x86571),x86572),f328(f328(f22(f882(x86574,a870)),x86575),f328(f328(f306(x86574),x86573),f192(f882(x86574,a870)))))),f328(f328(f6(x86574,x86571),x86572),x86575)) % 154.70/154.57 [8658]~P73(x86581)+~P1(f328(f61(x86584),x86585))+~P1(f328(f328(f330(x86584),x86583),x86585))+E(f328(f328(f81(x86581),f328(x86582,x86583)),f328(f328(f9(x86584,x86581),x86582),f328(f328(f22(f882(x86584,a870)),x86585),f328(f328(f306(x86584),x86583),f192(f882(x86584,a870)))))),f328(f328(f9(x86584,x86581),x86582),x86585)) % 154.70/154.57 [8713]~P20(x87131,x87134,x87135)+~P1(f328(f61(x87131),x87132))+E(f328(f328(f22(f882(x87131,a870)),x87132),f328(f328(f306(x87131),x87133),f192(f882(x87131,a870)))),f192(f882(x87131,a870)))+E(f328(f328(x87134,x87133),f328(x87135,f328(f328(f22(f882(x87131,a870)),x87132),f328(f328(f306(x87131),x87133),f192(f882(x87131,a870)))))),f328(x87135,f328(f328(f306(x87131),x87133),x87132))) % 154.70/154.57 [9089]~P66(x90891)+~P1(f328(f61(x90892),x90895))+~P1(f328(f61(x90892),x90894))+E(f328(f328(f80(x90891),f328(f328(f6(x90892,x90891),x90893),f328(f328(f114(f882(x90892,a870)),x90894),x90895))),f328(f328(f6(x90892,x90891),x90893),f328(f328(f105(f882(x90892,a870)),x90894),x90895))),f328(f328(f80(x90891),f328(f328(f6(x90892,x90891),x90893),x90894)),f328(f328(f6(x90892,x90891),x90893),x90895))) % 154.70/154.57 [9091]~P73(x90911)+~P1(f328(f61(x90912),x90915))+~P1(f328(f61(x90912),x90914))+E(f328(f328(f81(x90911),f328(f328(f9(x90912,x90911),x90913),f328(f328(f114(f882(x90912,a870)),x90914),x90915))),f328(f328(f9(x90912,x90911),x90913),f328(f328(f105(f882(x90912,a870)),x90914),x90915))),f328(f328(f81(x90911),f328(f328(f9(x90912,x90911),x90913),x90914)),f328(f328(f9(x90912,x90911),x90913),x90915))) % 154.70/154.57 [9232]~P65(x92321)+~P1(f328(f61(x92322),x92325))+~P1(f328(f61(x92322),x92324))+E(f328(f328(f22(x92321),f328(f328(f80(x92321),f328(f328(f6(x92322,x92321),x92323),x92324)),f328(f328(f6(x92322,x92321),x92323),x92325))),f328(f328(f6(x92322,x92321),x92323),f328(f328(f105(f882(x92322,a870)),x92324),x92325))),f328(f328(f6(x92322,x92321),x92323),f328(f328(f114(f882(x92322,a870)),x92324),x92325))) % 154.70/154.57 [9434]~P27(x94341,x94342,x94343,x94345)+~P27(x94341,x94342,x94343,x94344)+P27(x94341,x94342,x94343,f328(f328(f114(f882(x94341,a870)),x94344),x94345))+~E(f328(f328(f105(f882(x94342,a870)),f328(f307(x94341,x94342,x94343),f328(f328(f22(f882(x94341,a870)),x94344),x94345))),f328(f307(x94341,x94342,x94343),f328(f328(f22(f882(x94341,a870)),x94345),x94344))),f192(f882(x94342,a870))) % 154.70/154.57 [9549]E(x95491,f2(a1))+~P1(f328(f328(f243(a1),f2(a1)),x95493))+~P1(f328(f48(x95492,x95491),f328(f328(f263(a1,a1),x95494),x95495)))+P1(f328(f48(x95492,f328(f328(f81(a1),x95491),x95493)),f328(f328(f263(a1,a1),f328(f328(f38(a1),x95494),x95493)),f328(f328(f80(a1),f328(f328(f81(a1),x95491),f44(a1,x95494,x95493))),x95495)))) % 154.70/154.57 [9557]~P1(f328(f328(f243(a875),f2(a875)),x95573))+~P1(f328(f328(f243(a875),f2(a875)),x95572))+~P1(f328(f47(x95571,x95572),f328(f328(f263(a875,a875),x95574),x95575)))+P1(f328(f47(x95571,f328(f328(f81(a875),x95572),x95573)),f328(f328(f263(a875,a875),f328(f328(f38(a875),x95574),x95573)),f328(f328(f80(a875),f328(f328(f81(a875),x95572),f44(a875,x95574,x95573))),x95575)))) % 154.70/154.57 [9606]~P73(x96061)+~P1(f328(f61(x96062),x96065))+~P1(f328(f61(x96062),x96064))+E(f328(f328(f81(x96061),f328(f328(f328(f65(x96061,x96062,f81(x96061)),x96063),f78(x96061)),f328(f328(f114(f882(x96062,a870)),x96064),x96065))),f328(f328(f328(f65(x96061,x96062,f81(x96061)),x96063),f78(x96061)),f328(f328(f105(f882(x96062,a870)),x96064),x96065))),f328(f328(f81(x96061),f328(f328(f328(f65(x96061,x96062,f81(x96061)),x96063),f78(x96061)),x96064)),f328(f328(f328(f65(x96061,x96062,f81(x96061)),x96063),f78(x96061)),x96065))) % 154.70/154.57 [9608]~E(f328(f328(f173(x96081),x96085),x96082),f328(f328(f173(x96081),x96085),x96083))+P1(f328(f328(f330(f881(f876(x96081),f876(x96081))),f328(f328(f263(f876(x96081),f876(x96081)),x96082),x96083)),f144(x96081,x96084)))+~P1(f328(f328(f243(a875),x96085),f328(f328(f240(a875),f328(f193(f876(x96081)),x96082)),f328(f193(f876(x96081)),x96083))))+~P1(f328(f328(f330(f881(x96081,x96081)),f328(f328(f263(x96081,x96081),f328(f328(f162(x96081),x96082),x96085)),f328(f328(f162(x96081),x96083),x96085))),x96084)) % 154.70/154.57 [9718]~P82(x97185)+~P140(x97185)+P1(f328(f328(f330(x97181),f366(x97182,x97183,x97184,x97181,x97185)),x97184))+P1(f328(f328(f242(x97185),f328(f328(f6(x97181,x97185),x97183),x97184)),f328(f328(f81(x97185),f328(f104(x97185),f328(f37(x97181),x97184))),x97182))) % 154.70/154.57 [9913]~P82(x99131)+~P140(x99131)+~P1(f328(f328(f242(x99131),f328(x99133,f366(x99135,x99133,x99134,x99132,x99131))),x99135))+P1(f328(f328(f242(x99131),f328(f328(f6(x99132,x99131),x99133),x99134)),f328(f328(f81(x99131),f328(f104(x99131),f328(f37(x99132),x99134))),x99135))) % 154.70/154.57 [8685]E(f328(f328(f125(x86851),x86852),x86853),f328(f328(f125(x86851),x86854),x86855))+~E(f328(f328(f173(x86851),f328(f193(f876(x86851)),x86852)),x86854),x86852)+~E(f328(f328(f125(x86851),f328(f328(f135(x86851),f328(f193(f876(x86851)),x86852)),x86854)),x86855),x86853)+P1(f328(f328(f242(a875),f328(f193(f876(x86851)),x86854)),f328(f193(f876(x86851)),x86852))) % 154.70/154.57 [8805]E(f328(f328(f125(x88051),x88052),x88053),f328(f328(f125(x88051),x88054),x88055))+~E(f328(f328(f173(x88051),f328(f193(f876(x88051)),x88052)),x88054),x88052)+~E(x88053,f328(f328(f125(x88051),f328(f328(f135(x88051),f328(f193(f876(x88051)),x88052)),x88054)),x88055))+~P1(f328(f328(f242(a875),f328(f193(f876(x88051)),x88052)),f328(f193(f876(x88051)),x88054))) % 154.70/154.57 [10047]~P1(f328(x100475,x100474))+~P1(f328(f61(x100472),f328(f248(x100472),x100475)))+P1(f328(f61(x100471),f328(f248(x100471),f328(f328(f7(x100471,x100472,a870),x100473),x100474))))+~P1(f328(f61(x100471),f328(f248(x100471),f328(f328(f8(f882(x100472,a870),a870,x100471),f87(x100472)),f328(f328(f8(f882(x100472,a870),f882(x100472,a870),x100471),f328(f18(x100472,a870,a870),f328(f328(f8(a870,f882(a870,a870),x100472),a326),x100475))),x100473))))) % 154.70/154.57 [8470]~P21(x84705,x84701,x84706,x84702)+E(f328(f73(x84701,x84701,x84701,f328(x84702,x84703)),f328(x84702,x84704)),f328(f73(x84701,x84701,x84701,f328(x84702,x84704)),f328(x84702,x84703)))+~P1(f328(f61(x84705),x84704))+~P1(f328(f61(x84705),x84703)) % 154.70/154.57 [7855]~P27(x78551,x78552,x78554,x78553)+~E(f328(x78554,x78556),x78555)+E(f328(f77(x78551,x78552,x78553,x78554),x78555),x78556)+~P1(f328(f328(f330(x78551),x78556),x78553)) % 154.70/154.57 [8046]~P22(x80466,x80461,x80464,x80462)+E(f328(f73(x80461,x80461,x80461,f328(x80462,x80463)),f328(x80464,x80465)),f328(x80462,x80463))+~P1(f328(f61(x80466),x80463))+~P1(f328(f328(f330(x80466),x80465),x80463)) % 154.70/154.57 [9279]~P21(x92793,x92791,x92796,x92792)+E(f328(f73(x92791,x92791,x92791,f328(x92792,f328(f328(f22(f882(x92793,a870)),x92794),f328(f328(f306(x92793),x92795),f192(f882(x92793,a870)))))),f328(x92796,x92795)),f328(x92792,x92794))+~P1(f328(f61(x92793),x92794))+~P1(f328(f328(f330(x92793),x92795),x92794)) % 154.70/154.57 [6931]~P58(x69311)+~E(f44(x69311,x69313,x69314),f44(x69311,x69316,x69314))+~E(f44(x69311,x69312,x69314),f44(x69311,x69315,x69314))+E(f44(x69311,f328(f328(f22(x69311),x69312),x69313),x69314),f44(x69311,f328(f328(f22(x69311),x69315),x69316),x69314)) % 154.70/154.57 [6932]~P57(x69321)+~E(f44(x69321,x69323,x69324),f44(x69321,x69326,x69324))+~E(f44(x69321,x69322,x69324),f44(x69321,x69325,x69324))+E(f44(x69321,f328(f328(f80(x69321),x69322),x69323),x69324),f44(x69321,f328(f328(f80(x69321),x69325),x69326),x69324)) % 154.70/154.57 [6933]~P57(x69331)+~E(f44(x69331,x69333,x69334),f44(x69331,x69336,x69334))+~E(f44(x69331,x69332,x69334),f44(x69331,x69335,x69334))+E(f44(x69331,f328(f328(f81(x69331),x69332),x69333),x69334),f44(x69331,f328(f328(f81(x69331),x69335),x69336),x69334)) % 154.70/154.57 [7746]~P18(x77461,x77462,x77463)+~P1(f328(f61(x77461),x77466))+E(f328(f328(f64(x77461,x77462,x77463),x77464),f328(f328(f306(x77461),x77465),x77466)),f328(f328(f64(x77461,x77462,x77463),f328(f328(x77463,x77465),x77464)),x77466))+P1(f328(f328(f330(x77461),x77465),x77466)) % 154.70/154.57 [7813]~P5(x78131)+P1(f328(f328(f242(x78131),x78132),f328(x78133,x78134)))+~P1(f328(f328(f330(x78135),x78134),x78136))+~P1(f328(f328(f242(x78131),x78132),f328(f328(f42(x78135,x78131),x78136),x78133))) % 154.70/154.57 [7970]~P18(x79701,x79702,x79703)+~P1(f328(f61(x79701),x79706))+E(f328(f328(f64(x79701,x79702,x79703),x79704),f328(f328(f306(x79701),x79705),x79706)),f328(f328(x79703,x79705),f328(f328(f64(x79701,x79702,x79703),x79704),x79706)))+P1(f328(f328(f330(x79701),x79705),x79706)) % 154.70/154.57 [8062]~P105(x80623)+~P1(f328(x80622,x80625))+~P16(x80623,f328(f328(f151(x80621,x80623),x80624),x80626))+E(f328(f133(x80621,x80622),f328(f328(f145(x80621,x80623,x80624),x80625),x80626)),f328(f328(f145(x80621,x80623,x80624),x80625),f328(f133(x80621,x80622),x80626))) % 154.70/154.57 [8085]E(x80851,x80852)+E(x80853,f2(a1))+~P1(f328(f48(x80854,x80853),f328(f328(f263(a1,a1),x80855),x80852)))+~P1(f328(f48(x80854,x80853),f328(f328(f263(a1,a1),x80856),x80851))) % 154.70/154.57 [8086]E(x80861,x80862)+E(x80863,f2(a1))+~P1(f328(f48(x80864,x80863),f328(f328(f263(a1,a1),x80862),x80865)))+~P1(f328(f48(x80864,x80863),f328(f328(f263(a1,a1),x80861),x80866))) % 154.70/154.57 [8107]~P21(x81072,x81075,x81076,x81071)+~P1(f328(f61(x81072),x81074))+E(f328(x81071,f328(f328(f306(x81072),x81073),x81074)),f328(f73(x81075,x81075,x81075,f328(x81071,x81074)),f328(x81076,x81073)))+P1(f328(f328(f330(x81072),x81073),x81074)) % 154.70/154.57 [8345]~P22(x83455,x83451,x83456,x83452)+E(f328(f73(x83451,x83451,x83451,f328(x83452,x83453)),f328(x83452,x83454)),f328(x83452,x83453))+~P1(f328(f61(x83455),x83453))+~P1(f328(f328(f242(f882(x83455,a870)),x83454),x83453)) % 154.70/154.57 [9480]~P27(x94801,x94802,x94804,x94803)+~P1(f328(f328(f330(x94802),x94805),f328(f307(x94801,x94802,x94804),x94803)))+P1(f328(f328(f330(x94801),f328(f77(x94801,x94802,x94803,x94804),x94805)),x94806))+~P1(f328(f328(f242(f882(x94801,a870)),x94803),x94806)) % 154.70/154.57 [9858]~P66(x98582)+~E(f840(x98581,x98583,x98585,x98586,x98584,x98582),f841(x98581,x98583,x98585,x98586,x98584,x98582))+~P1(f328(f61(x98584),x98586))+E(f328(f328(f6(x98581,x98582),x98583),f328(f307(x98584,x98581,x98585),x98586)),f328(f328(f6(x98584,x98582),f328(f73(x98581,x98582,x98584,x98583),x98585)),x98586)) % 154.70/154.57 [9895]~P66(x98956)+E(f328(x98951,f840(x98952,x98953,x98951,x98954,x98955,x98956)),f328(x98951,f841(x98952,x98953,x98951,x98954,x98955,x98956)))+E(f328(f328(f6(x98952,x98956),x98953),f328(f307(x98955,x98952,x98951),x98954)),f328(f328(f6(x98955,x98956),f328(f73(x98952,x98956,x98955,x98953),x98951)),x98954))+~P1(f328(f61(x98955),x98954)) % 154.70/154.57 [9935]~P66(x99352)+~E(f328(x99353,f328(x99355,f841(x99351,x99353,x99355,x99356,x99354,x99352))),f2(x99352))+~P1(f328(f61(x99354),x99356))+E(f328(f328(f6(x99351,x99352),x99353),f328(f307(x99354,x99351,x99355),x99356)),f328(f328(f6(x99354,x99352),f328(f73(x99351,x99352,x99354,x99353),x99355)),x99356)) % 154.70/154.57 [9993]~P66(x99932)+~P1(f328(f61(x99934),x99936))+E(f328(f328(f6(x99931,x99932),x99933),f328(f307(x99934,x99931,x99935),x99936)),f328(f328(f6(x99934,x99932),f328(f73(x99931,x99932,x99934,x99933),x99935)),x99936))+P1(f328(f328(f330(x99934),f841(x99931,x99933,x99935,x99936,x99934,x99932)),x99936)) % 154.70/154.57 [9994]~P66(x99942)+~P1(f328(f61(x99944),x99946))+E(f328(f328(f6(x99941,x99942),x99943),f328(f307(x99944,x99941,x99945),x99946)),f328(f328(f6(x99944,x99942),f328(f73(x99941,x99942,x99944,x99943),x99945)),x99946))+P1(f328(f328(f330(x99944),f840(x99941,x99943,x99945,x99946,x99944,x99942)),x99946)) % 154.70/154.57 [10106]~P73(x101061)+~P1(f328(f61(x101062),x101066))+E(f328(f328(f328(f65(x101061,x101062,f81(x101061)),f328(f328(f18(x101062,f882(x101063,a870),x101061),f328(f328(f7(x101062,x101061,f882(f882(x101063,a870),x101061)),f328(f328(f8(f882(x101063,x101061),f882(x101061,f882(f882(x101063,a870),x101061)),x101062),f65(x101061,x101063,f81(x101061))),x101064)),f78(x101061))),x101065)),f78(x101061)),x101066),f328(f328(f328(f65(x101061,f881(x101062,x101063),f81(x101061)),f328(f267(x101062,x101063,x101061),x101064)),f78(x101061)),f328(f328(f265(x101062,x101063),x101066),x101065)))+P1(f328(f328(f330(x101062),f577(x101064,x101065,x101063,x101066,x101062,x101061)),x101066)) % 154.70/154.57 [10125]~P73(x101251)+~P1(f328(f61(x101252),x101256))+E(f328(f328(f328(f65(x101251,x101252,f81(x101251)),f328(f328(f18(x101252,f882(x101253,a870),x101251),f328(f328(f7(x101252,x101251,f882(f882(x101253,a870),x101251)),f328(f328(f8(f882(x101253,x101251),f882(x101251,f882(f882(x101253,a870),x101251)),x101252),f65(x101251,x101253,f81(x101251))),x101254)),f78(x101251))),x101255)),f78(x101251)),x101256),f328(f328(f328(f65(x101251,f881(x101252,x101253),f81(x101251)),f328(f267(x101252,x101253,x101251),x101254)),f78(x101251)),f328(f328(f265(x101252,x101253),x101256),x101255)))+~P1(f328(f61(x101253),f328(x101255,f577(x101254,x101255,x101253,x101256,x101252,x101251)))) % 154.70/154.57 [8257]~P22(x82572,x82575,x82576,x82571)+~P1(f328(f61(x82572),x82574))+~P1(f328(f61(x82572),x82573))+E(f328(x82571,f328(f328(f114(f882(x82572,a870)),x82573),x82574)),f328(f73(x82575,x82575,x82575,f328(x82571,x82573)),f328(x82571,x82574))) % 154.70/154.57 [8471]~P5(x84711)+P1(f328(f328(f242(x84711),f328(x84712,x84713)),x84714))+~P1(f328(f328(f330(x84715),x84713),x84716))+~P1(f328(f328(f242(x84711),f328(f328(f41(x84715,x84711),x84716),x84712)),x84714)) % 154.70/154.57 [8884]~P27(x88842,x88841,x88843,x88846)+E(f328(f328(f22(f882(x88841,a870)),f328(f307(x88842,x88841,x88843),x88844)),f328(f307(x88842,x88841,x88843),x88845)),f328(f307(x88842,x88841,x88843),f328(f328(f22(f882(x88842,a870)),x88844),x88845)))+~P1(f328(f328(f242(f882(x88842,a870)),x88845),x88846))+~P1(f328(f328(f242(f882(x88842,a870)),x88844),x88846)) % 154.70/154.57 [8885]~P27(x88852,x88851,x88853,x88856)+E(f328(f328(f105(f882(x88851,a870)),f328(f307(x88852,x88851,x88853),x88854)),f328(f307(x88852,x88851,x88853),x88855)),f328(f307(x88852,x88851,x88853),f328(f328(f105(f882(x88852,a870)),x88854),x88855)))+~P1(f328(f328(f242(f882(x88852,a870)),x88855),x88856))+~P1(f328(f328(f242(f882(x88852,a870)),x88854),x88856)) % 154.70/154.57 [8923]~P1(f328(x89231,x89233))+~P1(f328(f328(f328(f328(a200,x89232),x89233),x89234),x89236))+~P1(f328(f328(f328(f328(a200,f32(x89231,x89232)),x89236),x89234),x89235))+P1(f328(f328(f328(f328(a200,f32(x89231,x89232)),x89233),x89234),x89235)) % 154.70/154.57 [9154]E(x91541,x91542)+~P51(x91543,x91544,x91545)+~P1(f328(f328(f330(f881(x91543,x91544)),f328(f328(f263(x91543,x91544),x91546),x91542)),x91545))+~P1(f328(f328(f330(f881(x91543,x91544)),f328(f328(f263(x91543,x91544),x91546),x91541)),x91545)) % 154.70/154.57 [9930]~P70(x99301)+~E(f328(x99303,f525(x99304,x99306,x99303,x99305,x99302,x99301)),f328(x99306,f525(x99304,x99306,x99303,x99305,x99302,x99301)))+~P1(f328(f61(x99302),x99305))+E(f328(f328(f328(f65(x99301,x99302,f81(x99301)),x99303),x99304),x99305),f328(f328(f328(f65(x99301,x99302,f81(x99301)),x99306),x99304),x99305)) % 154.70/154.57 [9991]~P70(x99911)+~P1(f328(f61(x99912),x99915))+E(f328(f328(f328(f65(x99911,x99912,f81(x99911)),x99913),x99914),x99915),f328(f328(f328(f65(x99911,x99912,f81(x99911)),x99916),x99914),x99915))+P1(f328(f328(f330(x99912),f525(x99914,x99913,x99916,x99915,x99912,x99911)),x99915)) % 154.70/154.57 [8698]~P70(x86981)+~P1(f328(f61(x86982),x86986))+P1(f328(f328(f330(x86982),x86985),x86986))+E(f328(f328(f328(f65(x86981,x86982,f81(x86981)),x86983),x86984),f328(f328(f306(x86982),x86985),x86986)),f328(f328(f81(x86981),f328(x86983,x86985)),f328(f328(f328(f65(x86981,x86982,f81(x86981)),x86983),x86984),x86986))) % 154.70/154.57 [8744]~P8(x87441,x87446,x87443)+~P14(x87441,f882(x87442,a870),x87443,x87445)+~P1(f328(f328(f330(x87441),x87444),x87446))+E(f328(f328(f41(x87441,f882(x87442,a870)),f328(f282(x87441,x87441,x87443),f328(f328(f306(x87441),x87444),f192(f882(x87441,a870))))),x87445),f328(x87445,x87444)) % 154.70/154.57 [8861]~P18(x88613,x88614,x88611)+~P1(f328(f61(x88613),x88616))+~P1(f328(f328(f330(x88613),x88612),x88616))+E(f328(f328(x88611,x88612),f328(f328(f64(x88613,x88614,x88611),x88615),f328(f328(f22(f882(x88613,a870)),x88616),f328(f328(f306(x88613),x88612),f192(f882(x88613,a870)))))),f328(f328(f64(x88613,x88614,x88611),x88615),x88616)) % 154.70/154.57 [9167]~P21(x91673,x91671,x91676,x91672)+~P1(f328(f61(x91673),x91675))+~P1(f328(f61(x91673),x91674))+E(f328(f73(x91671,x91671,x91671,f328(x91672,f328(f328(f114(f882(x91673,a870)),x91674),x91675))),f328(x91672,f328(f328(f105(f882(x91673,a870)),x91674),x91675))),f328(f73(x91671,x91671,x91671,f328(x91672,x91674)),f328(x91672,x91675))) % 154.70/154.57 [9500]~E(x95003,f328(f328(f156(x95001,x95002),x95005),x95006))+P1(f328(f328(f330(f881(f876(x95001),f876(x95001))),f328(f328(f263(f876(x95001),f876(x95001)),x95002),x95003)),f154(x95001,x95004)))+~P1(f328(f328(f243(a875),x95005),f328(f193(f876(x95001)),x95002)))+~P1(f328(f328(f330(f881(x95001,x95001)),f328(f328(f263(x95001,x95001),f328(f328(f162(x95001),x95002),x95005)),x95006)),x95004)) % 154.70/154.57 [10004]~P66(x100042)+~P1(f328(f61(x100041),x100046))+P1(f328(f328(f330(x100041),f575(x100044,x100045,x100043,x100046,x100041,x100042)),x100046))+E(f328(f328(f6(x100041,x100042),f328(f328(f18(x100041,f882(x100043,a870),x100042),f328(f328(f8(f882(x100043,x100042),f882(f882(x100043,a870),x100042),x100041),f6(x100043,x100042)),x100044)),x100045)),x100046),f328(f328(f6(f881(x100041,x100043),x100042),f328(f267(x100041,x100043,x100042),x100044)),f328(f328(f265(x100041,x100043),x100046),x100045))) % 154.70/154.57 [10005]~P73(x100052)+~P1(f328(f61(x100051),x100056))+P1(f328(f328(f330(x100051),f576(x100054,x100055,x100053,x100056,x100051,x100052)),x100056))+E(f328(f328(f9(x100051,x100052),f328(f328(f18(x100051,f882(x100053,a870),x100052),f328(f328(f8(f882(x100053,x100052),f882(f882(x100053,a870),x100052),x100051),f9(x100053,x100052)),x100054)),x100055)),x100056),f328(f328(f9(f881(x100051,x100053),x100052),f328(f267(x100051,x100053,x100052),x100054)),f328(f328(f265(x100051,x100053),x100056),x100055))) % 154.70/154.57 [10044]~P66(x100442)+~P1(f328(f61(x100441),x100446))+~P1(f328(f61(x100443),f328(x100445,f575(x100444,x100445,x100443,x100446,x100441,x100442))))+E(f328(f328(f6(x100441,x100442),f328(f328(f18(x100441,f882(x100443,a870),x100442),f328(f328(f8(f882(x100443,x100442),f882(f882(x100443,a870),x100442),x100441),f6(x100443,x100442)),x100444)),x100445)),x100446),f328(f328(f6(f881(x100441,x100443),x100442),f328(f267(x100441,x100443,x100442),x100444)),f328(f328(f265(x100441,x100443),x100446),x100445))) % 154.70/154.57 [10045]~P73(x100452)+~P1(f328(f61(x100451),x100456))+~P1(f328(f61(x100453),f328(x100455,f576(x100454,x100455,x100453,x100456,x100451,x100452))))+E(f328(f328(f9(x100451,x100452),f328(f328(f18(x100451,f882(x100453,a870),x100452),f328(f328(f8(f882(x100453,x100452),f882(f882(x100453,a870),x100452),x100451),f9(x100453,x100452)),x100454)),x100455)),x100456),f328(f328(f9(f881(x100451,x100453),x100452),f328(f267(x100451,x100453,x100452),x100454)),f328(f328(f265(x100451,x100453),x100456),x100455))) % 154.70/154.57 [10027]~P73(x100272)+~P1(f328(f61(x100271),x100276))+P1(f328(f328(f330(x100271),x100273),x100276))+E(f328(f328(f9(x100271,x100272),f328(f328(f7(x100271,x100272,x100272),f328(f328(f18(x100271,x100272,f882(x100272,x100272)),f328(f328(f8(a870,f882(x100272,f882(x100272,x100272)),x100271),f100(x100272)),f328(f328(f7(x100271,x100271,a870),a325),x100273))),x100274)),x100275)),x100276),f328(f328(f253(x100272),x100275),f328(f37(x100271),x100276))) % 154.70/154.57 [10032]~P73(x100322)+~P1(f328(f61(x100321),x100326))+~P1(f328(f328(f330(x100321),x100323),x100326))+E(f328(f328(f9(x100321,x100322),f328(f328(f7(x100321,x100322,x100322),f328(f328(f18(x100321,x100322,f882(x100322,x100322)),f328(f328(f8(a870,f882(x100322,f882(x100322,x100322)),x100321),f100(x100322)),f328(f328(f7(x100321,x100321,a870),a325),x100323))),x100324)),x100325)),x100326),f328(f328(f81(x100322),f328(x100324,x100323)),f328(f328(f253(x100322),x100325),f328(f328(f22(a875),f328(f37(x100321),x100326)),f78(a875))))) % 154.70/154.57 [10099]~P1(f328(f61(x100991),x100995))+~P1(f328(f61(x100992),x100993))+P1(f328(f328(f330(x100992),f464(x100996,x100994,x100993,x100992,x100995,x100991)),x100993))+E(f328(f328(f6(x100991,a875),f328(f328(f8(f882(x100992,a870),a875,x100991),f37(x100992)),f328(f328(f8(f882(x100992,a870),f882(x100992,a870),x100991),f248(x100992)),f328(f328(f8(f882(x100992,a870),f882(x100992,a870),x100991),f328(f18(x100992,a870,a870),f328(f328(f8(a870,f882(a870,a870),x100992),a326),f328(f328(f7(x100992,f882(x100992,a870),a870),f330(x100992)),x100993)))),x100994)))),x100995),f328(f328(f81(a875),x100996),f328(f37(x100992),x100993))) % 154.70/154.57 [10100]~P1(f328(f61(x101001),x101005))+~P1(f328(f61(x101002),x101003))+P1(f328(f328(f330(x101002),f465(x101006,x101004,x101003,x101002,x101005,x101001)),x101003))+E(f328(f328(f6(x101001,a875),f328(f328(f8(f882(x101002,a870),a875,x101001),f37(x101002)),f328(f328(f8(f882(x101002,a870),f882(x101002,a870),x101001),f248(x101002)),f328(f328(f8(f882(x101002,a870),f882(x101002,a870),x101001),f328(f18(x101002,a870,a870),f328(f328(f8(a870,f882(a870,a870),x101002),a326),f328(f328(f7(x101002,f882(x101002,a870),a870),f330(x101002)),x101003)))),x101004)))),x101005),f328(f328(f6(x101002,a875),x101006),x101003)) % 154.70/154.57 [10131]~P1(f328(f61(x101312),x101313))+~P1(f328(f61(x101311),x101315))+~E(f328(f37(x101311),f328(f248(x101311),f328(f328(f18(x101311,a870,a870),f328(f328(f8(a870,f882(a870,a870),x101311),a326),f328(f328(f7(x101311,f882(x101311,a870),a870),f330(x101311)),x101315))),f328(f328(f7(x101311,x101312,a870),x101314),f464(x101316,x101314,x101313,x101312,x101315,x101311))))),x101316)+E(f328(f328(f6(x101311,a875),f328(f328(f8(f882(x101312,a870),a875,x101311),f37(x101312)),f328(f328(f8(f882(x101312,a870),f882(x101312,a870),x101311),f248(x101312)),f328(f328(f8(f882(x101312,a870),f882(x101312,a870),x101311),f328(f18(x101312,a870,a870),f328(f328(f8(a870,f882(a870,a870),x101312),a326),f328(f328(f7(x101312,f882(x101312,a870),a870),f330(x101312)),x101313)))),x101314)))),x101315),f328(f328(f81(a875),x101316),f328(f37(x101312),x101313))) % 154.70/154.57 [10133]~P1(f328(f61(x101332),x101333))+~P1(f328(f61(x101331),x101335))+~E(f328(f37(x101331),f328(f248(x101331),f328(f328(f18(x101331,a870,a870),f328(f328(f8(a870,f882(a870,a870),x101331),a326),f328(f328(f7(x101331,f882(x101331,a870),a870),f330(x101331)),x101335))),f328(f328(f7(x101331,x101332,a870),x101334),f465(x101336,x101334,x101333,x101332,x101335,x101331))))),f328(x101336,f465(x101336,x101334,x101333,x101332,x101335,x101331)))+E(f328(f328(f6(x101331,a875),f328(f328(f8(f882(x101332,a870),a875,x101331),f37(x101332)),f328(f328(f8(f882(x101332,a870),f882(x101332,a870),x101331),f248(x101332)),f328(f328(f8(f882(x101332,a870),f882(x101332,a870),x101331),f328(f18(x101332,a870,a870),f328(f328(f8(a870,f882(a870,a870),x101332),a326),f328(f328(f7(x101332,f882(x101332,a870),a870),f330(x101332)),x101333)))),x101334)))),x101335),f328(f328(f6(x101332,a875),x101336),x101333)) % 154.70/154.57 [9785]E(x97851,x97852)+~P18(x97853,x97854,x97855)+~P1(f328(f66(x97853,x97854,x97855,x97856,x97857),x97852))+~P1(f328(f66(x97853,x97854,x97855,x97856,x97857),x97851)) % 154.70/154.57 [9577]P1(f328(x95771,x95772))+~P1(f328(f328(f330(x95777),x95772),f328(x95776,x95774)))+~P1(f328(x95771,f710(x95771,x95776,x95775,x95773,x95777)))+~P1(f328(f328(f330(x95773),x95774),x95775)) % 154.70/154.57 [10019]~P18(x100197,x100196,x100191)+E(f328(f328(x100191,x100192),f838(x100192,x100193,x100194,x100195,x100191,x100196,x100197)),x100193)+~P1(f328(f66(x100197,x100196,x100191,x100195,x100194),x100193))+~P1(f328(f328(f330(x100197),x100192),x100194)) % 154.70/154.57 [10084]~P18(x100841,x100842,x100843)+~P1(f328(f66(x100841,x100842,x100843,x100844,x100845),x100847))+P1(f328(f66(x100841,x100842,x100843,x100844,f328(f328(f22(f882(x100841,a870)),x100845),f328(f328(f306(x100841),x100846),f192(f882(x100841,a870))))),f838(x100846,x100847,x100845,x100844,x100843,x100842,x100841)))+~P1(f328(f328(f330(x100841),x100846),x100845)) % 154.70/154.57 [9476]~P70(x94761)+~P27(x94765,x94762,x94766,x94767)+~P1(f328(f61(x94765),x94767))+E(f328(f328(f328(f65(x94761,x94762,f81(x94761)),x94763),x94764),f328(f307(x94765,x94762,x94766),x94767)),f328(f328(f328(f65(x94761,x94765,f81(x94761)),f328(f73(x94762,x94761,x94765,x94763),x94766)),x94764),x94767)) % 154.70/154.57 [9601]~E(f328(f328(f306(x96011),x96015),x96016),f328(f328(f306(x96011),x96012),x96013))+~P1(f328(f66(x96011,x96011,x96014,x96012,x96013),x96017))+P1(f328(f328(f330(x96011),x96012),x96013))+P1(f328(f62(x96011,x96014,f328(f328(f306(x96011),x96015),x96016)),x96017)) % 154.70/154.57 [9685]P1(f328(x96851,x96852))+~P1(f328(f328(f330(x96853),x96852),f328(x96854,x96857)))+~P1(f328(f328(f330(x96856),x96857),x96855))+P1(f328(f328(f330(x96853),f710(x96851,x96854,x96855,x96856,x96853)),f328(f328(f41(x96856,f882(x96853,a870)),x96855),x96854))) % 154.70/154.57 [9699]~P27(x96992,x96991,x96995,x96994)+~P27(x96991,x96993,x96996,f328(f307(x96992,x96991,x96995),x96994))+E(f328(f328(f73(x96991,x96992,x96993,f77(x96992,x96991,x96994,x96995)),f77(x96991,x96993,f328(f307(x96992,x96991,x96995),x96994),x96996)),x96997),f328(f77(x96992,x96993,x96994,f328(f73(x96991,x96993,x96992,x96996),x96995)),x96997))+~P1(f328(f328(f330(x96993),x96997),f328(f307(x96991,x96993,x96996),f328(f307(x96992,x96991,x96995),x96994)))) % 154.70/154.57 [10020]~P18(x100207,x100206,x100201)+E(f328(f328(x100201,x100202),f866(x100203,x100204,x100202,x100205,x100201,x100206,x100207)),x100203)+P1(f328(f328(f330(x100207),x100202),x100204))+~P1(f328(f66(x100207,x100206,x100201,x100205,f328(f328(f306(x100207),x100202),x100204)),x100203)) % 154.70/154.57 [10083]~P18(x100831,x100834,x100835)+P1(f328(f66(x100831,x100834,x100835,x100836,x100833),f866(x100837,x100833,x100832,x100836,x100835,x100834,x100831)))+P1(f328(f328(f330(x100831),x100832),x100833))+~P1(f328(f66(x100831,x100834,x100835,x100836,f328(f328(f306(x100831),x100832),x100833)),x100837)) % 154.70/154.57 [9767]E(x97671,f2(a1))+~P1(f328(f48(x97673,x97671),f328(f328(f263(a1,a1),x97675),x97677)))+~P1(f328(f48(x97672,x97671),f328(f328(f263(a1,a1),x97674),x97676)))+P1(f328(f48(f328(f328(f80(a1),x97672),x97673),x97671),f328(f328(f263(a1,a1),f328(f328(f80(a1),f328(f328(f80(a1),x97674),x97675)),f328(f328(f38(a1),f328(f328(f80(a1),x97676),x97677)),x97671))),f44(a1,f328(f328(f80(a1),x97676),x97677),x97671)))) % 154.70/154.57 [9769]~P1(f328(f328(f243(a875),f2(a875)),x97693))+~P1(f328(f47(x97692,x97693),f328(f328(f263(a875,a875),x97695),x97697)))+~P1(f328(f47(x97691,x97693),f328(f328(f263(a875,a875),x97694),x97696)))+P1(f328(f47(f328(f328(f80(a875),x97691),x97692),x97693),f328(f328(f263(a875,a875),f328(f328(f80(a875),f328(f328(f80(a875),x97694),x97695)),f328(f328(f38(a875),f328(f328(f80(a875),x97696),x97697)),x97693))),f44(a875,f328(f328(f80(a875),x97696),x97697),x97693)))) % 154.70/154.57 [10130]~P66(x101302)+~P1(f328(f61(x101303),x101305))+~P1(f328(f61(x101301),x101307))+E(f328(f328(f6(x101301,x101302),f328(f328(f18(x101301,f882(x101303,a870),x101302),f328(f328(f8(f882(x101303,x101302),f882(f882(x101303,a870),x101302),x101301),f6(x101303,x101302)),x101304)),f328(f328(f8(f882(x101303,a870),f882(x101303,a870),x101301),f248(x101303)),f328(f328(f8(f882(x101303,a870),f882(x101303,a870),x101301),f328(f18(x101303,a870,a870),f328(f328(f8(a870,f882(a870,a870),x101303),a326),f328(f328(f7(x101303,f882(x101303,a870),a870),f330(x101303)),x101305)))),x101306)))),x101307),f328(f328(f6(x101303,x101302),f328(f328(f18(x101303,f882(x101301,a870),x101302),f328(f328(f8(f882(x101301,x101302),f882(f882(x101301,a870),x101302),x101303),f6(x101301,x101302)),f328(f7(x101301,x101303,x101302),x101304))),f328(f328(f8(f882(x101301,a870),f882(x101301,a870),x101303),f248(x101301)),f328(f328(f8(f882(x101301,a870),f882(x101301,a870),x101303),f328(f18(x101301,a870,a870),f328(f328(f8(a870,f882(a870,a870),x101301),a326),f328(f328(f7(x101301,f882(x101301,a870),a870),f330(x101301)),x101307)))),f328(f7(x101301,x101303,a870),x101306))))),x101305)) % 154.70/154.57 [9637]~P24(x96377,x96376,x96371,x96378,x96372,x96374)+E(f328(f328(x96371,f328(x96372,x96373)),f328(x96374,x96375)),f328(x96374,x96375))+~P1(f328(f61(x96376),x96375))+~P1(f328(f328(f330(x96376),x96373),x96375)) % 154.70/154.57 [9641]~P15(x96416,x96411,x96412,x96418,x96413,x96414)+~P8(x96416,x96417,x96418)+P14(x96411,x96412,x96413,f328(x96414,x96415))+~P1(f328(f328(f330(x96416),x96415),x96417)) % 154.70/154.57 [8063]~P29(x80638,x80637,f328(f328(f328(f92(x80638),x80634),x80636),x80631))+P1(f328(f328(x80631,x80632),x80633))+~P1(f328(f328(x80634,x80632),x80635))+~P1(f328(f328(f328(f328(a200,x80636),x80635),x80637),x80633)) % 154.70/154.57 [9261]~P21(x92617,x92611,x92618,x92613)+~P1(f328(f61(x92617),x92615))+~P1(f328(f61(x92617),x92614))+E(f328(f73(x92611,x92611,x92612,f328(x92613,x92614)),f328(f73(x92611,x92611,x92612,f328(x92613,x92615)),x92616)),f328(f73(x92611,x92611,x92612,f328(x92613,x92615)),f328(f73(x92611,x92611,x92612,f328(x92613,x92614)),x92616))) % 154.70/154.57 [9269]~P36(x92691,x92692,x92693,x92694,x92697)+P36(x92691,x92692,x92693,f328(f328(f156(x92691,x92694),x92695),x92696),f328(f328(f156(x92692,x92697),x92695),x92698))+~P1(f328(f328(x92693,x92696),x92698))+~P1(f328(f328(f243(a875),x92695),f328(f193(f876(x92691)),x92694))) % 154.70/154.57 [9270]~P36(x92701,x92702,x92703,x92704,x92707)+P36(x92701,x92702,x92703,f328(f328(f156(x92701,x92704),x92705),x92706),f328(f328(f156(x92702,x92707),x92705),x92708))+~P1(f328(f328(x92703,x92706),x92708))+~P1(f328(f328(f243(a875),x92705),f328(f193(f876(x92702)),x92707))) % 154.70/154.57 [9349]~P27(x93492,x93492,x93495,x93496)+~P23(x93493,x93492,x93497,x93498,x93491)+~P1(f328(f61(x93492),x93496))+E(f328(f328(x93491,f328(f73(x93492,x93493,x93492,x93494),x93495)),x93496),f328(f328(x93491,x93494),f328(f307(x93492,x93492,x93495),x93496))) % 154.70/154.57 [9639]~P25(x96397,x96392,x96395,x96398,x96396,x96391)+~P1(f328(f61(x96392),x96394))+E(f328(x96391,f328(f328(f306(x96392),x96393),x96394)),f328(f328(x96395,f328(x96396,x96393)),f328(x96391,x96394)))+P1(f328(f328(f330(x96392),x96393),x96394)) % 154.70/154.57 [9650]~P24(x96506,x96505,x96501,x96507,x96508,x96502)+E(f328(f328(x96501,f328(x96502,x96503)),f328(x96502,x96504)),f328(x96502,x96504))+~P1(f328(f61(x96505),x96504))+~P1(f328(f328(f242(f882(x96505,a870)),x96503),x96504)) % 154.70/154.57 [9247]P1(f328(f328(f330(f881(f876(x92471),f876(x92471))),f328(f328(f263(f876(x92471),f876(x92471)),x92472),x92473)),f154(x92471,x92474)))+~E(x92473,f328(f328(f125(x92471),x92475),f328(f328(f148(x92471),x92476),x92477)))+~E(x92472,f328(f328(f125(x92471),x92475),f328(f328(f148(x92471),x92478),x92477)))+~P1(f328(f328(f330(f881(x92471,x92471)),f328(f328(f263(x92471,x92471),x92478),x92476)),x92474)) % 154.70/154.57 [9644]~P24(x96446,x96442,x96445,x96447,x96448,x96441)+~P1(f328(f61(x96442),x96444))+~P1(f328(f61(x96442),x96443))+E(f328(x96441,f328(f328(f114(f882(x96442,a870)),x96443),x96444)),f328(f328(x96445,f328(x96441,x96443)),f328(x96441,x96444))) % 154.70/154.57 [10169]~P27(x101694,x101692,x101695,x101698)+E(f328(f328(f42(x101691,f882(x101692,a870)),x101693),f328(f328(f8(f882(x101694,a870),f882(x101692,a870),x101691),f307(x101694,x101692,x101695)),x101696)),f328(f307(x101694,x101692,x101695),f328(f328(f42(x101691,f882(x101694,a870)),x101693),x101696)))+~P1(f328(f328(f330(x101691),x101697),x101693))+P1(f328(f328(f330(x101691),f445(x101697,x101696,x101693,x101691,x101698,x101695,x101692,x101694)),x101693)) % 154.70/154.57 [10193]~P27(x101934,x101932,x101935,x101937)+E(f328(f328(f42(x101931,f882(x101932,a870)),x101933),f328(f328(f8(f882(x101934,a870),f882(x101932,a870),x101931),f307(x101934,x101932,x101935)),x101936)),f328(f307(x101934,x101932,x101935),f328(f328(f42(x101931,f882(x101934,a870)),x101933),x101936)))+~P1(f328(f328(f330(x101931),x101938),x101933))+~P1(f328(f328(f242(f882(x101934,a870)),f328(x101936,f445(x101938,x101936,x101933,x101931,x101937,x101935,x101932,x101934))),x101937)) % 154.70/154.57 [9708]~P25(x97087,x97085,x97081,x97088,x97082,x97084)+~P1(f328(f61(x97085),x97086))+~P1(f328(f328(f330(x97085),x97083),x97086))+E(f328(f328(x97081,f328(x97082,x97083)),f328(x97084,f328(f328(f22(f882(x97085,a870)),x97086),f328(f328(f306(x97085),x97083),f192(f882(x97085,a870)))))),f328(x97084,x97086)) % 154.70/154.57 [9716]~P25(x97166,x97163,x97161,x97167,x97168,x97162)+~P1(f328(f61(x97163),x97165))+~P1(f328(f61(x97163),x97164))+E(f328(f328(x97161,f328(x97162,f328(f328(f114(f882(x97163,a870)),x97164),x97165))),f328(x97162,f328(f328(f105(f882(x97163,a870)),x97164),x97165))),f328(f328(x97161,f328(x97162,x97164)),f328(x97162,x97165))) % 154.70/154.57 [9808]P44(x98081,x98082,x98083,x98084,x98085,f328(f328(x98083,x98086),x98087))+~P44(x98081,x98082,x98083,x98084,f328(f328(f22(f882(x98081,a870)),x98085),f328(f328(f306(x98081),x98088),f192(f882(x98081,a870)))),x98089)+~E(f328(f328(x98083,x98086),x98087),f328(f328(x98083,x98088),x98089))+~P1(f328(f328(f330(x98081),x98088),x98085)) % 154.70/154.57 [10208]P26(x102081,x102082,f328(f328(f306(f874(x102081)),f328(f328(f328(f92(x102081),f328(x102083,f486(x102084,x102085,x102086,x102087,x102083,x102082,x102081,x102088,x102089))),f328(x102087,f486(x102084,x102085,x102086,x102087,x102083,x102082,x102081,x102088,x102089))),f328(x102086,f486(x102084,x102085,x102086,x102087,x102083,x102082,x102081,x102088,x102089)))),f192(f882(f874(x102081),a870))))+~P1(f328(f61(x102089),x102088))+~P26(x102081,x102082,f328(f307(x102089,f874(x102081),f328(f328(f18(x102089,f882(x102081,f882(a872,a870)),f874(x102081)),f328(f328(f18(x102089,a871,f882(f882(x102081,f882(a872,a870)),f874(x102081))),f328(f328(f8(f882(x102081,f882(a872,a870)),f882(a871,f882(f882(x102081,f882(a872,a870)),f874(x102081))),x102089),f92(x102081)),x102083)),x102087)),x102086)),x102088))+P26(x102081,x102082,f328(f307(x102089,f874(x102081),f328(f328(f18(x102089,f882(x102081,f882(a872,a870)),f874(x102081)),f328(f328(f18(x102089,a871,f882(f882(x102081,f882(a872,a870)),f874(x102081))),f328(f328(f8(f882(x102081,f882(a872,a870)),f882(a871,f882(f882(x102081,f882(a872,a870)),f874(x102081))),x102089),f92(x102081)),x102085)),x102087)),x102084)),x102088)) % 154.70/154.57 [10209]~P26(x102091,x102092,f328(f328(f306(f874(x102091)),f328(f328(f328(f92(x102091),f328(x102094,f486(x102096,x102094,x102098,x102095,x102099,x102092,x102091,x102097,x102093))),f328(x102095,f486(x102096,x102094,x102098,x102095,x102099,x102092,x102091,x102097,x102093))),f328(x102096,f486(x102096,x102094,x102098,x102095,x102099,x102092,x102091,x102097,x102093)))),f192(f882(f874(x102091),a870))))+~P1(f328(f61(x102093),x102097))+~P26(x102091,x102092,f328(f307(x102093,f874(x102091),f328(f328(f18(x102093,f882(x102091,f882(a872,a870)),f874(x102091)),f328(f328(f18(x102093,a871,f882(f882(x102091,f882(a872,a870)),f874(x102091))),f328(f328(f8(f882(x102091,f882(a872,a870)),f882(a871,f882(f882(x102091,f882(a872,a870)),f874(x102091))),x102093),f92(x102091)),x102099)),x102095)),x102098)),x102097))+P26(x102091,x102092,f328(f307(x102093,f874(x102091),f328(f328(f18(x102093,f882(x102091,f882(a872,a870)),f874(x102091)),f328(f328(f18(x102093,a871,f882(f882(x102091,f882(a872,a870)),f874(x102091))),f328(f328(f8(f882(x102091,f882(a872,a870)),f882(a871,f882(f882(x102091,f882(a872,a870)),f874(x102091))),x102093),f92(x102091)),x102094)),x102095)),x102096)),x102097)) % 154.70/154.57 [9742]~P15(x97426,x97427,x97428,x97429,x974210,x97421)+E(f328(f328(x97421,x97422),x97423),f328(f328(x97421,x97424),x97425))+~P1(f328(f328(f330(f881(x97427,x97427)),f328(f328(f263(x97427,x97427),x97423),x97425)),x974210))+~P1(f328(f328(f330(f881(x97426,x97426)),f328(f328(f263(x97426,x97426),x97422),x97424)),x97429)) % 154.70/154.57 [9351]~P2(x93512)+E(x93511,f192(f882(x93512,a870)))+~P1(f328(f61(x93512),x93511))+P1(f328(f328(f330(x93512),f10(x93512,x93511)),x93511))+~P1(f328(f328(f330(x93512),f328(f328(f114(x93512),f502(x93511,x93512)),f514(x93511,x93512))),f328(f328(f306(x93512),f502(x93511,x93512)),f328(f328(f306(x93512),f514(x93511,x93512)),f192(f882(x93512,a870)))))) % 154.70/154.57 [9352]~P2(x93522)+E(x93521,f192(f882(x93522,a870)))+~P1(f328(f61(x93522),x93521))+P1(f328(f328(f330(x93522),f11(x93522,x93521)),x93521))+~P1(f328(f328(f330(x93522),f328(f328(f105(x93522),f639(x93521,x93522)),f654(x93521,x93522))),f328(f328(f306(x93522),f639(x93521,x93522)),f328(f328(f306(x93522),f654(x93521,x93522)),f192(f882(x93522,a870)))))) % 154.70/154.57 [9383]~P70(x93832)+E(x93831,f192(f882(x93832,a870)))+~P1(f328(f61(x93832),x93831))+P1(f328(f328(f330(x93832),f328(f63(x93832,f81(x93832)),x93831)),x93831))+~P1(f328(f328(f330(x93832),f328(f328(f81(x93832),f359(x93831,x93832)),f361(x93831,x93832))),f328(f328(f306(x93832),f359(x93831,x93832)),f328(f328(f306(x93832),f361(x93831,x93832)),f192(f882(x93832,a870)))))) % 154.70/154.57 [9389]~P105(x93892)+E(x93891,f192(f882(x93892,a870)))+~P1(f328(f61(x93892),x93891))+P1(f328(f328(f330(x93892),f12(x93892,f241(x93892),x93891)),x93891))+~P1(f328(f328(f330(x93892),f328(f328(f241(x93892),f481(x93891,x93892)),f482(x93891,x93892))),f328(f328(f306(x93892),f481(x93891,x93892)),f328(f328(f306(x93892),f482(x93891,x93892)),f192(f882(x93892,a870)))))) % 154.70/154.57 [9390]~P105(x93902)+E(x93901,f192(f882(x93902,a870)))+~P1(f328(f61(x93902),x93901))+P1(f328(f328(f330(x93902),f13(x93902,f240(x93902),x93901)),x93901))+~P1(f328(f328(f330(x93902),f328(f328(f240(x93902),f483(x93901,x93902)),f484(x93901,x93902))),f328(f328(f306(x93902),f483(x93901,x93902)),f328(f328(f306(x93902),f484(x93901,x93902)),f192(f882(x93902,a870)))))) % 154.70/154.57 [6500]~P85(x65002)+E(x65001,f2(x65002))+~E(f328(f328(f80(x65002),x65003),x65001),f2(x65002))+~P1(f328(f328(f242(x65002),f2(x65002)),x65003))+~P1(f328(f328(f242(x65002),f2(x65002)),x65001)) % 154.70/154.57 [6501]~P85(x65012)+E(x65011,f2(x65012))+~E(f328(f328(f80(x65012),x65011),x65013),f2(x65012))+~P1(f328(f328(f242(x65012),f2(x65012)),x65013))+~P1(f328(f328(f242(x65012),f2(x65012)),x65011)) % 154.70/154.57 [7031]~P105(x70312)+~P16(x70312,x70311)+E(x70311,f117(x70312))+~P1(f328(f328(f330(x70312),x70313),f328(f170(x70312),f744(x70311,x70312))))+P1(f328(f328(f242(x70312),f762(x70311,x70312)),x70313)) % 154.70/154.57 [7199]~P105(x71991)+E(f14(x71991,x71992),x71993)+~P1(f328(f61(x71991),x71992))+~P1(f328(f328(f242(x71991),x71993),f522(x71993,x71992,x71991)))+~P1(f328(f328(f330(x71991),x71993),x71992)) % 154.70/154.57 [7230]~P105(x72301)+~P16(x72301,x72302)+~P16(x72301,x72303)+P16(x72301,f328(f328(f125(x72301),x72302),x72303))+P1(f328(f328(f330(x72301),f750(x72303,x72302,x72301)),f328(f170(x72301),x72302))) % 154.70/154.57 [7231]~P105(x72311)+~P16(x72311,x72312)+~P16(x72311,x72313)+P16(x72311,f328(f328(f125(x72311),x72312),x72313))+P1(f328(f328(f330(x72311),f751(x72313,x72312,x72311)),f328(f170(x72311),x72313))) % 154.70/154.57 [7287]~P105(x72871)+E(f14(x72871,x72872),x72873)+~P1(f328(f61(x72871),x72872))+P1(f328(f328(f330(x72871),f522(x72873,x72872,x72871)),x72872))+~P1(f328(f328(f330(x72871),x72873),x72872)) % 154.70/154.57 [7288]~P105(x72881)+E(f15(x72881,x72882),x72883)+~P1(f328(f61(x72881),x72882))+P1(f328(f328(f330(x72881),f523(x72883,x72882,x72881)),x72882))+~P1(f328(f328(f330(x72881),x72883),x72882)) % 154.70/154.57 [7873]~P105(x78731)+E(f15(x78731,x78732),x78733)+~P1(f328(f61(x78731),x78732))+~P1(f328(f328(f330(x78731),x78733),x78732))+~P1(f328(f328(f242(x78731),f523(x78733,x78732,x78731)),x78733)) % 154.70/154.57 [8199]~P105(x81991)+~P16(x81991,x81992)+~P16(x81991,x81993)+P16(x81991,f328(f328(f125(x81991),x81992),x81993))+~P1(f328(f328(f242(x81991),f750(x81993,x81992,x81991)),f751(x81993,x81992,x81991))) % 154.70/154.57 [8990]~P2(x89902)+E(x89901,f192(f882(x89902,a870)))+~E(f328(f328(f114(x89902),f328(x89903,f524(x89901,x89903,x89902))),f328(x89903,f535(x89901,x89903,x89902))),f328(x89903,f328(f328(f114(x89902),f524(x89901,x89903,x89902)),f535(x89901,x89903,x89902))))+E(f10(x89902,f328(f307(x89902,x89902,x89903),x89901)),f328(x89903,f10(x89902,x89901)))+~P1(f328(f61(x89902),x89901)) % 154.70/154.57 [8991]~P2(x89912)+E(x89911,f192(f882(x89912,a870)))+~E(f328(f328(f105(x89912),f328(x89913,f664(x89911,x89913,x89912))),f328(x89913,f678(x89911,x89913,x89912))),f328(x89913,f328(f328(f105(x89912),f664(x89911,x89913,x89912)),f678(x89911,x89913,x89912))))+E(f11(x89912,f328(f307(x89912,x89912,x89913),x89911)),f328(x89913,f11(x89912,x89911)))+~P1(f328(f61(x89912),x89911)) % 154.70/154.57 [8992]~P105(x89922)+E(x89921,f192(f882(x89922,a870)))+~E(f328(f328(f240(x89922),f328(x89923,f496(x89921,x89923,x89922))),f328(x89923,f497(x89921,x89923,x89922))),f328(x89923,f328(f328(f240(x89922),f496(x89921,x89923,x89922)),f497(x89921,x89923,x89922))))+E(f14(x89922,f328(f307(x89922,x89922,x89923),x89921)),f328(x89923,f14(x89922,x89921)))+~P1(f328(f61(x89922),x89921)) % 154.70/154.57 [8993]~P105(x89932)+E(x89931,f192(f882(x89932,a870)))+~E(f328(f328(f241(x89932),f328(x89933,f477(x89931,x89933,x89932))),f328(x89933,f494(x89931,x89933,x89932))),f328(x89933,f328(f328(f241(x89932),f477(x89931,x89933,x89932)),f494(x89931,x89933,x89932))))+E(f15(x89932,f328(f307(x89932,x89932,x89933),x89931)),f328(x89933,f15(x89932,x89931)))+~P1(f328(f61(x89932),x89931)) % 154.70/154.57 [9062]~P105(x90622)+E(x90621,f192(f882(x90622,a870)))+~E(f328(f328(f241(x90622),f328(x90623,f478(x90621,x90623,x90622))),f328(x90623,f491(x90621,x90623,x90622))),f328(x90623,f328(f328(f241(x90622),f478(x90621,x90623,x90622)),f491(x90621,x90623,x90622))))+E(f12(x90622,f241(x90622),f328(f307(x90622,x90622,x90623),x90621)),f328(x90623,f12(x90622,f241(x90622),x90621)))+~P1(f328(f61(x90622),x90621)) % 154.70/154.57 [9063]~P105(x90632)+E(x90631,f192(f882(x90632,a870)))+~E(f328(f328(f240(x90632),f328(x90633,f492(x90631,x90633,x90632))),f328(x90633,f493(x90631,x90633,x90632))),f328(x90633,f328(f328(f240(x90632),f492(x90631,x90633,x90632)),f493(x90631,x90633,x90632))))+E(f13(x90632,f240(x90632),f328(f307(x90632,x90632,x90633),x90631)),f328(x90633,f13(x90632,f240(x90632),x90631)))+~P1(f328(f61(x90632),x90631)) % 154.70/154.57 [6516]~P70(x65162)+E(x65161,f192(f882(x65162,a870)))+~P1(f328(f61(x65162),x65161))+E(f328(f63(x65162,f81(x65162)),f328(f328(f306(x65162),x65163),x65161)),f328(f328(f81(x65162),x65163),f328(f63(x65162,f81(x65162)),x65161)))+P1(f328(f328(f330(x65162),x65163),x65161)) % 154.70/154.57 [7037]~P2(x70372)+E(f328(f328(f114(x70372),f10(x70372,x70371)),f10(x70372,x70373)),f10(x70372,x70373))+E(x70371,f192(f882(x70372,a870)))+~P1(f328(f61(x70372),x70373))+~P1(f328(f328(f242(f882(x70372,a870)),x70371),x70373)) % 154.70/154.57 [7038]~P2(x70382)+E(f328(f328(f105(x70382),f11(x70382,x70381)),f11(x70382,x70383)),f11(x70382,x70383))+E(x70381,f192(f882(x70382,a870)))+~P1(f328(f61(x70382),x70383))+~P1(f328(f328(f242(f882(x70382,a870)),x70381),x70383)) % 154.70/154.57 [7039]~P105(x70392)+E(f328(f328(f240(x70392),f14(x70392,x70391)),f14(x70392,x70393)),f14(x70392,x70393))+E(x70391,f192(f882(x70392,a870)))+~P1(f328(f61(x70392),x70393))+~P1(f328(f328(f242(f882(x70392,a870)),x70391),x70393)) % 154.70/154.57 [7040]~P105(x70402)+E(f328(f328(f241(x70402),f15(x70402,x70401)),f15(x70402,x70403)),f15(x70402,x70403))+E(x70401,f192(f882(x70402,a870)))+~P1(f328(f61(x70402),x70403))+~P1(f328(f328(f242(f882(x70402,a870)),x70401),x70403)) % 154.70/154.57 [7339]~P105(x73392)+E(x73391,f192(f882(x73392,a870)))+~P1(f328(f61(x73392),x73393))+P1(f328(f328(f242(x73392),f14(x73392,x73393)),f14(x73392,x73391)))+~P1(f328(f328(f242(f882(x73392,a870)),x73391),x73393)) % 154.70/154.57 [7340]~P105(x73402)+E(x73401,f192(f882(x73402,a870)))+~P1(f328(f61(x73402),x73403))+P1(f328(f328(f242(x73402),f15(x73402,x73401)),f15(x73402,x73403)))+~P1(f328(f328(f242(f882(x73402,a870)),x73401),x73403)) % 154.70/154.57 [7398]~P2(x73981)+E(f10(x73981,x73982),x73983)+~P1(f328(f61(x73981),x73982))+~E(f328(f328(f22(f882(x73981,a870)),x73982),f328(f328(f306(x73981),x73983),f192(f882(x73981,a870)))),f192(f882(x73981,a870)))+~P1(f328(f328(f330(x73981),x73983),x73982)) % 154.70/154.57 [7399]~P2(x73991)+E(f11(x73991,x73992),x73993)+~P1(f328(f61(x73991),x73992))+~E(f328(f328(f22(f882(x73991,a870)),x73992),f328(f328(f306(x73991),x73993),f192(f882(x73991,a870)))),f192(f882(x73991,a870)))+~P1(f328(f328(f330(x73991),x73993),x73992)) % 154.70/154.57 [7400]~P105(x74001)+E(f14(x74001,x74002),x74003)+~P1(f328(f61(x74001),x74002))+~E(f328(f328(f22(f882(x74001,a870)),x74002),f328(f328(f306(x74001),x74003),f192(f882(x74001,a870)))),f192(f882(x74001,a870)))+~P1(f328(f328(f330(x74001),x74003),x74002)) % 154.70/154.57 [7401]~P105(x74011)+E(f15(x74011,x74012),x74013)+~P1(f328(f61(x74011),x74012))+~E(f328(f328(f22(f882(x74011,a870)),x74012),f328(f328(f306(x74011),x74013),f192(f882(x74011,a870)))),f192(f882(x74011,a870)))+~P1(f328(f328(f330(x74011),x74013),x74012)) % 154.70/154.57 [7499]~P105(x74991)+E(f12(x74991,f241(x74991),x74992),x74993)+~P1(f328(f61(x74991),x74992))+~E(f328(f328(f22(f882(x74991,a870)),x74992),f328(f328(f306(x74991),x74993),f192(f882(x74991,a870)))),f192(f882(x74991,a870)))+~P1(f328(f328(f330(x74991),x74993),x74992)) % 154.70/154.57 [7500]~P105(x75001)+E(f13(x75001,f240(x75001),x75002),x75003)+~P1(f328(f61(x75001),x75002))+~E(f328(f328(f22(f882(x75001,a870)),x75002),f328(f328(f306(x75001),x75003),f192(f882(x75001,a870)))),f192(f882(x75001,a870)))+~P1(f328(f328(f330(x75001),x75003),x75002)) % 154.70/154.57 [7536]~P105(x75362)+E(x75361,f192(f882(x75362,a870)))+~P1(f328(f61(x75362),x75361))+~P1(f328(f328(f243(x75362),x75363),f469(x75363,x75361,x75362)))+P1(f328(f328(f243(x75362),x75363),f328(f63(x75362,f240(x75362)),x75361))) % 154.70/154.57 [7537]~P100(x75372)+E(x75371,f192(f882(x75372,a870)))+~P1(f328(f61(x75372),x75371))+~P1(f328(f328(f242(x75372),x75373),f346(x75373,x75371,x75372)))+P1(f328(f328(f242(x75372),x75373),f328(f63(x75372,f105(x75372)),x75371))) % 154.70/154.57 [7538]~P105(x75382)+E(x75381,f192(f882(x75382,a870)))+~P1(f328(f61(x75382),x75381))+~P1(f328(f328(f242(x75382),x75383),f470(x75383,x75381,x75382)))+P1(f328(f328(f242(x75382),x75383),f328(f63(x75382,f240(x75382)),x75381))) % 154.70/154.57 [7625]~P100(x76252)+E(x76251,f192(f882(x76252,a870)))+~P1(f328(f61(x76252),x76251))+P1(f328(f328(f330(x76252),f346(x76253,x76251,x76252)),x76251))+P1(f328(f328(f242(x76252),x76253),f328(f63(x76252,f105(x76252)),x76251))) % 154.70/154.57 [7626]~P105(x76262)+E(x76261,f192(f882(x76262,a870)))+~P1(f328(f61(x76262),x76261))+P1(f328(f328(f330(x76262),f470(x76263,x76261,x76262)),x76261))+P1(f328(f328(f242(x76262),x76263),f328(f63(x76262,f240(x76262)),x76261))) % 154.70/154.57 [7627]~P105(x76272)+E(x76271,f192(f882(x76272,a870)))+~P1(f328(f61(x76272),x76271))+P1(f328(f328(f330(x76272),f469(x76273,x76271,x76272)),x76271))+P1(f328(f328(f243(x76272),x76273),f328(f63(x76272,f240(x76272)),x76271))) % 154.70/154.57 [7748]~P105(x77482)+E(x77481,f192(f882(x77482,a870)))+E(f328(f328(f240(x77482),f13(x77482,f240(x77482),x77481)),f13(x77482,f240(x77482),x77483)),f13(x77482,f240(x77482),x77483))+~P1(f328(f61(x77482),x77483))+~P1(f328(f328(f242(f882(x77482,a870)),x77481),x77483)) % 154.70/154.57 [7749]~P105(x77492)+E(x77491,f192(f882(x77492,a870)))+E(f328(f328(f241(x77492),f12(x77492,f241(x77492),x77491)),f12(x77492,f241(x77492),x77493)),f12(x77492,f241(x77492),x77493))+~P1(f328(f61(x77492),x77493))+~P1(f328(f328(f242(f882(x77492,a870)),x77491),x77493)) % 154.70/154.57 [7952]~E(f457(x79521,x79523,x79522),f458(x79521,x79523,x79522))+~E(f328(f37(x79522),f459(x79521,x79523,x79522)),x79521)+E(f328(f328(f81(a875),x79521),f328(f37(f882(x79522,a870)),x79523)),f328(f37(x79522),f39(f882(x79522,a870),x79523)))+~P1(f328(f61(x79522),f39(f882(x79522,a870),x79523)))+~P1(f328(f61(f882(x79522,a870)),x79523)) % 154.70/154.57 [8128]~P105(x81282)+E(x81281,f192(f882(x81282,a870)))+~P1(f328(f61(x81282),x81283))+P1(f328(f328(f242(x81282),f328(f63(x81282,f240(x81282)),x81283)),f328(f63(x81282,f240(x81282)),x81281)))+~P1(f328(f328(f242(f882(x81282,a870)),x81281),x81283)) % 154.70/154.57 [8443]~E(f457(x84431,x84433,x84432),f458(x84431,x84433,x84432))+E(f328(f328(f81(a875),x84431),f328(f37(f882(x84432,a870)),x84433)),f328(f37(x84432),f39(f882(x84432,a870),x84433)))+P1(f328(f328(f330(f882(x84432,a870)),f459(x84431,x84433,x84432)),x84433))+~P1(f328(f61(x84432),f39(f882(x84432,a870),x84433)))+~P1(f328(f61(f882(x84432,a870)),x84433)) % 154.70/154.57 [8467]~E(f328(f37(x84672),f459(x84671,x84673,x84672)),x84671)+E(f328(f328(f81(a875),x84671),f328(f37(f882(x84672,a870)),x84673)),f328(f37(x84672),f39(f882(x84672,a870),x84673)))+P1(f328(f328(f330(f882(x84672,a870)),f458(x84671,x84673,x84672)),x84673))+~P1(f328(f61(x84672),f39(f882(x84672,a870),x84673)))+~P1(f328(f61(f882(x84672,a870)),x84673)) % 154.70/154.57 [8468]~E(f328(f37(x84682),f459(x84681,x84683,x84682)),x84681)+E(f328(f328(f81(a875),x84681),f328(f37(f882(x84682,a870)),x84683)),f328(f37(x84682),f39(f882(x84682,a870),x84683)))+P1(f328(f328(f330(f882(x84682,a870)),f457(x84681,x84683,x84682)),x84683))+~P1(f328(f61(x84682),f39(f882(x84682,a870),x84683)))+~P1(f328(f61(f882(x84682,a870)),x84683)) % 154.70/154.57 [8494]~E(f328(f37(x84942),f459(x84941,x84943,x84942)),x84941)+~E(f328(f328(f105(f882(x84942,a870)),f458(x84941,x84943,x84942)),f457(x84941,x84943,x84942)),f192(f882(x84942,a870)))+E(f328(f328(f81(a875),x84941),f328(f37(f882(x84942,a870)),x84943)),f328(f37(x84942),f39(f882(x84942,a870),x84943)))+~P1(f328(f61(f882(x84942,a870)),x84943))+~P1(f328(f61(x84942),f39(f882(x84942,a870),x84943))) % 154.70/154.57 [8749]E(f328(f328(f81(a875),x87491),f328(f37(f882(x87492,a870)),x87493)),f328(f37(x87492),f39(f882(x87492,a870),x87493)))+P1(f328(f328(f330(f882(x87492,a870)),f459(x87491,x87493,x87492)),x87493))+P1(f328(f328(f330(f882(x87492,a870)),f458(x87491,x87493,x87492)),x87493))+~P1(f328(f61(f882(x87492,a870)),x87493))+~P1(f328(f61(x87492),f39(f882(x87492,a870),x87493))) % 154.70/154.57 [8750]E(f328(f328(f81(a875),x87501),f328(f37(f882(x87502,a870)),x87503)),f328(f37(x87502),f39(f882(x87502,a870),x87503)))+P1(f328(f328(f330(f882(x87502,a870)),f459(x87501,x87503,x87502)),x87503))+P1(f328(f328(f330(f882(x87502,a870)),f457(x87501,x87503,x87502)),x87503))+~P1(f328(f61(f882(x87502,a870)),x87503))+~P1(f328(f61(x87502),f39(f882(x87502,a870),x87503))) % 154.70/154.57 [8775]~E(f328(f328(f105(f882(x87752,a870)),f458(x87751,x87753,x87752)),f457(x87751,x87753,x87752)),f192(f882(x87752,a870)))+E(f328(f328(f81(a875),x87751),f328(f37(f882(x87752,a870)),x87753)),f328(f37(x87752),f39(f882(x87752,a870),x87753)))+~P1(f328(f61(f882(x87752,a870)),x87753))+P1(f328(f328(f330(f882(x87752,a870)),f459(x87751,x87753,x87752)),x87753))+~P1(f328(f61(x87752),f39(f882(x87752,a870),x87753))) % 154.70/154.57 [9036]~P94(x90362)+E(x90361,f192(f882(x90362,a870)))+~E(f328(f328(f81(x90362),f328(x90363,f387(x90361,x90363,x90362))),f328(x90363,f388(x90361,x90363,x90362))),f328(x90363,f328(f328(f81(x90362),f387(x90361,x90363,x90362)),f388(x90361,x90363,x90362))))+~P1(f328(f61(x90362),x90361))+E(f328(f63(x90362,f81(x90362)),f328(f307(x90362,x90362,x90363),x90361)),f328(x90363,f328(f63(x90362,f81(x90362)),x90361))) % 154.70/154.57 [9965]P1(f328(f328(x99651,x99652),x99653))+P1(f328(f328(f243(a1),f536(x99651,x99653,x99652)),f537(x99651,x99653,x99652)))+P1(f328(f328(f242(a1),f537(x99651,x99653,x99652)),f2(a1)))+P1(f328(f328(x99651,f536(x99651,x99653,x99652)),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f537(x99651,x99653,x99652))))+~P1(f328(f316(f881(a1,a1),a56),f328(f328(f263(a1,a1),x99652),x99653))) % 154.70/154.57 [9971]P1(f328(f328(x99711,x99712),x99713))+P1(f328(f328(f242(a1),f534(x99711,x99713,x99712)),f2(a1)))+P1(f328(f328(x99711,f530(x99711,x99713,x99712)),f328(f328(f81(a1),f328(f107(a1),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f534(x99711,x99713,x99712))))+P1(f328(f328(f242(a1),f2(a1)),f328(f328(f80(a1),f530(x99711,x99713,x99712)),f534(x99711,x99713,x99712))))+~P1(f328(f316(f881(a1,a1),a51),f328(f328(f263(a1,a1),x99712),x99713))) % 154.70/154.57 [7923]~P121(x79231)+~P1(f328(f328(f242(x79231),x79232),f78(x79231)))+~P1(f328(f328(f242(x79231),f2(x79231)),x79232))+~P1(f328(f328(f242(x79231),f2(x79231)),x79233))+P1(f328(f328(f242(x79231),f328(f328(f81(x79231),x79232),x79233)),x79233)) % 154.70/154.57 [7924]~P121(x79241)+~P1(f328(f328(f242(x79241),x79243),f78(x79241)))+~P1(f328(f328(f242(x79241),f2(x79241)),x79243))+~P1(f328(f328(f242(x79241),f2(x79241)),x79242))+P1(f328(f328(f242(x79241),f328(f328(f81(x79241),x79242),x79243)),x79242)) % 154.70/154.57 [8288]~P105(x82882)+E(x82881,f192(f882(x82882,a870)))+~P1(f328(f61(x82882),x82881))+P1(f328(f328(f330(x82882),f472(x82883,x82881,x82882)),x82881))+~P1(f328(f328(f242(x82882),f328(f63(x82882,f240(x82882)),x82881)),x82883)) % 154.70/154.57 [8289]~P105(x82892)+E(x82891,f192(f882(x82892,a870)))+~P1(f328(f61(x82892),x82891))+P1(f328(f328(f330(x82892),f474(x82893,x82891,x82892)),x82891))+~P1(f328(f328(f243(x82892),f328(f63(x82892,f240(x82892)),x82891)),x82893)) % 154.70/154.57 [8290]~P105(x82902)+E(x82901,f192(f882(x82902,a870)))+~P1(f328(f61(x82902),x82901))+P1(f328(f328(f243(x82902),f474(x82903,x82901,x82902)),x82903))+~P1(f328(f328(f243(x82902),f328(f63(x82902,f240(x82902)),x82901)),x82903)) % 154.70/154.57 [8291]~P105(x82912)+E(x82911,f192(f882(x82912,a870)))+~P1(f328(f61(x82912),x82911))+P1(f328(f328(f242(x82912),f472(x82913,x82911,x82912)),x82913))+~P1(f328(f328(f242(x82912),f328(f63(x82912,f240(x82912)),x82911)),x82913)) % 154.70/154.57 [8376]~P1(f328(x83761,x83763))+P1(f328(x83761,f421(x83761,x83762)))+P1(f328(x83761,f413(x83761,x83762)))+~P1(f328(f328(f243(a1),f2(a1)),x83762))+P1(f328(x83761,f328(f328(f22(a1),f413(x83761,x83762)),f328(f328(f81(a1),f422(x83761,x83762)),x83762)))) % 154.70/154.57 [8599]~P1(f328(x85991,x85993))+P1(f328(x85991,f413(x85991,x85992)))+~P1(f328(f328(f243(a1),f2(a1)),x85992))+P1(f328(f328(f330(a1),f421(x85991,x85992)),f299(a1,f78(a1),x85992)))+P1(f328(x85991,f328(f328(f22(a1),f413(x85991,x85992)),f328(f328(f81(a1),f422(x85991,x85992)),x85992)))) % 154.70/154.57 [8797]~P1(f328(x87971,x87973))+~P1(f328(x87971,f413(x87971,x87972)))+P1(f328(x87971,f421(x87971,x87972)))+~P1(f328(f328(f243(a1),f2(a1)),x87972))+~P1(f328(x87971,f328(f328(f22(a1),f413(x87971,x87972)),f328(f328(f81(a1),f422(x87971,x87972)),x87972)))) % 154.70/154.57 [8921]~P1(f328(x89211,x89213))+~P1(f328(x89211,f413(x89211,x89212)))+~P1(f328(f328(f243(a1),f2(a1)),x89212))+P1(f328(f328(f330(a1),f421(x89211,x89212)),f299(a1,f78(a1),x89212)))+~P1(f328(x89211,f328(f328(f22(a1),f413(x89211,x89212)),f328(f328(f81(a1),f422(x89211,x89212)),x89212)))) % 154.70/154.57 [8709]~P2(x87091)+~P1(f328(f61(x87091),x87092))+E(f328(f328(f22(f882(x87091,a870)),x87092),f328(f328(f306(x87091),x87093),f192(f882(x87091,a870)))),f192(f882(x87091,a870)))+~P1(f328(f328(f330(x87091),x87093),x87092))+E(f328(f328(f114(x87091),x87093),f10(x87091,f328(f328(f22(f882(x87091,a870)),x87092),f328(f328(f306(x87091),x87093),f192(f882(x87091,a870)))))),f10(x87091,x87092)) % 154.70/154.57 [8710]~P2(x87101)+~P1(f328(f61(x87101),x87102))+E(f328(f328(f22(f882(x87101,a870)),x87102),f328(f328(f306(x87101),x87103),f192(f882(x87101,a870)))),f192(f882(x87101,a870)))+~P1(f328(f328(f330(x87101),x87103),x87102))+E(f328(f328(f105(x87101),x87103),f11(x87101,f328(f328(f22(f882(x87101,a870)),x87102),f328(f328(f306(x87101),x87103),f192(f882(x87101,a870)))))),f11(x87101,x87102)) % 154.70/154.57 [8711]~P105(x87111)+~P1(f328(f61(x87111),x87112))+E(f328(f328(f22(f882(x87111,a870)),x87112),f328(f328(f306(x87111),x87113),f192(f882(x87111,a870)))),f192(f882(x87111,a870)))+~P1(f328(f328(f330(x87111),x87113),x87112))+E(f328(f328(f240(x87111),x87113),f14(x87111,f328(f328(f22(f882(x87111,a870)),x87112),f328(f328(f306(x87111),x87113),f192(f882(x87111,a870)))))),f14(x87111,x87112)) % 154.70/154.57 [8712]~P105(x87121)+~P1(f328(f61(x87121),x87122))+E(f328(f328(f22(f882(x87121,a870)),x87122),f328(f328(f306(x87121),x87123),f192(f882(x87121,a870)))),f192(f882(x87121,a870)))+~P1(f328(f328(f330(x87121),x87123),x87122))+E(f328(f328(f241(x87121),x87123),f15(x87121,f328(f328(f22(f882(x87121,a870)),x87122),f328(f328(f306(x87121),x87123),f192(f882(x87121,a870)))))),f15(x87121,x87122)) % 154.70/154.57 [8769]~P105(x87691)+~P1(f328(f61(x87691),x87692))+E(f328(f328(f22(f882(x87691,a870)),x87692),f328(f328(f306(x87691),x87693),f192(f882(x87691,a870)))),f192(f882(x87691,a870)))+~P1(f328(f328(f330(x87691),x87693),x87692))+E(f328(f328(f241(x87691),x87693),f12(x87691,f241(x87691),f328(f328(f22(f882(x87691,a870)),x87692),f328(f328(f306(x87691),x87693),f192(f882(x87691,a870)))))),f12(x87691,f241(x87691),x87692)) % 154.70/154.57 [8770]~P105(x87701)+~P1(f328(f61(x87701),x87702))+E(f328(f328(f22(f882(x87701,a870)),x87702),f328(f328(f306(x87701),x87703),f192(f882(x87701,a870)))),f192(f882(x87701,a870)))+~P1(f328(f328(f330(x87701),x87703),x87702))+E(f328(f328(f240(x87701),x87703),f13(x87701,f240(x87701),f328(f328(f22(f882(x87701,a870)),x87702),f328(f328(f306(x87701),x87703),f192(f882(x87701,a870)))))),f13(x87701,f240(x87701),x87702)) % 154.70/154.57 [8784]~P2(x87841)+~P1(f328(f61(x87841),x87843))+~P1(f328(f61(x87841),x87842))+E(f328(f328(f105(f882(x87841,a870)),x87842),x87843),f192(f882(x87841,a870)))+E(f328(f328(f114(x87841),f10(x87841,f328(f328(f114(f882(x87841,a870)),x87842),x87843))),f10(x87841,f328(f328(f105(f882(x87841,a870)),x87842),x87843))),f328(f328(f114(x87841),f10(x87841,x87842)),f10(x87841,x87843))) % 154.70/154.57 [8785]~P2(x87851)+~P1(f328(f61(x87851),x87853))+~P1(f328(f61(x87851),x87852))+E(f328(f328(f105(f882(x87851,a870)),x87852),x87853),f192(f882(x87851,a870)))+E(f328(f328(f105(x87851),f11(x87851,f328(f328(f114(f882(x87851,a870)),x87852),x87853))),f11(x87851,f328(f328(f105(f882(x87851,a870)),x87852),x87853))),f328(f328(f105(x87851),f11(x87851,x87852)),f11(x87851,x87853))) % 154.70/154.57 [8786]~P105(x87861)+~P1(f328(f61(x87861),x87863))+~P1(f328(f61(x87861),x87862))+E(f328(f328(f105(f882(x87861,a870)),x87862),x87863),f192(f882(x87861,a870)))+E(f328(f328(f240(x87861),f14(x87861,f328(f328(f114(f882(x87861,a870)),x87862),x87863))),f14(x87861,f328(f328(f105(f882(x87861,a870)),x87862),x87863))),f328(f328(f240(x87861),f14(x87861,x87862)),f14(x87861,x87863))) % 154.70/154.57 [8787]~P105(x87871)+~P1(f328(f61(x87871),x87873))+~P1(f328(f61(x87871),x87872))+E(f328(f328(f105(f882(x87871,a870)),x87872),x87873),f192(f882(x87871,a870)))+E(f328(f328(f241(x87871),f15(x87871,f328(f328(f114(f882(x87871,a870)),x87872),x87873))),f15(x87871,f328(f328(f105(f882(x87871,a870)),x87872),x87873))),f328(f328(f241(x87871),f15(x87871,x87872)),f15(x87871,x87873))) % 154.70/154.57 [9008]~P105(x90081)+~P1(f328(f61(x90081),x90083))+~P1(f328(f61(x90081),x90082))+E(f328(f328(f105(f882(x90081,a870)),x90082),x90083),f192(f882(x90081,a870)))+E(f328(f328(f240(x90081),f13(x90081,f240(x90081),f328(f328(f114(f882(x90081,a870)),x90082),x90083))),f13(x90081,f240(x90081),f328(f328(f105(f882(x90081,a870)),x90082),x90083))),f328(f328(f240(x90081),f13(x90081,f240(x90081),x90082)),f13(x90081,f240(x90081),x90083))) % 154.70/154.57 [9009]~P105(x90091)+~P1(f328(f61(x90091),x90093))+~P1(f328(f61(x90091),x90092))+E(f328(f328(f105(f882(x90091,a870)),x90092),x90093),f192(f882(x90091,a870)))+E(f328(f328(f241(x90091),f12(x90091,f241(x90091),f328(f328(f114(f882(x90091,a870)),x90092),x90093))),f12(x90091,f241(x90091),f328(f328(f105(f882(x90091,a870)),x90092),x90093))),f328(f328(f241(x90091),f12(x90091,f241(x90091),x90092)),f12(x90091,f241(x90091),x90093))) % 154.70/154.57 [9805]~P123(x98053)+E(x98051,x98052)+~P1(f328(f328(f242(x98053),f2(x98053)),x98052))+~P1(f328(f328(f242(x98053),f2(x98053)),x98051))+~E(f328(f328(f253(x98053),x98051),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)))),f328(f328(f253(x98053),x98052),f328(f107(a875),f328(f328(f80(a1),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101)),f328(f328(f22(a1),f328(f328(f80(a1),a83),a83)),a101))))) % 154.70/154.57 [6318]E(f809(x63181,x63182,x63183),x63184)+E(f328(x63181,x63184),f2(a875))+~E(f328(f328(f6(x63183,a875),x63181),x63182),f78(a875))+~P1(f328(f61(x63183),x63182))+~P1(f328(f328(f330(x63183),x63184),x63182)) % 154.70/154.57 [6379]E(f851(x63791,x63792,x63793),x63794)+E(f328(x63791,x63794),f2(a875))+~E(f328(f328(f6(x63793,a875),x63791),x63792),f328(a116,f2(a875)))+~P1(f328(f61(x63793),x63792))+~P1(f328(f328(f330(x63793),x63794),x63792)) % 154.70/154.57 [6485]~P5(x64851)+~P105(x64851)+P1(f328(f328(f243(x64851),x64852),f39(x64851,x64853)))+~P1(f328(f328(f243(x64851),x64852),x64854))+~P1(f328(f328(f330(x64851),x64854),x64853)) % 154.70/154.57 [6658]~P5(x66581)+~P105(x66581)+~P1(f328(f328(f243(x66581),x66584),x66583))+P1(f328(f328(f243(x66581),f40(x66581,x66582)),x66583))+~P1(f328(f328(f330(x66581),x66584),x66582)) % 154.70/154.57 [6917]~P123(x69173)+E(x69171,x69172)+~E(f328(f328(f253(x69173),x69171),f328(a116,x69174)),f328(f328(f253(x69173),x69172),f328(a116,x69174)))+~P1(f328(f328(f242(x69173),f2(x69173)),x69172))+~P1(f328(f328(f242(x69173),f2(x69173)),x69171)) % 154.70/154.57 [7126]~E(f842(x71262,x71263,x71261,x71264),x71264)+~E(f328(x71262,x71264),f78(a875))+E(f328(f328(f6(x71261,a875),x71262),x71263),f78(a875))+~P1(f328(f61(x71261),x71263))+~P1(f328(f328(f330(x71261),x71264),x71263)) % 154.70/154.57 [7133]~P109(x71334)+~P129(x71334)+E(f328(x71331,f456(x71331,x71332,x71333,x71334)),f2(x71334))+~E(f328(f328(f9(x71333,x71334),x71331),x71332),f2(x71334))+~P1(f328(f61(x71333),x71332)) % 154.70/154.57 [7221]~E(f859(x72212,x72213,x72211,x72214),x72214)+~E(f328(x72212,x72214),f328(a116,f2(a875)))+E(f328(f328(f6(x72211,a875),x72212),x72213),f328(a116,f2(a875)))+~P1(f328(f61(x72211),x72213))+~P1(f328(f328(f330(x72211),x72214),x72213)) % 154.70/154.57 [7963]~E(f328(x79632,x79634),f78(a875))+~E(f328(x79632,f842(x79632,x79633,x79631,x79634)),f2(a875))+E(f328(f328(f6(x79631,a875),x79632),x79633),f78(a875))+~P1(f328(f61(x79631),x79633))+~P1(f328(f328(f330(x79631),x79634),x79633)) % 154.70/154.57 [8001]~E(f328(x80012,x80014),f328(a116,f2(a875)))+~E(f328(x80012,f859(x80012,x80013,x80011,x80014)),f2(a875))+E(f328(f328(f6(x80011,a875),x80012),x80013),f328(a116,f2(a875)))+~P1(f328(f61(x80011),x80013))+~P1(f328(f328(f330(x80011),x80014),x80013)) % 154.70/154.57 [8569]~P105(x85691)+~P16(x85691,x85694)+P16(x85691,x85692)+~E(x85692,f328(f328(f148(x85691),x85693),x85694))+~P1(f328(f328(f242(x85691),x85693),f766(x85692,x85691,x85694,x85693))) % 154.70/154.57 [8603]E(x86031,x86032)+E(f328(f328(f22(a1),f396(x86033,x86032,x86034,x86031)),f397(x86033,x86032,x86034,x86031)),x86031)+~E(f328(f328(f80(a1),x86031),x86034),x86032)+~P1(f328(f328(f243(a1),f2(a1)),x86034))+~P1(f328(f328(f330(a1),x86032),x86033)) % 154.70/154.57 [8604]E(x86041,x86042)+E(f328(f328(f80(a1),f402(x86043,x86042,x86044,x86041)),f403(x86043,x86042,x86044,x86041)),x86041)+~E(f328(f328(f22(a1),x86041),x86044),x86042)+~P1(f328(f328(f243(a1),f2(a1)),x86044))+~P1(f328(f328(f330(a1),x86042),x86043)) % 154.70/154.57 [8782]E(f328(x87821,f622(x87822,x87821,x87823,x87824)),x87822)+P1(f328(f328(f242(a875),x87824),f623(x87822,x87821,x87823,x87824)))+~P1(f328(f328(f242(a1),x87822),f328(x87821,x87823)))+~P1(f328(f328(f243(a875),x87824),x87823))+~P1(f328(f328(f242(a1),f328(x87821,x87824)),x87822)) % 154.70/154.57 [8783]~P105(x87831)+~P16(x87831,x87833)+P16(x87831,x87832)+~E(x87832,f328(f328(f148(x87831),x87834),x87833))+P1(f328(f328(f330(x87831),f766(x87832,x87831,x87833,x87834)),f328(f170(x87831),x87833))) % 154.70/154.57 [8801]~P109(x88014)+~P129(x88014)+~E(f328(f328(f9(x88011,x88014),x88012),x88013),f2(x88014))+~P1(f328(f61(x88011),x88013))+P1(f328(f328(f330(x88011),f456(x88012,x88013,x88011,x88014)),x88013)) % 154.70/154.57 [8835]~E(f328(x88352,x88354),f78(a875))+E(f328(f328(f6(x88351,a875),x88352),x88353),f78(a875))+~P1(f328(f61(x88351),x88353))+~P1(f328(f328(f330(x88351),x88354),x88353))+P1(f328(f328(f330(x88351),f842(x88352,x88353,x88351,x88354)),x88353)) % 154.70/154.57 [8844]E(x88441,x88442)+~E(f328(f328(f80(a1),x88442),x88444),x88441)+~P1(f328(f328(f243(a1),f2(a1)),x88444))+~P1(f328(f328(f330(a1),x88441),x88443))+P1(f328(f328(f330(a1),f396(x88443,x88441,x88444,x88442)),x88443)) % 154.70/154.57 [8845]E(x88451,x88452)+~E(f328(f328(f22(a1),x88452),x88454),x88451)+~P1(f328(f328(f243(a1),f2(a1)),x88454))+~P1(f328(f328(f330(a1),x88451),x88453))+P1(f328(f328(f330(a1),f402(x88453,x88451,x88454,x88452)),x88453)) % 154.70/154.57 [8847]~E(f328(x88472,x88474),f328(a116,f2(a875)))+E(f328(f328(f6(x88471,a875),x88472),x88473),f328(a116,f2(a875)))+~P1(f328(f61(x88471),x88473))+~P1(f328(f328(f330(x88471),x88474),x88473))+P1(f328(f328(f330(x88471),f859(x88472,x88473,x88471,x88474)),x88473)) % 154.70/154.57 [8852]P55(x88522,x88523,x88524,x88521)+E(x88521,f192(f882(x88522,a870)))+~P1(f328(f61(x88522),x88524))+~P1(f328(f61(x88522),x88521))+P1(f328(f328(f330(x88522),f559(x88521,x88524,x88523,x88522)),x88524)) % 154.70/154.57 [8935]E(x89351,x89352)+~E(f328(f328(f80(a1),x89352),x89354),x89351)+~P1(f328(f328(f243(a1),f2(a1)),x89354))+~P1(f328(f328(f330(a1),x89351),x89353))+P1(f328(f328(f330(a1),f397(x89353,x89351,x89354,x89352)),f299(a1,f78(a1),x89354))) % 154.70/154.57 [8936]E(x89361,x89362)+~E(f328(f328(f22(a1),x89362),x89364),x89361)+~P1(f328(f328(f243(a1),f2(a1)),x89364))+~P1(f328(f328(f330(a1),x89361),x89363))+P1(f328(f328(f330(a1),f403(x89363,x89361,x89364,x89362)),f299(a1,f78(a1),x89364))) % 154.70/154.57 [9014]P1(f328(f328(f242(a875),x90141),f622(x90142,x90143,x90144,x90141)))+~P1(f328(f328(f242(a1),x90142),f328(x90143,x90144)))+P1(f328(f328(f242(a875),x90141),f623(x90142,x90143,x90144,x90141)))+~P1(f328(f328(f243(a875),x90141),x90144))+~P1(f328(f328(f242(a1),f328(x90143,x90141)),x90142)) % 154.70/154.57 [9127]E(f328(x91271,f622(x91272,x91271,x91273,x91274)),x91272)+~P1(f328(f328(f242(a1),x91272),f328(x91271,x91273)))+P1(f328(f328(f243(a875),f623(x91272,x91271,x91273,x91274)),x91273))+~P1(f328(f328(f243(a875),x91274),x91273))+~P1(f328(f328(f242(a1),f328(x91271,x91274)),x91272)) % 154.70/154.57 [9258]~P1(f328(f328(f242(a1),x92582),f328(x92583,x92584)))+P1(f328(f328(f242(a875),x92581),f623(x92582,x92583,x92584,x92581)))+P1(f328(f328(f242(a875),f622(x92582,x92583,x92584,x92581)),x92584))+~P1(f328(f328(f243(a875),x92581),x92584))+~P1(f328(f328(f242(a1),f328(x92583,x92581)),x92582)) % 154.70/154.57 [9259]~P1(f328(f328(f242(a1),x92592),f328(x92593,x92594)))+P1(f328(f328(f242(a875),x92591),f622(x92592,x92593,x92594,x92591)))+P1(f328(f328(f243(a875),f623(x92592,x92593,x92594,x92591)),x92594))+~P1(f328(f328(f243(a875),x92591),x92594))+~P1(f328(f328(f242(a1),f328(x92593,x92591)),x92592)) % 154.70/154.57 [9366]~P1(f328(f328(f242(a1),x93661),f328(x93662,x93663)))+P1(f328(f328(f242(a875),f622(x93661,x93662,x93663,x93664)),x93663))+~P1(f328(f328(f243(a875),x93664),x93663))+~P1(f328(f328(f242(a1),f328(x93662,x93664)),x93661))+P1(f328(f328(f243(a875),f623(x93661,x93662,x93663,x93664)),x93663)) % 154.70/154.57 [9444]E(x94441,f192(f882(x94442,a870)))+~P1(f328(f61(x94442),x94444))+~P1(f328(f61(x94442),x94441))+P1(f328(f328(f330(f881(f882(x94442,a870),f882(x94442,a870))),f328(f328(f263(f882(x94442,a870),f882(x94442,a870)),x94444),x94441)),f319(x94442,x94443)))+P1(f328(f328(f330(x94442),f561(x94443,x94441,x94444,x94442)),x94444)) % 154.70/154.57 [9445]E(x94451,f192(f882(x94452,a870)))+~P1(f328(f61(x94452),x94454))+~P1(f328(f61(x94452),x94451))+P1(f328(f328(f330(f881(f882(x94452,a870),f882(x94452,a870))),f328(f328(f263(f882(x94452,a870),f882(x94452,a870)),x94454),x94451)),f319(x94452,x94453)))+P1(f328(f328(f330(x94452),f618(x94453,x94451,x94454,x94452)),x94454)) % 154.70/154.57 [10107]E(f328(x101071,f622(x101072,x101071,x101073,x101074)),x101072)+~P1(f328(f328(f242(a1),x101072),f328(x101071,x101073)))+~P1(f328(f328(f242(a1),f328(f75(a1),f328(f328(f22(a1),f328(x101071,f328(f328(f80(a875),f623(x101072,x101071,x101073,x101074)),f78(a875)))),f328(x101071,f623(x101072,x101071,x101073,x101074))))),f78(a1)))+~P1(f328(f328(f243(a875),x101074),x101073))+~P1(f328(f328(f242(a1),f328(x101071,x101074)),x101072)) % 154.70/154.57 [10108]~P1(f328(f328(f242(a1),x101082),f328(x101083,x101084)))+P1(f328(f328(f242(a875),x101081),f622(x101082,x101083,x101084,x101081)))+~P1(f328(f328(f242(a1),f328(f75(a1),f328(f328(f22(a1),f328(x101083,f328(f328(f80(a875),f623(x101082,x101083,x101084,x101081)),f78(a875)))),f328(x101083,f623(x101082,x101083,x101084,x101081))))),f78(a1)))+~P1(f328(f328(f243(a875),x101081),x101084))+~P1(f328(f328(f242(a1),f328(x101083,x101081)),x101082)) % 154.70/154.57 [10109]~P1(f328(f328(f242(a1),x101091),f328(x101092,x101093)))+~P1(f328(f328(f242(a1),f328(f75(a1),f328(f328(f22(a1),f328(x101092,f328(f328(f80(a875),f623(x101091,x101092,x101093,x101094)),f78(a875)))),f328(x101092,f623(x101091,x101092,x101093,x101094))))),f78(a1)))+~P1(f328(f328(f243(a875),x101094),x101093))+~P1(f328(f328(f242(a1),f328(x101092,x101094)),x101091))+P1(f328(f328(f242(a875),f622(x101091,x101092,x101093,x101094)),x101093)) % 154.70/154.57 [7188]~P62(x71881)+P1(f328(f328(f243(x71881),x71882),f2(x71881)))+~P1(f328(f328(f243(x71881),x71883),f2(x71881)))+P1(f328(f328(f243(x71881),f2(x71881)),x71882))+P1(f328(f328(f243(x71881),x71883),f328(f328(f286(x71881),x71884),x71882))) % 154.70/154.57 [7189]~P62(x71891)+P1(f328(f328(f243(x71891),x71892),f2(x71891)))+~P1(f328(f328(f242(x71891),x71893),f2(x71891)))+P1(f328(f328(f243(x71891),f2(x71891)),x71892))+P1(f328(f328(f242(x71891),x71893),f328(f328(f286(x71891),x71894),x71892))) % 154.70/154.57 [7437]~P62(x74371)+P1(f328(f328(f243(x74371),x74372),f2(x74371)))+P1(f328(f328(f243(x74371),x74373),f2(x74371)))+P1(f328(f328(f243(x74371),f2(x74371)),x74373))+~P1(f328(f328(f243(x74371),x74372),f328(f328(f286(x74371),x74374),x74373))) % 154.70/154.57 [7438]~P62(x74381)+P1(f328(f328(f243(x74381),x74382),f2(x74381)))+P1(f328(f328(f242(x74381),x74383),f2(x74381)))+P1(f328(f328(f243(x74381),f2(x74381)),x74382))+~P1(f328(f328(f242(x74381),x74383),f328(f328(f286(x74381),x74384),x74382))) % 154.70/154.57 [7556]E(x75561,x75562)+~E(f328(f328(f162(x75563),x75564),x75561),f328(f328(f162(x75563),x75564),x75562))+~P1(f328(f134(x75563),x75564))+~P1(f328(f328(f243(a875),x75562),f328(f193(f876(x75563)),x75564)))+~P1(f328(f328(f243(a875),x75561),f328(f193(f876(x75563)),x75564))) % 154.70/154.57 [7925]~P62(x79251)+~P1(f328(f328(f243(x79251),x79253),f2(x79251)))+P1(f328(f328(f243(x79251),f2(x79251)),x79252))+~P1(f328(f328(f243(x79251),x79254),f328(f328(f81(x79251),x79253),x79252)))+P1(f328(f328(f243(x79251),x79253),f328(f328(f286(x79251),x79254),x79252))) % 154.70/154.57 [7926]~P62(x79261)+~P1(f328(f328(f242(x79261),x79263),f2(x79261)))+P1(f328(f328(f243(x79261),f2(x79261)),x79262))+~P1(f328(f328(f242(x79261),x79264),f328(f328(f81(x79261),x79263),x79262)))+P1(f328(f328(f242(x79261),x79263),f328(f328(f286(x79261),x79264),x79262))) % 154.70/154.57 [7927]~P62(x79271)+~P1(f328(f328(f243(x79271),x79272),f2(x79271)))+P1(f328(f328(f243(x79271),f2(x79271)),x79272))+~P1(f328(f328(f243(x79271),x79274),f328(f328(f81(x79271),x79273),x79272)))+P1(f328(f328(f243(x79271),x79273),f328(f328(f286(x79271),x79274),x79272))) % 154.70/154.57 [7928]~P62(x79281)+~P1(f328(f328(f243(x79281),x79282),f2(x79281)))+P1(f328(f328(f243(x79281),f2(x79281)),x79282))+~P1(f328(f328(f243(x79281),x79284),f328(f328(f286(x79281),x79283),x79282)))+P1(f328(f328(f243(x79281),x79283),f328(f328(f81(x79281),x79284),x79282))) % 154.70/154.57 [7929]~P62(x79291)+~P1(f328(f328(f243(x79291),x79292),f2(x79291)))+P1(f328(f328(f243(x79291),f2(x79291)),x79292))+~P1(f328(f328(f242(x79291),x79294),f328(f328(f81(x79291),x79293),x79292)))+P1(f328(f328(f242(x79291),x79293),f328(f328(f286(x79291),x79294),x79292))) % 154.70/154.57 [7930]~P62(x79301)+~P1(f328(f328(f243(x79301),x79302),f2(x79301)))+P1(f328(f328(f243(x79301),f2(x79301)),x79302))+~P1(f328(f328(f242(x79301),x79304),f328(f328(f286(x79301),x79303),x79302)))+P1(f328(f328(f242(x79301),x79303),f328(f328(f81(x79301),x79304),x79302))) % 154.70/154.57 [8067]~P105(x80671)+~P16(x80671,x80672)+~P1(f328(f328(f242(a875),x80673),x80674))+P1(f328(f328(f242(x80671),f328(f328(f162(x80671),x80672),x80673)),f328(f328(f162(x80671),x80672),x80674)))+~P1(f328(f328(f243(a875),x80674),f328(f193(f876(x80671)),x80672))) % 154.70/154.57 [8119]~P123(x81191)+~P1(f328(f328(f243(x81191),x81192),f78(x81191)))+~P1(f328(f328(f243(x81191),f2(x81191)),x81192))+~P1(f328(f328(f243(a875),x81194),x81193))+P1(f328(f328(f243(x81191),f328(f328(f253(x81191),x81192),x81193)),f328(f328(f253(x81191),x81192),x81194))) % 154.70/154.57 [8120]~P123(x81201)+~P1(f328(f328(f242(x81201),x81202),f78(x81201)))+~P1(f328(f328(f242(x81201),f2(x81201)),x81202))+~P1(f328(f328(f242(a875),x81204),x81203))+P1(f328(f328(f242(x81201),f328(f328(f253(x81201),x81202),x81203)),f328(f328(f253(x81201),x81202),x81204))) % 154.70/154.57 [8121]~P123(x81211)+~P1(f328(f328(f242(x81211),f2(x81211)),x81212))+~P1(f328(f328(f243(a875),f2(a875)),x81213))+~P1(f328(f328(f243(x81211),x81212),x81214))+P1(f328(f328(f243(x81211),f328(f328(f253(x81211),x81212),x81213)),f328(f328(f253(x81211),x81214),x81213))) % 154.70/154.57 [8142]~P105(x81421)+~P16(x81421,f328(f166(x81421),x81422))+~P1(f328(f328(f242(a875),x81424),x81423))+P1(f328(f328(f242(x81421),f328(f328(f162(x81421),x81422),x81423)),f328(f328(f162(x81421),x81422),x81424)))+~P1(f328(f328(f243(a875),x81423),f328(f193(f876(x81421)),x81422))) % 154.70/154.57 [8398]~P63(x83981)+~P1(f328(f328(f243(x83981),x83982),f2(x83981)))+~P1(f328(f328(f243(x83981),x83983),x83984))+~P1(f328(f328(f243(x83981),f2(x83981)),f328(f328(f81(x83981),x83983),x83984)))+P1(f328(f328(f243(x83981),f328(f328(f286(x83981),x83982),x83983)),f328(f328(f286(x83981),x83982),x83984))) % 154.70/154.57 [8399]~P62(x83991)+~P1(f328(f328(f242(x83991),x83992),f2(x83991)))+~P1(f328(f328(f242(x83991),x83993),x83994))+~P1(f328(f328(f243(x83991),f2(x83991)),f328(f328(f81(x83991),x83993),x83994)))+P1(f328(f328(f242(x83991),f328(f328(f286(x83991),x83992),x83993)),f328(f328(f286(x83991),x83992),x83994))) % 154.70/154.57 [8409]~P63(x84091)+~P1(f328(f328(f243(x84091),x84094),x84093))+~P1(f328(f328(f243(x84091),f2(x84091)),x84092))+~P1(f328(f328(f243(x84091),f2(x84091)),f328(f328(f81(x84091),x84093),x84094)))+P1(f328(f328(f243(x84091),f328(f328(f286(x84091),x84092),x84093)),f328(f328(f286(x84091),x84092),x84094))) % 154.70/154.57 [8410]~P63(x84101)+~P1(f328(f328(f242(x84101),x84104),x84103))+~P1(f328(f328(f242(x84101),f2(x84101)),x84102))+~P1(f328(f328(f243(x84101),f2(x84101)),f328(f328(f81(x84101),x84103),x84104)))+P1(f328(f328(f242(x84101),f328(f328(f286(x84101),x84102),x84103)),f328(f328(f286(x84101),x84102),x84104))) % 154.70/154.57 [8512]P1(f328(x85121,x85122))+~P1(f328(f61(x85124),x85122))+P1(f328(x85121,f431(x85121,x85123,x85122,x85124)))+~P1(f328(x85121,f192(f882(x85124,a870))))+~P1(f328(f328(f242(f882(x85124,a870)),x85122),x85123)) % 154.70/154.57 [8520]P1(f328(x85201,x85202))+P1(f328(f61(x85203),f431(x85201,x85204,x85202,x85203)))+~P1(f328(f61(x85203),x85202))+~P1(f328(x85201,f192(f882(x85203,a870))))+~P1(f328(f328(f242(f882(x85203,a870)),x85202),x85204)) % 154.70/154.57 [8777]E(f328(f328(f80(a1),f416(x87771,x87772,x87773,x87774)),f417(x87771,x87772,x87773,x87774)),x87774)+~P1(f328(f328(f243(a1),f2(a1)),x87773))+~P1(f328(f328(f243(a1),x87772),x87774))+~P1(f328(f328(f330(a1),x87772),x87771))+P1(f328(f328(f243(a1),x87772),f328(f328(f22(a1),x87774),x87773))) % 154.70/154.57 [8996]~P1(f328(f328(f243(a1),f2(a1)),x89963))+~P1(f328(f328(f243(a1),x89962),x89964))+~P1(f328(f328(f330(a1),x89962),x89961))+P1(f328(f328(f330(a1),f416(x89961,x89962,x89963,x89964)),x89961))+P1(f328(f328(f243(a1),x89962),f328(f328(f22(a1),x89964),x89963))) % 154.70/154.57 [9007]P1(f328(x90071,x90072))+~P1(f328(f61(x90073),x90072))+P1(f328(f328(f330(x90073),f432(x90071,x90074,x90072,x90073)),x90074))+~P1(f328(x90071,f192(f882(x90073,a870))))+~P1(f328(f328(f242(f882(x90073,a870)),x90072),x90074)) % 154.70/154.57 [9024]E(f328(f328(f80(a1),f398(x90241,x90242,x90243,x90244)),f399(x90241,x90242,x90243,x90244)),x90244)+~P1(f328(f328(f243(a1),f2(a1)),x90243))+~P1(f328(f328(f242(a1),x90242),x90244))+P1(f328(f328(f242(a1),x90242),f328(f328(f22(a1),x90244),x90243)))+~P1(f328(f328(f330(a1),f328(f328(f22(a1),x90242),f78(a1))),x90241)) % 154.70/154.57 [9079]~P1(f328(f328(f243(a1),f2(a1)),x90793))+~P1(f328(f328(f243(a1),x90791),x90792))+~P1(f328(f328(f330(a1),x90791),x90794))+P1(f328(f328(f330(a1),f417(x90794,x90791,x90793,x90792)),f299(a1,f78(a1),x90793)))+P1(f328(f328(f243(a1),x90791),f328(f328(f22(a1),x90792),x90793))) % 154.70/154.57 [9174]~P1(f328(f328(f243(a1),f2(a1)),x91743))+~P1(f328(f328(f242(a1),x91742),x91744))+P1(f328(f328(f330(a1),f398(x91741,x91742,x91743,x91744)),x91741))+P1(f328(f328(f242(a1),x91742),f328(f328(f22(a1),x91744),x91743)))+~P1(f328(f328(f330(a1),f328(f328(f22(a1),x91742),f78(a1))),x91741)) % 154.70/154.57 [9214]~P1(f328(f328(f243(a1),f2(a1)),x92143))+~P1(f328(f328(f242(a1),x92141),x92142))+P1(f328(f328(f330(a1),f399(x92144,x92141,x92143,x92142)),f299(a1,f78(a1),x92143)))+P1(f328(f328(f242(a1),x92141),f328(f328(f22(a1),x92142),x92143)))+~P1(f328(f328(f330(a1),f328(f328(f22(a1),x92141),f78(a1))),x92144)) % 154.70/154.57 [9447]P1(f328(x94471,x94472))+~P1(f328(f328(f330(x94473),f432(x94471,x94474,x94472,x94473)),f431(x94471,x94474,x94472,x94473)))+~P1(f328(f61(x94473),x94472))+~P1(f328(x94471,f192(f882(x94473,a870))))+~P1(f328(f328(f242(f882(x94473,a870)),x94472),x94474)) % 154.70/154.57 [9664]P1(f328(x96641,x96642))+~P1(f328(f61(x96643),x96642))+~P1(f328(x96641,f328(f328(f306(x96643),f432(x96641,x96644,x96642,x96643)),f431(x96641,x96644,x96642,x96643))))+~P1(f328(x96641,f192(f882(x96643,a870))))+~P1(f328(f328(f242(f882(x96643,a870)),x96642),x96644)) % 154.70/154.57 [7694]~P62(x76941)+P1(f328(f328(f243(x76941),x76942),f2(x76941)))+P1(f328(f328(f243(x76941),f2(x76941)),x76942))+~P1(f328(f328(f243(x76941),f2(x76941)),x76944))+P1(f328(f328(f243(x76941),f328(f328(f286(x76941),x76943),x76942)),x76944)) % 154.70/154.57 [7695]~P62(x76951)+P1(f328(f328(f243(x76951),x76952),f2(x76951)))+~P1(f328(f328(f242(x76951),f2(x76951)),x76954))+P1(f328(f328(f243(x76951),f2(x76951)),x76952))+P1(f328(f328(f242(x76951),f328(f328(f286(x76951),x76953),x76952)),x76954)) % 154.70/154.57 [7976]~P1(f328(f328(f242(a1),x79764),f2(a1)))+~E(x79762,f328(f328(f80(a1),f328(f328(f81(a1),x79761),x79763)),x79764))+P1(f328(f328(f243(a1),f2(a1)),x79761))+~P1(f328(f328(f243(a1),x79761),x79764))+P1(f328(f48(x79762,x79761),f328(f328(f263(a1,a1),x79763),x79764))) % 154.70/154.57 [8010]~P1(f328(x80101,x80104))+P1(f328(x80101,f385(x80102,x80101,x80103)))+~P1(f328(f328(f243(a1),f2(a1)),x80103))+~P1(f328(f328(f242(a1),f2(a1)),x80102))+P1(f328(x80101,f328(f328(f22(a1),x80104),f328(f328(f81(a1),x80102),x80103)))) % 154.70/154.57 [8011]~P1(f328(x80111,x80114))+P1(f328(x80111,f386(x80112,x80111,x80113)))+~P1(f328(f328(f243(a1),f2(a1)),x80113))+~P1(f328(f328(f242(a1),f2(a1)),x80112))+P1(f328(x80111,f328(f328(f80(a1),x80114),f328(f328(f81(a1),x80112),x80113)))) % 154.70/154.57 [8012]~P62(x80121)+P1(f328(f328(f243(x80121),x80122),f2(x80121)))+P1(f328(f328(f243(x80121),f2(x80121)),x80122))+P1(f328(f328(f243(x80121),f2(x80121)),x80123))+~P1(f328(f328(f243(x80121),f328(f328(f286(x80121),x80124),x80122)),x80123)) % 154.70/154.57 [8013]~P62(x80131)+P1(f328(f328(f243(x80131),x80132),f2(x80131)))+P1(f328(f328(f243(x80131),f2(x80131)),x80132))+P1(f328(f328(f242(x80131),f2(x80131)),x80133))+~P1(f328(f328(f242(x80131),f328(f328(f286(x80131),x80134),x80132)),x80133)) % 154.70/154.57 [8061]~E(x80611,f328(f328(f80(a1),f328(f328(f81(a1),x80612),x80613)),x80614))+~P1(f328(f328(f243(a1),f2(a1)),x80612))+~P1(f328(f328(f242(a1),f2(a1)),x80614))+~P1(f328(f328(f243(a1),x80614),x80612))+P1(f328(f48(x80611,x80612),f328(f328(f263(a1,a1),x80613),x80614))) % 154.70/154.57 [8189]~P62(x81891)+P1(f328(f328(f243(x81891),x81892),f2(x81891)))+~P1(f328(f328(f243(x81891),f2(x81891)),x81894))+~P1(f328(f328(f243(x81891),x81893),f328(f328(f81(x81891),x81894),x81892)))+P1(f328(f328(f243(x81891),f328(f328(f286(x81891),x81893),x81892)),x81894)) % 154.70/154.57 [8190]~P62(x81901)+P1(f328(f328(f243(x81901),x81902),f2(x81901)))+~P1(f328(f328(f242(x81901),f2(x81901)),x81904))+~P1(f328(f328(f242(x81901),x81903),f328(f328(f81(x81901),x81904),x81902)))+P1(f328(f328(f242(x81901),f328(f328(f286(x81901),x81903),x81902)),x81904)) % 154.70/154.57 [8278]~P62(x82781)+P1(f328(f328(f243(x82781),x82782),f2(x82781)))+~P1(f328(f328(f243(x82781),x82783),f2(x82781)))+P1(f328(f328(f243(x82781),x82783),f328(f328(f286(x82781),x82784),x82782)))+~P1(f328(f328(f243(x82781),f328(f328(f81(x82781),x82783),x82782)),x82784)) % 154.70/154.57 [8279]~P62(x82791)+P1(f328(f328(f243(x82791),x82792),f2(x82791)))+~P1(f328(f328(f242(x82791),x82793),f2(x82791)))+P1(f328(f328(f242(x82791),x82793),f328(f328(f286(x82791),x82794),x82792)))+~P1(f328(f328(f242(x82791),f328(f328(f81(x82791),x82793),x82792)),x82794)) % 154.70/154.57 [8432]~P62(x84321)+~P1(f328(f328(f243(x84321),x84322),f2(x84321)))+P1(f328(f328(f243(x84321),f2(x84321)),x84322))+~P1(f328(f328(f243(x84321),f328(f328(f286(x84321),x84324),x84322)),x84323))+P1(f328(f328(f243(x84321),f328(f328(f81(x84321),x84323),x84322)),x84324)) % 154.70/154.57 [8433]~P62(x84331)+~P1(f328(f328(f243(x84331),x84332),f2(x84331)))+P1(f328(f328(f243(x84331),f2(x84331)),x84332))+~P1(f328(f328(f243(x84331),f328(f328(f81(x84331),x84334),x84332)),x84333))+P1(f328(f328(f243(x84331),f328(f328(f286(x84331),x84333),x84332)),x84334)) % 154.70/154.57 [8434]~P62(x84341)+~P1(f328(f328(f243(x84341),x84342),f2(x84341)))+P1(f328(f328(f243(x84341),f2(x84341)),x84342))+~P1(f328(f328(f242(x84341),f328(f328(f286(x84341),x84344),x84342)),x84343))+P1(f328(f328(f242(x84341),f328(f328(f81(x84341),x84343),x84342)),x84344)) % 154.70/154.57 [8435]~P62(x84351)+~P1(f328(f328(f243(x84351),x84352),f2(x84351)))+P1(f328(f328(f243(x84351),f2(x84351)),x84352))+~P1(f328(f328(f242(x84351),f328(f328(f81(x84351),x84354),x84352)),x84353))+P1(f328(f328(f242(x84351),f328(f328(f286(x84351),x84353),x84352)),x84354)) % 154.70/154.57 [8454]~P62(x84541)+~P1(f328(f328(f243(x84541),f2(x84541)),x84544))+P1(f328(f328(f243(x84541),f2(x84541)),x84542))+~P1(f328(f328(f243(x84541),f328(f328(f81(x84541),x84544),x84542)),x84543))+P1(f328(f328(f243(x84541),f328(f328(f286(x84541),x84543),x84542)),x84544)) % 154.70/154.57 [8455]~P62(x84551)+~P1(f328(f328(f242(x84551),f2(x84551)),x84554))+P1(f328(f328(f243(x84551),f2(x84551)),x84552))+~P1(f328(f328(f242(x84551),f328(f328(f81(x84551),x84554),x84552)),x84553))+P1(f328(f328(f242(x84551),f328(f328(f286(x84551),x84553),x84552)),x84554)) % 154.70/154.57 [8528]~P62(x85281)+~P1(f328(f328(f243(x85281),x85284),f2(x85281)))+~P1(f328(f328(f243(x85281),x85283),f328(f328(f81(x85281),x85282),x85284)))+P1(f328(f328(f243(x85281),x85282),f328(f328(f286(x85281),x85283),x85284)))+~P1(f328(f328(f243(x85281),f328(f328(f81(x85281),x85282),x85284)),x85283)) % 154.70/154.57 [8529]~P62(x85291)+~P1(f328(f328(f243(x85291),x85292),f2(x85291)))+~P1(f328(f328(f243(x85291),x85293),f328(f328(f81(x85291),x85292),x85294)))+P1(f328(f328(f243(x85291),x85292),f328(f328(f286(x85291),x85293),x85294)))+~P1(f328(f328(f243(x85291),f328(f328(f81(x85291),x85292),x85294)),x85293)) % 154.70/154.57 [8530]~P62(x85301)+~P1(f328(f328(f243(x85301),x85304),f2(x85301)))+~P1(f328(f328(f242(x85301),x85303),f328(f328(f81(x85301),x85302),x85304)))+P1(f328(f328(f242(x85301),x85302),f328(f328(f286(x85301),x85303),x85304)))+~P1(f328(f328(f242(x85301),f328(f328(f81(x85301),x85302),x85304)),x85303)) % 154.70/154.57 [8531]~P62(x85311)+~P1(f328(f328(f242(x85311),x85312),f2(x85311)))+~P1(f328(f328(f242(x85311),x85313),f328(f328(f81(x85311),x85312),x85314)))+P1(f328(f328(f242(x85311),x85312),f328(f328(f286(x85311),x85313),x85314)))+~P1(f328(f328(f242(x85311),f328(f328(f81(x85311),x85312),x85314)),x85313)) % 154.70/154.57 [8654]~P62(x86541)+~P1(f328(f328(f243(x86541),x86543),f2(x86541)))+~P1(f328(f328(f243(x86541),x86542),f328(f328(f81(x86541),x86544),x86543)))+~P1(f328(f328(f243(x86541),f328(f328(f81(x86541),x86544),x86543)),x86542))+P1(f328(f328(f243(x86541),f328(f328(f286(x86541),x86542),x86543)),x86544)) % 154.70/154.57 [8655]~P62(x86551)+~P1(f328(f328(f243(x86551),x86553),f2(x86551)))+~P1(f328(f328(f242(x86551),x86552),f328(f328(f81(x86551),x86554),x86553)))+~P1(f328(f328(f242(x86551),f328(f328(f81(x86551),x86554),x86553)),x86552))+P1(f328(f328(f242(x86551),f328(f328(f286(x86551),x86552),x86553)),x86554)) % 154.70/154.57 [8670]~P62(x86701)+~P1(f328(f328(f243(x86701),f2(x86701)),x86704))+~P1(f328(f328(f243(x86701),x86702),f328(f328(f81(x86701),x86704),x86703)))+~P1(f328(f328(f243(x86701),f328(f328(f81(x86701),x86704),x86703)),x86702))+P1(f328(f328(f243(x86701),f328(f328(f286(x86701),x86702),x86703)),x86704)) % 154.70/154.57 [8671]~P62(x86711)+~P1(f328(f328(f242(x86711),f2(x86711)),x86714))+~P1(f328(f328(f242(x86711),x86712),f328(f328(f81(x86711),x86714),x86713)))+~P1(f328(f328(f242(x86711),f328(f328(f81(x86711),x86714),x86713)),x86712))+P1(f328(f328(f242(x86711),f328(f328(f286(x86711),x86712),x86713)),x86714)) % 154.70/154.57 [8837]E(f328(f328(f22(a1),f407(x88371,x88372,x88373,x88374)),f408(x88371,x88372,x88373,x88374)),x88374)+~P1(f328(f328(f243(a1),f2(a1)),x88373))+~P1(f328(f328(f330(a1),x88372),x88371))+~P1(f328(f328(f243(a1),x88374),x88372))+P1(f328(f328(f243(a1),f328(f328(f80(a1),x88374),x88373)),x88372)) % 154.70/154.57 [8916]~P1(f328(x89161,x89162))+~P1(f328(f328(f243(a1),f2(a1)),x89164))+~P1(f328(f328(f242(a1),f2(a1)),x89163))+~P1(f328(x89161,f328(f328(f22(a1),f385(x89163,x89161,x89164)),x89164)))+P1(f328(x89161,f328(f328(f22(a1),x89162),f328(f328(f81(a1),x89163),x89164)))) % 154.70/154.57 [8917]~P1(f328(x89171,x89172))+~P1(f328(f328(f243(a1),f2(a1)),x89174))+~P1(f328(f328(f242(a1),f2(a1)),x89173))+~P1(f328(x89171,f328(f328(f80(a1),f386(x89173,x89171,x89174)),x89174)))+P1(f328(x89171,f328(f328(f80(a1),x89172),f328(f328(f81(a1),x89173),x89174)))) % 154.70/154.57 [9071]~P1(f328(f328(f243(a1),f2(a1)),x90713))+~P1(f328(f328(f330(a1),x90712),x90711))+~P1(f328(f328(f243(a1),x90714),x90712))+P1(f328(f328(f330(a1),f407(x90711,x90712,x90713,x90714)),x90711))+P1(f328(f328(f243(a1),f328(f328(f80(a1),x90714),x90713)),x90712)) % 154.70/154.57 [9093]E(f328(f328(f22(a1),f400(x90931,x90932,x90933,x90934)),f401(x90931,x90932,x90933,x90934)),x90934)+~P1(f328(f328(f243(a1),f2(a1)),x90933))+~P1(f328(f328(f242(a1),x90934),x90932))+~P1(f328(f328(f330(a1),f328(f328(f80(a1),x90932),f78(a1))),x90931))+P1(f328(f328(f242(a1),f328(f328(f80(a1),x90934),x90933)),x90932)) % 154.70/154.57 [9119]~P1(f328(f328(f243(a1),f2(a1)),x91192))+~P1(f328(f328(f330(a1),x91193),x91194))+~P1(f328(f328(f243(a1),x91191),x91193))+P1(f328(f328(f330(a1),f408(x91194,x91193,x91192,x91191)),f299(a1,f78(a1),x91192)))+P1(f328(f328(f243(a1),f328(f328(f80(a1),x91191),x91192)),x91193)) % 154.70/154.57 [9209]~P1(f328(f328(f243(a1),f2(a1)),x92093))+~P1(f328(f328(f242(a1),x92094),x92092))+P1(f328(f328(f330(a1),f400(x92091,x92092,x92093,x92094)),x92091))+~P1(f328(f328(f330(a1),f328(f328(f80(a1),x92092),f78(a1))),x92091))+P1(f328(f328(f242(a1),f328(f328(f80(a1),x92094),x92093)),x92092)) % 154.70/154.57 [9254]~P1(f328(f328(f243(a1),f2(a1)),x92542))+~P1(f328(f328(f242(a1),x92541),x92543))+P1(f328(f328(f330(a1),f401(x92544,x92543,x92542,x92541)),f299(a1,f78(a1),x92542)))+~P1(f328(f328(f330(a1),f328(f328(f80(a1),x92543),f78(a1))),x92544))+P1(f328(f328(f242(a1),f328(f328(f80(a1),x92541),x92542)),x92543)) % 154.70/154.57 [9540]~P39(x95401,x95403)+~P28(x95401,x95404)+P39(x95401,f328(f328(f114(f882(f881(x95401,x95401),a870)),x95402),x95403))+~P1(f328(f328(f242(f882(f881(x95401,x95401),a870)),x95402),f328(f262(f882(f881(x95401,x95401),a870),f882(f881(x95401,x95401),a870)),x95404)))+~P1(f328(f328(f242(f882(f881(x95401,x95401),a870)),x95403),f328(f266(f882(f881(x95401,x95401),a870),f882(f881(x95401,x95401),a870)),x95404))) % 154.70/154.57 [9833]~E(f328(f726(x98331,x98334,x98333,x98332),f728(x98331,x98334,x98333,x98332)),f205(f876(a324)))+P1(f328(f328(f243(a1),f727(x98331,x98334,x98333,x98332)),f728(x98331,x98334,x98333,x98332)))+P1(f328(f328(f328(x98331,x98332),x98333),x98334))+P1(f328(f328(f328(x98331,f726(x98331,x98334,x98333,x98332)),f727(x98331,x98334,x98333,x98332)),f328(f328(f80(a1),f728(x98331,x98334,x98333,x98332)),f78(a1))))+~P1(f328(f316(f881(f882(a1,f879(f876(a324))),f881(a1,a1)),a314),f328(f328(f263(f882(a1,f879(f876(a324))),f881(a1,a1)),x98332),f328(f328(f263(a1,a1),x98333),x98334)))) % 154.70/154.57 [9934]~P20(x99342,x99344,x99343)+E(x99341,f192(f882(x99342,a870)))+~P1(f328(f61(x99342),x99341))+P1(f328(f328(f330(x99342),f328(x99343,x99341)),x99341))+~P1(f328(f328(f330(x99342),f328(f328(x99344,f544(x99341,x99343,x99344,x99342)),f555(x99341,x99343,x99344,x99342))),f328(f328(f306(x99342),f544(x99341,x99343,x99344,x99342)),f328(f328(f306(x99342),f555(x99341,x99343,x99344,x99342)),f192(f882(x99342,a870)))))) % 154.70/154.57 [9865]~P107(x98652)+~P59(x98651)+~P1(f328(f328(f242(f882(x98651,x98652)),x98653),x98654))+P1(f328(f328(f243(f882(x98651,x98652)),x98653),x98654))+~P1(f328(f57(x98651),f328(f328(f8(a870,a870,x98651),a323),f328(f328(f18(x98651,x98652,a870),f328(f328(f8(x98652,f882(x98652,a870),x98651),a325),x98653)),x98654)))) % 154.70/154.57 [9455]~P51(x94551,x94551,x94554)+P1(f328(f328(f330(f881(x94551,x94551)),f328(f328(f263(x94551,x94551),x94552),x94553)),f304(x94551,x94554)))+P1(f328(f328(f330(f881(x94551,x94551)),f328(f328(f263(x94551,x94551),x94553),x94552)),f304(x94551,x94554)))+~P1(f328(f328(f330(f881(x94551,x94551)),f328(f328(f263(x94551,x94551),x94555),x94552)),f304(x94551,x94554)))+~P1(f328(f328(f330(f881(x94551,x94551)),f328(f328(f263(x94551,x94551),x94555),x94553)),f304(x94551,x94554))) % 154.70/154.57 [5602]E(x56021,f2(a875))+~E(f328(f37(x56022),x56025),x56021)+E(f328(f37(x56022),x56023),f328(a116,x56021))+~E(x56023,f328(f328(f306(x56022),x56024),x56025))+P1(f328(f328(f330(x56022),x56024),x56025)) % 154.70/154.57 [5728]~P61(x57282)+E(x57281,f2(x57282))+E(x57283,f2(x57282))+~E(f328(f328(f286(x57282),x57284),x57283),f328(f328(f286(x57282),x57285),x57281))+E(f328(f328(f81(x57282),x57284),x57281),f328(f328(f81(x57282),x57285),x57283)) % 154.70/154.57 [5729]~P61(x57292)+E(x57291,f2(x57292))+E(x57293,f2(x57292))+~E(f328(f328(f81(x57292),x57294),x57293),f328(f328(f81(x57292),x57295),x57291))+E(f328(f328(f286(x57292),x57294),x57291),f328(f328(f286(x57292),x57295),x57293)) % 154.70/154.57 [5795]~E(f328(f37(x57951),x57955),x57953)+~E(x57955,f192(f882(x57951,a870)))+E(f328(f37(x57951),x57952),f328(a116,x57953))+~E(x57952,f328(f328(f306(x57951),x57954),x57955))+P1(f328(f328(f330(x57951),x57954),x57955)) % 154.70/154.57 [6018]~P109(x60182)+~E(f328(x60183,x60185),f2(x60182))+E(f328(f328(f9(x60181,x60182),x60183),x60184),f2(x60182))+~P1(f328(f61(x60181),x60184))+~P1(f328(f328(f330(x60181),x60185),x60184)) % 154.70/154.57 [6392]~P105(x63923)+E(x63921,x63922)+~E(f328(f298(x63923,x63924),x63921),f328(f298(x63923,x63925),x63922))+~P1(f328(f328(f243(x63923),x63925),x63922))+~P1(f328(f328(f243(x63923),x63924),x63921)) % 154.70/154.57 [6393]~P105(x63933)+E(x63931,x63932)+~E(f328(f298(x63933,x63931),x63934),f328(f298(x63933,x63932),x63935))+~P1(f328(f328(f243(x63933),x63932),x63935))+~P1(f328(f328(f243(x63933),x63931),x63934)) % 154.70/154.57 [7454]~P105(x74541)+~P16(x74541,f328(f328(f125(x74541),x74544),x74545))+~P1(f328(f328(f330(x74541),x74543),f328(f170(x74541),x74545)))+~P1(f328(f328(f330(x74541),x74542),f328(f170(x74541),x74544)))+P1(f328(f328(f242(x74541),x74542),x74543)) % 154.70/154.57 [8571]~P107(x85711)+~P1(f328(f328(f243(f882(x85711,a870)),f299(x85711,x85715,x85712)),f299(x85711,x85714,x85713)))+~P1(f328(f328(f242(x85711),x85715),x85712))+P1(f328(f328(f243(x85711),x85712),x85713))+P1(f328(f328(f243(x85711),x85714),x85715)) % 154.70/154.57 [9977]~P19(x99772,x99775,x99773)+E(x99771,f192(f882(x99772,a870)))+~E(f328(f328(x99775,f328(x99774,f590(x99771,x99774,x99773,x99775,x99772))),f328(x99774,f603(x99771,x99774,x99773,x99775,x99772))),f328(x99774,f328(f328(x99775,f590(x99771,x99774,x99773,x99775,x99772)),f603(x99771,x99774,x99773,x99775,x99772))))+E(f328(x99773,f328(f307(x99772,x99772,x99774),x99771)),f328(x99774,f328(x99773,x99771)))+~P1(f328(f61(x99772),x99771)) % 154.70/154.57 [6389]~P20(x63892,x63895,x63893)+E(x63891,f192(f882(x63892,a870)))+~P1(f328(f61(x63892),x63891))+E(f328(x63893,f328(f328(f306(x63892),x63894),x63891)),f328(f328(x63895,x63894),f328(x63893,x63891)))+P1(f328(f328(f330(x63892),x63894),x63891)) % 154.70/154.57 [7212]~P19(x72122,x72123,x72124)+E(f328(f328(x72123,f328(x72124,x72121)),f328(x72124,x72125)),f328(x72124,x72125))+E(x72121,f192(f882(x72122,a870)))+~P1(f328(f61(x72122),x72125))+~P1(f328(f328(f242(f882(x72122,a870)),x72121),x72125)) % 154.70/154.57 [7430]~P59(x74304)+~P92(x74305)+E(f328(x74301,x74302),f328(x74303,x74302))+~P1(f328(f328(f330(x74304),x74302),f328(f170(x74304),f55(x74304))))+~P1(f328(f328(f91(f882(x74304,x74305)),x74301),x74303)) % 154.70/154.57 [7591]~P20(x75914,x75915,x75911)+E(f328(x75911,x75912),x75913)+~P1(f328(f61(x75914),x75912))+~E(f328(f328(f22(f882(x75914,a870)),x75912),f328(f328(f306(x75914),x75913),f192(f882(x75914,a870)))),f192(f882(x75914,a870)))+~P1(f328(f328(f330(x75914),x75913),x75912)) % 154.70/154.57 [7677]E(x76771,x76772)+~E(f328(f193(f876(x76773)),x76772),f328(f193(f876(x76774)),x76775))+~E(f328(f193(f876(x76773)),x76771),f328(f193(f876(x76774)),x76775))+~E(f328(f176(x76774,x76773),f328(f328(f180(x76774,x76773),x76775),x76771)),f328(f176(x76774,x76773),f328(f328(f180(x76774,x76773),x76775),x76772)))+~P1(f328(f134(x76774),x76775)) % 154.70/154.57 [8536]E(x85361,x85362)+~P8(x85363,x85364,x85365)+E(f328(f328(f105(f882(x85363,a870)),x85361),x85362),f192(f882(x85363,a870)))+~P1(f328(f328(f330(f882(x85363,a870)),x85362),f328(f328(f60(x85363),x85364),x85365)))+~P1(f328(f328(f330(f882(x85363,a870)),x85361),f328(f328(f60(x85363),x85364),x85365))) % 154.70/154.57 [9336]~P66(x93362)+~E(f328(x93363,f433(x93363,x93364,x93365,x93361,x93362)),f2(x93362))+E(f328(f328(f6(x93361,x93362),x93363),x93364),f328(f328(f6(x93361,x93362),x93363),x93365))+~P1(f328(f61(x93361),x93365))+~P1(f328(f328(f242(f882(x93361,a870)),x93364),x93365)) % 154.70/154.57 [9337]~P66(x93372)+~E(f328(x93373,f434(x93373,x93374,x93375,x93371,x93372)),f2(x93372))+E(f328(f328(f6(x93371,x93372),x93373),x93374),f328(f328(f6(x93371,x93372),x93373),x93375))+~P1(f328(f61(x93371),x93375))+~P1(f328(f328(f242(f882(x93371,a870)),x93374),x93375)) % 154.70/154.57 [9338]~P73(x93382)+~E(f328(x93383,f499(x93383,x93384,x93385,x93381,x93382)),f78(x93382))+E(f328(f328(f9(x93381,x93382),x93383),x93384),f328(f328(f9(x93381,x93382),x93383),x93385))+~P1(f328(f61(x93381),x93385))+~P1(f328(f328(f242(f882(x93381,a870)),x93384),x93385)) % 154.70/154.57 [9339]~P73(x93392)+~E(f328(x93393,f501(x93393,x93394,x93395,x93391,x93392)),f78(x93392))+E(f328(f328(f9(x93391,x93392),x93393),x93394),f328(f328(f9(x93391,x93392),x93393),x93395))+~P1(f328(f61(x93391),x93395))+~P1(f328(f328(f242(f882(x93391,a870)),x93394),x93395)) % 154.70/154.57 [9813]~P85(x98131)+~P1(f328(f61(x98132),x98135))+~P1(f328(f328(f242(x98131),f2(x98131)),f328(x98133,f360(x98133,x98134,x98135,x98132,x98131))))+P1(f328(f328(f242(x98131),f328(f328(f6(x98132,x98131),x98133),x98134)),f328(f328(f6(x98132,x98131),x98133),x98135)))+~P1(f328(f328(f242(f882(x98132,a870)),x98134),x98135)) % 154.70/154.57 [7451]E(x74511,f2(a875))+P1(f328(x74512,x74513))+~E(x74514,f328(f328(f80(a875),f328(f328(f81(a875),x74511),x74513)),x74515))+~P1(f328(f328(f243(a875),x74515),x74511))+~P1(f328(x74512,f328(f328(f38(a875),x74514),x74511))) % 154.70/154.57 [7530]E(x75301,f2(a875))+P1(f328(x75302,x75303))+~P1(f328(x75302,f44(a875,x75304,x75301)))+~E(x75304,f328(f328(f80(a875),f328(f328(f81(a875),x75301),x75305)),x75303))+~P1(f328(f328(f243(a875),x75303),x75301)) % 154.70/154.57 [7826]~P61(x78263)+E(f328(x78261,x78262),f2(x78263))+~P1(f328(f61(x78264),x78265))+E(f328(f328(f9(x78264,x78263),x78261),f328(f328(f22(f882(x78264,a870)),x78265),f328(f328(f306(x78264),x78262),f192(f882(x78264,a870))))),f328(f328(f9(x78264,x78263),x78261),x78265))+P1(f328(f328(f330(x78264),x78262),x78265)) % 154.70/154.57 [8236]~P66(x82361)+~P1(f328(f61(x82362),x82365))+~P1(f328(f61(x82362),x82364))+~E(f328(f328(f105(f882(x82362,a870)),x82364),x82365),f192(f882(x82362,a870)))+E(f328(f328(f80(x82361),f328(f328(f6(x82362,x82361),x82363),x82364)),f328(f328(f6(x82362,x82361),x82363),x82365)),f328(f328(f6(x82362,x82361),x82363),f328(f328(f114(f882(x82362,a870)),x82364),x82365))) % 154.70/154.57 [8238]~P73(x82381)+~P1(f328(f61(x82382),x82385))+~P1(f328(f61(x82382),x82384))+~E(f328(f328(f105(f882(x82382,a870)),x82384),x82385),f192(f882(x82382,a870)))+E(f328(f328(f81(x82381),f328(f328(f9(x82382,x82381),x82383),x82384)),f328(f328(f9(x82382,x82381),x82383),x82385)),f328(f328(f9(x82382,x82381),x82383),f328(f328(f114(f882(x82382,a870)),x82384),x82385))) % 154.70/154.57 [8331]~P61(x83313)+E(f328(x83311,x83312),f2(x83313))+~P1(f328(f61(x83314),x83315))+E(f328(f328(f9(x83314,x83313),x83311),f328(f328(f22(f882(x83314,a870)),x83315),f328(f328(f306(x83314),x83312),f192(f882(x83314,a870))))),f328(f328(f286(x83313),f328(f328(f9(x83314,x83313),x83311),x83315)),f328(x83311,x83312)))+~P1(f328(f328(f330(x83314),x83312),x83315)) % 154.70/154.57 [9049]~P8(x90491,x90495,x90494)+~E(f328(f328(f60(x90491),f328(f328(f306(x90491),x90492),f192(f882(x90491,a870)))),x90494),f328(f328(f60(x90491),f328(f328(f306(x90491),x90493),f192(f882(x90491,a870)))),x90494))+~P1(f328(f328(f330(x90491),x90493),x90495))+~P1(f328(f328(f330(x90491),x90492),x90495))+P1(f328(f328(f330(f881(x90491,x90491)),f328(f328(f263(x90491,x90491),x90492),x90493)),x90494)) % 154.70/154.57 [9070]~P8(x90701,x90705,x90703)+E(f328(f328(f60(x90701),f328(f328(f306(x90701),x90702),f192(f882(x90701,a870)))),x90703),f328(f328(f60(x90701),f328(f328(f306(x90701),x90704),f192(f882(x90701,a870)))),x90703))+~P1(f328(f328(f330(x90701),x90704),x90705))+~P1(f328(f328(f330(x90701),x90702),x90705))+~P1(f328(f328(f330(f881(x90701,x90701)),f328(f328(f263(x90701,x90701),x90702),x90704)),x90703)) % 154.70/154.57 [9365]~P73(x93651)+~P1(f328(f61(x93652),x93655))+~P1(f328(f61(x93652),x93654))+~E(f328(f328(f105(f882(x93652,a870)),x93654),x93655),f192(f882(x93652,a870)))+E(f328(f328(f81(x93651),f328(f328(f328(f65(x93651,x93652,f81(x93651)),x93653),f78(x93651)),x93654)),f328(f328(f328(f65(x93651,x93652,f81(x93651)),x93653),f78(x93651)),x93655)),f328(f328(f328(f65(x93651,x93652,f81(x93651)),x93653),f78(x93651)),f328(f328(f114(f882(x93652,a870)),x93654),x93655))) % 154.70/154.57 [9374]~P66(x93741)+~E(f328(x93743,f837(x93743,x93745,x93744,x93742,x93741)),f2(x93741))+~P1(f328(f61(x93742),x93744))+~P1(f328(f61(x93742),x93745))+E(f328(f328(f80(x93741),f328(f328(f6(x93742,x93741),x93743),x93744)),f328(f328(f6(x93742,x93741),x93743),x93745)),f328(f328(f6(x93742,x93741),x93743),f328(f328(f114(f882(x93742,a870)),x93744),x93745))) % 154.70/154.57 [9375]~P66(x93751)+~E(f328(x93753,f839(x93753,x93755,x93754,x93752,x93751)),f2(x93751))+~P1(f328(f61(x93752),x93754))+~P1(f328(f61(x93752),x93755))+E(f328(f328(f80(x93751),f328(f328(f6(x93752,x93751),x93753),x93754)),f328(f328(f6(x93752,x93751),x93753),x93755)),f328(f328(f6(x93752,x93751),x93753),f328(f328(f114(f882(x93752,a870)),x93754),x93755))) % 154.70/154.57 [9376]~P73(x93761)+~E(f328(x93763,f488(x93763,x93765,x93764,x93762,x93761)),f78(x93761))+~P1(f328(f61(x93762),x93764))+~P1(f328(f61(x93762),x93765))+E(f328(f328(f81(x93761),f328(f328(f9(x93762,x93761),x93763),x93764)),f328(f328(f9(x93762,x93761),x93763),x93765)),f328(f328(f9(x93762,x93761),x93763),f328(f328(f114(f882(x93762,a870)),x93764),x93765))) % 154.70/154.57 [9377]~P73(x93771)+~E(f328(x93773,f489(x93773,x93775,x93774,x93772,x93771)),f78(x93771))+~P1(f328(f61(x93772),x93774))+~P1(f328(f61(x93772),x93775))+E(f328(f328(f81(x93771),f328(f328(f9(x93772,x93771),x93773),x93774)),f328(f328(f9(x93772,x93771),x93773),x93775)),f328(f328(f9(x93772,x93771),x93773),f328(f328(f114(f882(x93772,a870)),x93774),x93775))) % 154.70/154.57 [9584]~P73(x95841)+~E(f328(x95843,f861(x95843,x95845,x95844,x95842,x95841)),f78(x95841))+~P1(f328(f61(x95842),x95844))+~P1(f328(f61(x95842),x95845))+E(f328(f328(f81(x95841),f328(f328(f328(f65(x95841,x95842,f81(x95841)),x95843),f78(x95841)),x95844)),f328(f328(f328(f65(x95841,x95842,f81(x95841)),x95843),f78(x95841)),x95845)),f328(f328(f328(f65(x95841,x95842,f81(x95841)),x95843),f78(x95841)),f328(f328(f114(f882(x95842,a870)),x95844),x95845))) % 154.70/154.57 [9692]~P66(x96922)+E(f328(f328(f6(x96921,x96922),x96923),x96924),f328(f328(f6(x96921,x96922),x96923),x96925))+~P1(f328(f61(x96921),x96925))+~P1(f328(f328(f242(f882(x96921,a870)),x96924),x96925))+P1(f328(f328(f330(x96921),f433(x96923,x96924,x96925,x96921,x96922)),f328(f328(f22(f882(x96921,a870)),x96925),x96924))) % 154.70/154.57 [9693]~P66(x96932)+E(f328(f328(f6(x96931,x96932),x96933),x96934),f328(f328(f6(x96931,x96932),x96933),x96935))+~P1(f328(f61(x96931),x96935))+~P1(f328(f328(f242(f882(x96931,a870)),x96934),x96935))+P1(f328(f328(f330(x96931),f434(x96933,x96934,x96935,x96931,x96932)),f328(f328(f22(f882(x96931,a870)),x96935),x96934))) % 154.70/154.57 [9694]~P73(x96942)+E(f328(f328(f9(x96941,x96942),x96943),x96944),f328(f328(f9(x96941,x96942),x96943),x96945))+~P1(f328(f61(x96941),x96945))+~P1(f328(f328(f242(f882(x96941,a870)),x96944),x96945))+P1(f328(f328(f330(x96941),f499(x96943,x96944,x96945,x96941,x96942)),f328(f328(f22(f882(x96941,a870)),x96945),x96944))) % 154.70/154.57 [9695]~P73(x96952)+E(f328(f328(f9(x96951,x96952),x96953),x96954),f328(f328(f9(x96951,x96952),x96953),x96955))+~P1(f328(f61(x96951),x96955))+~P1(f328(f328(f242(f882(x96951,a870)),x96954),x96955))+P1(f328(f328(f330(x96951),f501(x96953,x96954,x96955,x96951,x96952)),f328(f328(f22(f882(x96951,a870)),x96955),x96954))) % 154.70/154.57 [9712]~P66(x97121)+~P1(f328(f61(x97122),x97124))+~P1(f328(f61(x97122),x97125))+E(f328(f328(f80(x97121),f328(f328(f6(x97122,x97121),x97123),x97124)),f328(f328(f6(x97122,x97121),x97123),x97125)),f328(f328(f6(x97122,x97121),x97123),f328(f328(f114(f882(x97122,a870)),x97124),x97125)))+P1(f328(f328(f330(x97122),f837(x97123,x97125,x97124,x97122,x97121)),f328(f328(f105(f882(x97122,a870)),x97124),x97125))) % 154.70/154.57 [9713]~P66(x97131)+~P1(f328(f61(x97132),x97134))+~P1(f328(f61(x97132),x97135))+E(f328(f328(f80(x97131),f328(f328(f6(x97132,x97131),x97133),x97134)),f328(f328(f6(x97132,x97131),x97133),x97135)),f328(f328(f6(x97132,x97131),x97133),f328(f328(f114(f882(x97132,a870)),x97134),x97135)))+P1(f328(f328(f330(x97132),f839(x97133,x97135,x97134,x97132,x97131)),f328(f328(f105(f882(x97132,a870)),x97134),x97135))) % 154.70/154.57 [9714]~P73(x97141)+~P1(f328(f61(x97142),x97144))+~P1(f328(f61(x97142),x97145))+E(f328(f328(f81(x97141),f328(f328(f9(x97142,x97141),x97143),x97144)),f328(f328(f9(x97142,x97141),x97143),x97145)),f328(f328(f9(x97142,x97141),x97143),f328(f328(f114(f882(x97142,a870)),x97144),x97145)))+P1(f328(f328(f330(x97142),f488(x97143,x97145,x97144,x97142,x97141)),f328(f328(f105(f882(x97142,a870)),x97144),x97145))) % 154.70/154.57 [9715]~P73(x97151)+~P1(f328(f61(x97152),x97154))+~P1(f328(f61(x97152),x97155))+E(f328(f328(f81(x97151),f328(f328(f9(x97152,x97151),x97153),x97154)),f328(f328(f9(x97152,x97151),x97153),x97155)),f328(f328(f9(x97152,x97151),x97153),f328(f328(f114(f882(x97152,a870)),x97154),x97155)))+P1(f328(f328(f330(x97152),f489(x97153,x97155,x97154,x97152,x97151)),f328(f328(f105(f882(x97152,a870)),x97154),x97155))) % 154.70/154.57 [9722]~P85(x97225)+~P1(f328(f61(x97221),x97224))+P1(f328(f328(f242(x97225),f328(f328(f6(x97221,x97225),x97222),x97223)),f328(f328(f6(x97221,x97225),x97222),x97224)))+~P1(f328(f328(f242(f882(x97221,a870)),x97223),x97224))+P1(f328(f328(f330(x97221),f360(x97222,x97223,x97224,x97221,x97225)),f328(f328(f22(f882(x97221,a870)),x97224),x97223))) % 154.70/154.57 [9776]~P73(x97761)+~P1(f328(f61(x97762),x97764))+~P1(f328(f61(x97762),x97765))+E(f328(f328(f81(x97761),f328(f328(f328(f65(x97761,x97762,f81(x97761)),x97763),f78(x97761)),x97764)),f328(f328(f328(f65(x97761,x97762,f81(x97761)),x97763),f78(x97761)),x97765)),f328(f328(f328(f65(x97761,x97762,f81(x97761)),x97763),f78(x97761)),f328(f328(f114(f882(x97762,a870)),x97764),x97765)))+P1(f328(f328(f330(x97762),f861(x97763,x97765,x97764,x97762,x97761)),f328(f328(f105(f882(x97762,a870)),x97764),x97765))) % 154.70/154.57 [8738]~P20(x87381,x87384,x87385)+~P1(f328(f61(x87381),x87382))+E(f328(f328(f22(f882(x87381,a870)),x87382),f328(f328(f306(x87381),x87383),f192(f882(x87381,a870)))),f192(f882(x87381,a870)))+~P1(f328(f328(f330(x87381),x87383),x87382))+E(f328(f328(x87384,x87383),f328(x87385,f328(f328(f22(f882(x87381,a870)),x87382),f328(f328(f306(x87381),x87383),f192(f882(x87381,a870)))))),f328(x87385,x87382)) % 154.70/154.57 [8811]~P20(x88111,x88114,x88115)+~P1(f328(f61(x88111),x88113))+~P1(f328(f61(x88111),x88112))+E(f328(f328(f105(f882(x88111,a870)),x88112),x88113),f192(f882(x88111,a870)))+E(f328(f328(x88114,f328(x88115,f328(f328(f114(f882(x88111,a870)),x88112),x88113))),f328(x88115,f328(f328(f105(f882(x88111,a870)),x88112),x88113))),f328(f328(x88114,f328(x88115,x88112)),f328(x88115,x88113))) % 154.70/154.57 [9379]~P1(f328(f328(f242(a1),x93794),f2(a1)))+~P1(f328(f328(f243(a1),x93793),x93795))+P1(f328(f328(f242(a1),x93791),x93792))+~P1(f328(f328(f243(a1),x93793),x93794))+~P1(f328(f328(f242(a1),f328(f328(f80(a1),f328(f328(f81(a1),x93793),x93792)),x93795)),f328(f328(f80(a1),f328(f328(f81(a1),x93793),x93791)),x93794))) % 154.70/154.57 [9381]~P1(f328(f328(f242(a1),f2(a1)),x93815))+P1(f328(f328(f242(a1),x93811),x93812))+~P1(f328(f328(f243(a1),x93813),x93814))+~P1(f328(f328(f243(a1),x93815),x93814))+~P1(f328(f328(f242(a1),f328(f328(f80(a1),f328(f328(f81(a1),x93814),x93811)),x93815)),f328(f328(f80(a1),f328(f328(f81(a1),x93814),x93812)),x93813))) % 154.70/154.57 [9492]~P61(x94925)+E(f328(x94921,f490(x94921,x94922,x94923,x94924,x94925)),f2(x94925))+~P1(f328(f61(x94924),x94923))+~P1(f328(f61(x94924),x94922))+E(f328(f328(f286(x94925),f328(f328(f81(x94925),f328(f328(f9(x94924,x94925),x94921),x94923)),f328(f328(f9(x94924,x94925),x94921),x94922))),f328(f328(f9(x94924,x94925),x94921),f328(f328(f105(f882(x94924,a870)),x94923),x94922))),f328(f328(f9(x94924,x94925),x94921),f328(f328(f114(f882(x94924,a870)),x94923),x94922))) % 154.70/154.57 [9768]~P61(x97681)+~P1(f328(f61(x97682),x97684))+~P1(f328(f61(x97682),x97685))+E(f328(f328(f286(x97681),f328(f328(f81(x97681),f328(f328(f9(x97682,x97681),x97683),x97684)),f328(f328(f9(x97682,x97681),x97683),x97685))),f328(f328(f9(x97682,x97681),x97683),f328(f328(f105(f882(x97682,a870)),x97684),x97685))),f328(f328(f9(x97682,x97681),x97683),f328(f328(f114(f882(x97682,a870)),x97684),x97685)))+P1(f328(f328(f330(x97682),f490(x97683,x97685,x97684,x97682,x97681)),f328(f328(f105(f882(x97682,a870)),x97684),x97685))) % 154.70/154.57 [9092]E(f328(f328(f125(x90921),x90922),x90923),f328(f328(f125(x90921),x90924),x90925))+~E(f328(f328(f173(x90921),f328(f193(f876(x90921)),x90924)),x90922),x90924)+~E(f328(f328(f173(x90921),f328(f193(f876(x90921)),x90922)),x90924),x90922)+~E(x90925,f328(f328(f125(x90921),f328(f328(f135(x90921),f328(f193(f876(x90921)),x90924)),x90922)),x90923))+~E(f328(f328(f125(x90921),f328(f328(f135(x90921),f328(f193(f876(x90921)),x90922)),x90924)),x90925),x90923) % 154.70/154.57 [9490]~P105(x94902)+E(f328(f328(f145(x94901,x94902,x94903),x94904),f167(x94901,x94904,x94905)),x94905)+~P16(x94902,f328(f328(f151(x94901,x94902),x94903),x94905))+~P1(f328(f328(f330(x94901),x94904),f328(f170(x94901),x94905)))+~E(f328(f138(x94901),f328(f133(x94901,f328(f328(f8(x94902,a870,x94901),f328(a325,f328(x94903,x94904))),x94903)),x94905)),x94904) % 154.70/154.57 [9830]~P70(x98301)+~P1(f328(f66(x98301,x98301,f81(x98301),x98302,x98303),x98305))+~P1(f328(f328(f330(x98301),x98304),x98303))+P1(f328(f328(f330(x98301),x98302),x98303))+P1(f328(f66(x98301,x98301,f81(x98301),x98304,f328(f328(f306(x98301),x98302),f328(f328(f22(f882(x98301,a870)),x98303),f328(f328(f306(x98301),x98304),f192(f882(x98301,a870)))))),x98305)) % 154.70/154.57 [7220]E(x72201,x72202)+~P27(x72204,x72205,x72203,x72206)+~E(f328(x72203,x72201),f328(x72203,x72202))+~P1(f328(f328(f330(x72204),x72202),x72206))+~P1(f328(f328(f330(x72204),x72201),x72206)) % 154.70/154.57 [6480]~P141(x64804)+E(x64801,x64802)+~E(x64805,x64806)+E(x64803,f2(x64804))+~E(f328(f328(f80(x64804),x64805),f328(f328(f81(x64804),x64803),x64801)),f328(f328(f80(x64804),x64806),f328(f328(f81(x64804),x64803),x64802))) % 154.70/154.57 [7511]~P5(x75111)+~P105(x75111)+~P1(f328(f328(f243(x75111),x75112),f328(x75115,x75116)))+~P1(f328(f328(f330(x75113),x75116),x75114))+P1(f328(f328(f243(x75111),x75112),f328(f328(f41(x75113,x75111),x75114),x75115))) % 154.70/154.57 [8200]~P5(x82001)+~P105(x82001)+~P1(f328(f328(f243(x82001),f328(x82004,x82006)),x82005))+~P1(f328(f328(f330(x82002),x82006),x82003))+P1(f328(f328(f243(x82001),f328(f328(f42(x82002,x82001),x82003),x82004)),x82005)) % 154.70/154.57 [8461]~P21(x84612,x84615,x84616,x84611)+~P1(f328(f61(x84612),x84614))+~P1(f328(f61(x84612),x84613))+~E(f328(f328(f105(f882(x84612,a870)),x84613),x84614),f192(f882(x84612,a870)))+E(f328(x84611,f328(f328(f114(f882(x84612,a870)),x84613),x84614)),f328(f73(x84615,x84615,x84615,f328(x84611,x84613)),f328(x84611,x84614))) % 154.70/154.57 [8781]E(x87811,x87812)+~P53(x87814,x87815,x87816,x87813,x87817)+~E(f328(x87813,x87811),f328(x87813,x87812))+~P1(f328(f328(f330(x87815),x87812),x87817))+~P1(f328(f328(f330(x87815),x87811),x87817)) % 154.70/154.57 [10075]~P1(f328(x100752,x100754))+~E(x100755,f328(f133(x100751,x100752),x100757))+E(f328(f133(x100751,x100752),x100753),f328(f328(f148(x100751),x100754),x100755))+~E(x100753,f328(f328(f125(x100751),x100756),f328(f328(f148(x100751),x100754),x100757)))+P1(f328(x100752,f790(x100755,x100754,x100753,x100752,x100751,x100756,x100757))) % 154.70/154.57 [10076]~P1(f328(x100764,x100762))+~E(x100763,f328(f133(x100761,x100764),x100767))+E(f328(f328(f148(x100761),x100762),x100763),f328(f133(x100761,x100764),x100765))+~E(x100765,f328(f328(f125(x100761),x100766),f328(f328(f148(x100761),x100762),x100767)))+P1(f328(x100764,f792(x100765,x100764,x100763,x100762,x100761,x100766,x100767))) % 154.70/154.57 [10110]~P1(f328(x101102,x101104))+~E(x101105,f328(f133(x101101,x101102),x101107))+E(f328(f133(x101101,x101102),x101103),f328(f328(f148(x101101),x101104),x101105))+~E(x101103,f328(f328(f125(x101101),x101106),f328(f328(f148(x101101),x101104),x101107)))+P1(f328(f328(f330(x101101),f790(x101105,x101104,x101103,x101102,x101101,x101106,x101107)),f328(f170(x101101),x101106))) % 154.70/154.57 [10111]~P1(f328(x101114,x101112))+~E(x101113,f328(f133(x101111,x101114),x101117))+E(f328(f328(f148(x101111),x101112),x101113),f328(f133(x101111,x101114),x101115))+~E(x101115,f328(f328(f125(x101111),x101116),f328(f328(f148(x101111),x101112),x101117)))+P1(f328(f328(f330(x101111),f792(x101115,x101114,x101113,x101112,x101111,x101116,x101117)),f328(f170(x101111),x101116))) % 154.70/154.57 [10114]~P8(x101141,x101147,x101146)+~P14(x101141,f882(x101145,a870),x101146,x101144)+P1(f328(f328(f330(x101141),f547(x101142,x101143,x101144,x101145,x101146,x101147,x101141)),x101147))+~P1(f328(f328(f330(f882(x101141,a870)),x101143),f328(f328(f60(x101141),x101147),x101146)))+P1(f328(f328(f330(f882(x101145,a870)),f328(f328(f41(x101141,f882(x101145,a870)),x101143),x101144)),x101142)) % 154.70/154.57 [10161]~P8(x101612,x101616,x101617)+~P14(x101612,f882(x101611,a870),x101617,x101614)+~P1(f328(f328(f330(f882(x101612,a870)),x101613),f328(f328(f60(x101612),x101616),x101617)))+~P1(f328(f328(f330(f882(x101611,a870)),f328(x101614,f547(x101615,x101613,x101614,x101611,x101617,x101616,x101612))),x101615))+P1(f328(f328(f330(f882(x101611,a870)),f328(f328(f41(x101612,f882(x101611,a870)),x101613),x101614)),x101615)) % 154.70/154.57 [8375]~P73(x83752)+~P27(x83751,x83755,x83758,x83754)+~E(x83753,f328(f73(x83755,x83752,x83751,x83756),x83758))+~E(x83757,f328(f307(x83751,x83755,x83758),x83754))+E(f328(f328(f9(x83751,x83752),x83753),x83754),f328(f328(f9(x83755,x83752),x83756),x83757)) % 154.70/154.57 [10165]~P73(x101652)+~P27(x101655,x101651,x101658,x101657)+~E(f328(x101656,f500(x101653,x101656,x101654,x101657,x101658,x101651,x101655,x101652)),f328(f328(f73(x101651,x101652,x101655,x101653),x101658),f500(x101653,x101656,x101654,x101657,x101658,x101651,x101655,x101652)))+~E(x101654,f328(f307(x101655,x101651,x101658),x101657))+E(f328(f328(f9(x101651,x101652),x101653),x101654),f328(f328(f9(x101655,x101652),x101656),x101657)) % 154.70/154.57 [10167]~P66(x101672)+~P27(x101671,x101675,x101678,x101674)+~E(x101677,f328(f307(x101671,x101675,x101678),x101674))+E(f328(f328(f6(x101671,x101672),x101673),x101674),f328(f328(f6(x101675,x101672),x101676),x101677))+P1(f328(f328(f330(x101671),f621(x101676,x101673,x101677,x101674,x101678,x101675,x101671,x101672)),x101674)) % 154.70/154.57 [10168]~P73(x101682)+~P27(x101681,x101685,x101688,x101684)+~E(x101687,f328(f307(x101681,x101685,x101688),x101684))+E(f328(f328(f9(x101681,x101682),x101683),x101684),f328(f328(f9(x101685,x101682),x101686),x101687))+P1(f328(f328(f330(x101681),f500(x101686,x101683,x101687,x101684,x101688,x101685,x101681,x101682)),x101684)) % 154.70/154.57 [10174]~P66(x101742)+~P27(x101745,x101741,x101748,x101747)+~E(x101744,f328(f307(x101745,x101741,x101748),x101747))+~E(f328(x101746,f621(x101743,x101746,x101744,x101747,x101748,x101741,x101745,x101742)),f328(x101743,f328(x101748,f621(x101743,x101746,x101744,x101747,x101748,x101741,x101745,x101742))))+E(f328(f328(f6(x101741,x101742),x101743),x101744),f328(f328(f6(x101745,x101742),x101746),x101747)) % 154.70/154.57 [9546]~E(f328(f193(f876(x95462)),x95465),f328(f193(f876(x95461)),x95463))+~E(f328(f193(f876(x95462)),x95464),f328(f193(f876(x95461)),x95463))+~E(f328(f328(f328(f72(x95461,f879(x95462)),f328(f176(x95461,x95462),f328(f328(f180(x95461,x95462),x95463),x95464))),x95466),f328(f235(x95462),x95467)),f328(f328(f328(f72(x95461,f879(x95462)),f328(f176(x95461,x95462),f328(f328(f180(x95461,x95462),x95463),x95465))),x95466),f328(f235(x95462),x95468)))+E(f328(f176(x95461,x95462),f328(f328(f180(x95461,x95462),x95463),x95464)),f328(f176(x95461,x95462),f328(f328(f180(x95461,x95462),x95463),x95465)))+P1(f328(f328(f330(x95461),x95466),f328(f170(x95461),x95463))) % 154.70/154.57 [9659]~P25(x96596,x96592,x96595,x96597,x96598,x96591)+~P1(f328(f61(x96592),x96594))+~P1(f328(f61(x96592),x96593))+~E(f328(f328(f105(f882(x96592,a870)),x96593),x96594),f192(f882(x96592,a870)))+E(f328(x96591,f328(f328(f114(f882(x96592,a870)),x96593),x96594)),f328(f328(x96595,f328(x96591,x96593)),f328(x96591,x96594))) % 154.70/154.57 [10062]~P25(x100628,x100622,x100625,x100627,x100626,x100621)+~E(f328(x100626,f637(x100624,x100623,x100621,x100626,x100627,x100625,x100622)),x100627)+~P1(f328(f61(x100622),x100623))+~P1(f328(f61(x100622),x100624))+E(f328(x100621,f328(f328(f114(f882(x100622,a870)),x100623),x100624)),f328(f328(x100625,f328(x100621,x100623)),f328(x100621,x100624))) % 154.70/154.57 [10120]~P25(x101208,x101202,x101205,x101207,x101206,x101201)+~P1(f328(f61(x101202),x101203))+~P1(f328(f61(x101202),x101204))+E(f328(x101201,f328(f328(f114(f882(x101202,a870)),x101203),x101204)),f328(f328(x101205,f328(x101201,x101203)),f328(x101201,x101204)))+P1(f328(f328(f330(x101202),f637(x101204,x101203,x101201,x101206,x101207,x101205,x101202)),f328(f328(f105(f882(x101202,a870)),x101203),x101204))) % 154.70/154.57 [9818]~P8(x98184,x98188,x98185)+~P8(x98181,x98189,x98183)+~P15(x98181,x98184,f882(x98182,a870),x98183,x98185,x98187)+P14(x98181,f882(x98182,a870),x98183,f328(f328(f8(f882(x98184,f882(x98182,a870)),f882(x98182,a870),x98181),f328(f41(x98184,f882(x98182,a870)),f328(f282(x98184,x98184,x98185),f328(f328(f306(x98184),x98186),f192(f882(x98184,a870)))))),x98187))+~P1(f328(f328(f330(x98184),x98186),x98188)) % 154.70/154.57 [5409]~P105(x54093)+~P16(x54093,x54091)+E(x54091,f761(x54092,x54093))+~E(f328(f170(x54093),x54091),x54092)+~P1(f328(f61(x54093),x54092))+~P1(f328(f134(x54093),x54091)) % 154.70/154.57 [5031]~P134(x50312)+~P128(x50312)+~P129(x50312)+~P112(x50312)+E(x50311,f2(x50312))+~E(f328(f328(f253(x50312),x50311),x50313),f2(x50312)) % 154.70/154.57 [5032]~P134(x50322)+~P128(x50322)+~P129(x50322)+~P112(x50322)+~E(x50321,f2(a875))+~E(f328(f328(f253(x50322),x50323),x50321),f2(x50322)) % 154.70/154.57 [6462]~P85(x64621)+~E(x64623,f2(x64621))+~E(x64622,f2(x64621))+E(f328(f328(f80(x64621),x64622),x64623),f2(x64621))+~P1(f328(f328(f242(x64621),f2(x64621)),x64623))+~P1(f328(f328(f242(x64621),f2(x64621)),x64622)) % 154.70/154.57 [8842]~E(f328(f262(a875,a875),x88423),f2(a875))+~E(x88421,f328(f328(f80(a875),f328(f328(f81(a875),f328(f262(a875,a875),x88423)),x88422)),f328(f266(a875,a875),x88423)))+P1(f328(f47(x88421,x88422),x88423))+~P1(f328(f328(f242(a875),f328(f266(a875,a875),x88423)),f2(a875)))+P1(f328(f328(f243(a875),f2(a875)),x88422))+~P1(f328(f328(f243(a875),x88422),f328(f266(a875,a875),x88423))) % 154.70/154.57 [8850]E(x88501,f2(a875))+~E(x88502,f328(f328(f80(a875),f328(f328(f81(a875),f328(f262(a875,a875),x88503)),x88501)),f328(f266(a875,a875),x88503)))+P1(f328(f47(x88502,x88501),x88503))+~P1(f328(f328(f243(a875),f2(a875)),x88501))+~P1(f328(f328(f242(a875),f2(a875)),f328(f266(a875,a875),x88503)))+~P1(f328(f328(f243(a875),f328(f266(a875,a875),x88503)),x88501)) % 154.70/154.57 [8868]~E(f328(f262(a875,a875),x88683),f2(a875))+~E(x88681,f328(f328(f80(a875),f328(f328(f81(a875),f328(f262(a875,a875),x88683)),x88682)),f328(f266(a875,a875),x88683)))+P1(f328(f47(x88681,x88682),x88683))+~P1(f328(f328(f243(a875),f2(a875)),x88682))+~P1(f328(f328(f242(a875),f2(a875)),f328(f266(a875,a875),x88683)))+~P1(f328(f328(f243(a875),f328(f266(a875,a875),x88683)),x88682)) % 154.70/154.57 [6844]~P2(x68442)+E(x68441,f192(f882(x68442,a870)))+E(x68443,f192(f882(x68442,a870)))+~P1(f328(f61(x68442),x68441))+~P1(f328(f61(x68442),x68443))+E(f10(x68442,f328(f328(f114(f882(x68442,a870)),x68443),x68441)),f328(f328(f114(x68442),f10(x68442,x68443)),f10(x68442,x68441))) % 154.70/154.57 [6845]~P2(x68452)+E(x68451,f192(f882(x68452,a870)))+E(x68453,f192(f882(x68452,a870)))+~P1(f328(f61(x68452),x68451))+~P1(f328(f61(x68452),x68453))+E(f11(x68452,f328(f328(f114(f882(x68452,a870)),x68453),x68451)),f328(f328(f105(x68452),f11(x68452,x68453)),f11(x68452,x68451))) % 154.70/154.57 [6846]~P105(x68462)+E(x68461,f192(f882(x68462,a870)))+E(x68463,f192(f882(x68462,a870)))+~P1(f328(f61(x68462),x68461))+~P1(f328(f61(x68462),x68463))+E(f14(x68462,f328(f328(f114(f882(x68462,a870)),x68463),x68461)),f328(f328(f240(x68462),f14(x68462,x68463)),f14(x68462,x68461))) % 154.70/154.57 [6847]~P105(x68472)+E(x68471,f192(f882(x68472,a870)))+E(x68473,f192(f882(x68472,a870)))+~P1(f328(f61(x68472),x68471))+~P1(f328(f61(x68472),x68473))+E(f15(x68472,f328(f328(f114(f882(x68472,a870)),x68473),x68471)),f328(f328(f241(x68472),f15(x68472,x68473)),f15(x68472,x68471))) % 154.70/154.57 [7486]~P94(x74862)+E(x74861,f192(f882(x74862,a870)))+E(x74863,f192(f882(x74862,a870)))+~P1(f328(f61(x74862),x74861))+~P1(f328(f61(x74862),x74863))+E(f328(f328(f81(x74862),f328(f63(x74862,f81(x74862)),x74863)),f328(f63(x74862,f81(x74862)),x74861)),f328(f63(x74862,f81(x74862)),f328(f328(f114(f882(x74862,a870)),x74863),x74861))) % 154.70/154.57 [7645]~P105(x76452)+E(x76451,f192(f882(x76452,a870)))+E(x76453,f192(f882(x76452,a870)))+~P1(f328(f61(x76452),x76451))+~P1(f328(f61(x76452),x76453))+E(f328(f328(f241(x76452),f12(x76452,f241(x76452),x76453)),f12(x76452,f241(x76452),x76451)),f12(x76452,f241(x76452),f328(f328(f114(f882(x76452,a870)),x76453),x76451))) % 154.70/154.57 [7646]~P105(x76462)+E(x76461,f192(f882(x76462,a870)))+E(x76463,f192(f882(x76462,a870)))+~P1(f328(f61(x76462),x76461))+~P1(f328(f61(x76462),x76463))+E(f328(f328(f240(x76462),f13(x76462,f240(x76462),x76463)),f13(x76462,f240(x76462),x76461)),f13(x76462,f240(x76462),f328(f328(f114(f882(x76462,a870)),x76463),x76461))) % 154.70/154.57 [8691]~P1(f328(x86911,x86913))+P1(f328(x86911,f423(x86911,x86912)))+P1(f328(x86911,f413(x86911,x86912)))+~P1(f328(f328(f243(a1),f2(a1)),x86912))+~P1(f328(f328(f330(a1),x86913),f299(a1,f78(a1),x86912)))+P1(f328(x86911,f328(f328(f22(a1),f413(x86911,x86912)),f328(f328(f81(a1),f422(x86911,x86912)),x86912)))) % 154.70/154.57 [8989]~P1(f328(x89891,x89893))+~P1(f328(x89891,f413(x89891,x89892)))+P1(f328(x89891,f423(x89891,x89892)))+~P1(f328(f328(f243(a1),f2(a1)),x89892))+~P1(f328(f328(f330(a1),x89893),f299(a1,f78(a1),x89892)))+~P1(f328(x89891,f328(f328(f22(a1),f413(x89891,x89892)),f328(f328(f81(a1),f422(x89891,x89892)),x89892)))) % 154.70/154.57 [10199]~P96(x101992)+E(x101991,f192(f882(x101992,a870)))+E(x101993,f192(f882(x101992,a870)))+~P1(f328(f61(x101992),x101991))+~P1(f328(f61(x101992),x101993))+E(f11(x101992,f328(f248(x101992),f328(f328(f8(f882(x101992,a870),a870,x101992),f87(x101992)),f328(f328(f8(f882(x101992,f882(x101992,a870)),f882(x101992,a870),x101992),f328(f8(f882(x101992,a870),a870,x101992),f87(x101992))),f328(f328(f7(x101992,f882(x101992,f882(x101992,a870)),f882(x101992,f882(x101992,a870))),f328(f328(f8(f882(x101992,f882(f882(x101992,a870),f882(x101992,a870))),f882(f882(x101992,f882(x101992,a870)),f882(x101992,f882(x101992,a870))),x101992),f18(x101992,f882(x101992,a870),f882(x101992,a870))),f328(f328(f8(f882(x101992,f882(x101992,f882(a870,a870))),f882(x101992,f882(f882(x101992,a870),f882(x101992,a870))),x101992),f328(f8(f882(x101992,f882(a870,a870)),f882(f882(x101992,a870),f882(x101992,a870)),x101992),f18(x101992,a870,a870))),f328(f328(f8(f882(x101992,f882(x101992,a870)),f882(x101992,f882(x101992,f882(a870,a870))),x101992),f328(f8(f882(x101992,a870),f882(x101992,f882(a870,a870)),x101992),f328(f8(a870,f882(a870,a870),x101992),a326))),f328(f328(f7(x101992,f882(x101992,f882(x101992,x101992)),f882(x101992,f882(x101992,a870))),f328(f328(f8(f882(f882(x101992,x101992),f882(x101992,a870)),f882(f882(x101992,f882(x101992,x101992)),f882(x101992,f882(x101992,a870))),x101992),f8(f882(x101992,x101992),f882(x101992,a870),x101992)),f328(f328(f8(f882(x101992,a870),f882(f882(x101992,x101992),f882(x101992,a870)),x101992),f8(x101992,a870,x101992)),a325))),f114(x101992)))))),f328(f328(f7(x101992,f882(x101992,a870),f882(x101992,a870)),f328(f328(f8(f882(a870,a870),f882(f882(x101992,a870),f882(x101992,a870)),x101992),f8(a870,a870,x101992)),f328(f328(f8(a870,f882(a870,a870),x101992),a326),f328(f328(f7(x101992,f882(x101992,a870),a870),f330(x101992)),x101993)))),f328(f328(f7(x101992,f882(x101992,a870),a870),f330(x101992)),x101991))))))),f328(f328(f114(x101992),f11(x101992,x101993)),f11(x101992,x101991))) % 154.70/154.57 [10200]~P96(x102002)+E(x102001,f192(f882(x102002,a870)))+E(x102003,f192(f882(x102002,a870)))+~P1(f328(f61(x102002),x102001))+~P1(f328(f61(x102002),x102003))+E(f10(x102002,f328(f248(x102002),f328(f328(f8(f882(x102002,a870),a870,x102002),f87(x102002)),f328(f328(f8(f882(x102002,f882(x102002,a870)),f882(x102002,a870),x102002),f328(f8(f882(x102002,a870),a870,x102002),f87(x102002))),f328(f328(f7(x102002,f882(x102002,f882(x102002,a870)),f882(x102002,f882(x102002,a870))),f328(f328(f8(f882(x102002,f882(f882(x102002,a870),f882(x102002,a870))),f882(f882(x102002,f882(x102002,a870)),f882(x102002,f882(x102002,a870))),x102002),f18(x102002,f882(x102002,a870),f882(x102002,a870))),f328(f328(f8(f882(x102002,f882(x102002,f882(a870,a870))),f882(x102002,f882(f882(x102002,a870),f882(x102002,a870))),x102002),f328(f8(f882(x102002,f882(a870,a870)),f882(f882(x102002,a870),f882(x102002,a870)),x102002),f18(x102002,a870,a870))),f328(f328(f8(f882(x102002,f882(x102002,a870)),f882(x102002,f882(x102002,f882(a870,a870))),x102002),f328(f8(f882(x102002,a870),f882(x102002,f882(a870,a870)),x102002),f328(f8(a870,f882(a870,a870),x102002),a326))),f328(f328(f7(x102002,f882(x102002,f882(x102002,x102002)),f882(x102002,f882(x102002,a870))),f328(f328(f8(f882(f882(x102002,x102002),f882(x102002,a870)),f882(f882(x102002,f882(x102002,x102002)),f882(x102002,f882(x102002,a870))),x102002),f8(f882(x102002,x102002),f882(x102002,a870),x102002)),f328(f328(f8(f882(x102002,a870),f882(f882(x102002,x102002),f882(x102002,a870)),x102002),f8(x102002,a870,x102002)),a325))),f105(x102002)))))),f328(f328(f7(x102002,f882(x102002,a870),f882(x102002,a870)),f328(f328(f8(f882(a870,a870),f882(f882(x102002,a870),f882(x102002,a870)),x102002),f8(a870,a870,x102002)),f328(f328(f8(a870,f882(a870,a870),x102002),a326),f328(f328(f7(x102002,f882(x102002,a870),a870),f330(x102002)),x102003)))),f328(f328(f7(x102002,f882(x102002,a870),a870),f330(x102002)),x102001))))))),f328(f328(f105(x102002),f10(x102002,x102003)),f10(x102002,x102001))) % 154.70/154.57 [10201]~P105(x102012)+E(x102011,f192(f882(x102012,a870)))+E(x102013,f192(f882(x102012,a870)))+~P1(f328(f61(x102012),x102011))+~P1(f328(f61(x102012),x102013))+E(f12(x102012,f241(x102012),f328(f248(x102012),f328(f328(f8(f882(x102012,a870),a870,x102012),f87(x102012)),f328(f328(f8(f882(x102012,f882(x102012,a870)),f882(x102012,a870),x102012),f328(f8(f882(x102012,a870),a870,x102012),f87(x102012))),f328(f328(f7(x102012,f882(x102012,f882(x102012,a870)),f882(x102012,f882(x102012,a870))),f328(f328(f8(f882(x102012,f882(f882(x102012,a870),f882(x102012,a870))),f882(f882(x102012,f882(x102012,a870)),f882(x102012,f882(x102012,a870))),x102012),f18(x102012,f882(x102012,a870),f882(x102012,a870))),f328(f328(f8(f882(x102012,f882(x102012,f882(a870,a870))),f882(x102012,f882(f882(x102012,a870),f882(x102012,a870))),x102012),f328(f8(f882(x102012,f882(a870,a870)),f882(f882(x102012,a870),f882(x102012,a870)),x102012),f18(x102012,a870,a870))),f328(f328(f8(f882(x102012,f882(x102012,a870)),f882(x102012,f882(x102012,f882(a870,a870))),x102012),f328(f8(f882(x102012,a870),f882(x102012,f882(a870,a870)),x102012),f328(f8(a870,f882(a870,a870),x102012),a326))),f328(f328(f7(x102012,f882(x102012,f882(x102012,x102012)),f882(x102012,f882(x102012,a870))),f328(f328(f8(f882(f882(x102012,x102012),f882(x102012,a870)),f882(f882(x102012,f882(x102012,x102012)),f882(x102012,f882(x102012,a870))),x102012),f8(f882(x102012,x102012),f882(x102012,a870),x102012)),f328(f328(f8(f882(x102012,a870),f882(f882(x102012,x102012),f882(x102012,a870)),x102012),f8(x102012,a870,x102012)),a325))),f240(x102012)))))),f328(f328(f7(x102012,f882(x102012,a870),f882(x102012,a870)),f328(f328(f8(f882(a870,a870),f882(f882(x102012,a870),f882(x102012,a870)),x102012),f8(a870,a870,x102012)),f328(f328(f8(a870,f882(a870,a870),x102012),a326),f328(f328(f7(x102012,f882(x102012,a870),a870),f330(x102012)),x102013)))),f328(f328(f7(x102012,f882(x102012,a870),a870),f330(x102012)),x102011))))))),f328(f328(f240(x102012),f12(x102012,f241(x102012),x102013)),f12(x102012,f241(x102012),x102011))) % 154.70/154.57 [10202]~P105(x102022)+E(x102021,f192(f882(x102022,a870)))+E(x102023,f192(f882(x102022,a870)))+~P1(f328(f61(x102022),x102021))+~P1(f328(f61(x102022),x102023))+E(f13(x102022,f240(x102022),f328(f248(x102022),f328(f328(f8(f882(x102022,a870),a870,x102022),f87(x102022)),f328(f328(f8(f882(x102022,f882(x102022,a870)),f882(x102022,a870),x102022),f328(f8(f882(x102022,a870),a870,x102022),f87(x102022))),f328(f328(f7(x102022,f882(x102022,f882(x102022,a870)),f882(x102022,f882(x102022,a870))),f328(f328(f8(f882(x102022,f882(f882(x102022,a870),f882(x102022,a870))),f882(f882(x102022,f882(x102022,a870)),f882(x102022,f882(x102022,a870))),x102022),f18(x102022,f882(x102022,a870),f882(x102022,a870))),f328(f328(f8(f882(x102022,f882(x102022,f882(a870,a870))),f882(x102022,f882(f882(x102022,a870),f882(x102022,a870))),x102022),f328(f8(f882(x102022,f882(a870,a870)),f882(f882(x102022,a870),f882(x102022,a870)),x102022),f18(x102022,a870,a870))),f328(f328(f8(f882(x102022,f882(x102022,a870)),f882(x102022,f882(x102022,f882(a870,a870))),x102022),f328(f8(f882(x102022,a870),f882(x102022,f882(a870,a870)),x102022),f328(f8(a870,f882(a870,a870),x102022),a326))),f328(f328(f7(x102022,f882(x102022,f882(x102022,x102022)),f882(x102022,f882(x102022,a870))),f328(f328(f8(f882(f882(x102022,x102022),f882(x102022,a870)),f882(f882(x102022,f882(x102022,x102022)),f882(x102022,f882(x102022,a870))),x102022),f8(f882(x102022,x102022),f882(x102022,a870),x102022)),f328(f328(f8(f882(x102022,a870),f882(f882(x102022,x102022),f882(x102022,a870)),x102022),f8(x102022,a870,x102022)),a325))),f241(x102022)))))),f328(f328(f7(x102022,f882(x102022,a870),f882(x102022,a870)),f328(f328(f8(f882(a870,a870),f882(f882(x102022,a870),f882(x102022,a870)),x102022),f8(a870,a870,x102022)),f328(f328(f8(a870,f882(a870,a870),x102022),a326),f328(f328(f7(x102022,f882(x102022,a870),a870),f330(x102022)),x102023)))),f328(f328(f7(x102022,f882(x102022,a870),a870),f330(x102022)),x102021))))))),f328(f328(f241(x102022),f13(x102022,f240(x102022),x102023)),f13(x102022,f240(x102022),x102021))) % 154.70/154.57 [7169]~P123(x71693)+E(x71691,x71692)+~E(f328(f328(f253(x71693),x71691),x71694),f328(f328(f253(x71693),x71692),x71694))+~P1(f328(f328(f242(x71693),f2(x71693)),x71692))+~P1(f328(f328(f242(x71693),f2(x71693)),x71691))+~P1(f328(f328(f243(a875),f2(a875)),x71694)) % 154.70/154.57 [7443]~P105(x74432)+E(x74431,f192(f882(x74432,a870)))+~P1(f328(f61(x74432),x74431))+~P1(f328(f328(f330(x74432),x74434),x74431))+P1(f328(f328(f243(x74432),x74433),x74434))+~P1(f328(f328(f243(x74432),x74433),f328(f63(x74432,f240(x74432)),x74431))) % 154.70/154.57 [7444]~P100(x74442)+E(x74441,f192(f882(x74442,a870)))+~P1(f328(f61(x74442),x74441))+~P1(f328(f328(f330(x74442),x74444),x74441))+P1(f328(f328(f242(x74442),x74443),x74444))+~P1(f328(f328(f242(x74442),x74443),f328(f63(x74442,f105(x74442)),x74441))) % 154.70/154.57 [7445]~P105(x74452)+E(x74451,f192(f882(x74452,a870)))+~P1(f328(f61(x74452),x74451))+~P1(f328(f328(f330(x74452),x74454),x74451))+P1(f328(f328(f242(x74452),x74453),x74454))+~P1(f328(f328(f242(x74452),x74453),f328(f63(x74452,f240(x74452)),x74451))) % 154.70/154.57 [7345]E(x73451,f2(a1))+E(f328(f328(f38(a1),x73452),x73451),x73453)+~P1(f328(f328(f242(a1),x73454),f2(a1)))+~E(x73452,f328(f328(f80(a1),f328(f328(f81(a1),x73451),x73453)),x73454))+P1(f328(f328(f243(a1),f2(a1)),x73451))+~P1(f328(f328(f243(a1),x73451),x73454)) % 154.70/154.57 [7360]E(f44(a1,x73602,x73601),x73603)+E(x73601,f2(a1))+~P1(f328(f328(f242(a1),x73603),f2(a1)))+~E(x73602,f328(f328(f80(a1),f328(f328(f81(a1),x73601),x73604)),x73603))+P1(f328(f328(f243(a1),f2(a1)),x73601))+~P1(f328(f328(f243(a1),x73601),x73603)) % 154.70/154.57 [7485]E(x74851,f2(a1))+E(f328(f328(f38(a1),x74852),x74851),x74853)+~E(x74852,f328(f328(f80(a1),f328(f328(f81(a1),x74851),x74853)),x74854))+~P1(f328(f328(f243(a1),f2(a1)),x74851))+~P1(f328(f328(f242(a1),f2(a1)),x74854))+~P1(f328(f328(f243(a1),x74854),x74851)) % 154.70/154.57 [7507]E(f44(a1,x75072,x75071),x75073)+E(x75071,f2(a1))+~E(x75072,f328(f328(f80(a1),f328(f328(f81(a1),x75071),x75074)),x75073))+~P1(f328(f328(f243(a1),f2(a1)),x75071))+~P1(f328(f328(f242(a1),f2(a1)),x75073))+~P1(f328(f328(f243(a1),x75073),x75071)) % 154.70/154.57 [7649]~P105(x76492)+E(x76491,f192(f882(x76492,a870)))+~P1(f328(f61(x76492),x76491))+~P1(f328(f328(f243(x76492),x76494),x76493))+~P1(f328(f328(f330(x76492),x76494),x76491))+P1(f328(f328(f243(x76492),f328(f63(x76492,f240(x76492)),x76491)),x76493)) % 154.70/154.57 [7650]~P105(x76502)+E(x76501,f192(f882(x76502,a870)))+~P1(f328(f61(x76502),x76501))+~P1(f328(f328(f242(x76502),x76504),x76503))+~P1(f328(f328(f330(x76502),x76504),x76501))+P1(f328(f328(f242(x76502),f328(f63(x76502,f240(x76502)),x76501)),x76503)) % 154.70/154.57 [8231]~P1(f328(f328(f242(a1),x82314),f2(a1)))+~E(x82311,f328(f328(f80(a1),f328(f328(f81(a1),x82312),x82313)),x82314))+~P1(f328(f328(f242(a1),f2(a1)),x82314))+~P1(f328(f328(f243(a1),x82314),x82312))+~P1(f328(f328(f243(a1),x82312),x82314))+P1(f328(f48(x82311,x82312),f328(f328(f263(a1,a1),x82313),x82314))) % 154.70/154.57 [9184]~P59(x91843)+~P59(x91844)+E(x91841,x91842)+~E(f328(f193(f876(x91843)),x91842),f328(f193(f876(x91844)),f55(x91844)))+~E(f328(f193(f876(x91843)),x91841),f328(f193(f876(x91844)),f55(x91844)))+~E(f328(f73(f879(x91843),x91843,x91844,f239(x91843)),f328(f176(x91844,x91843),f328(f328(f180(x91844,x91843),f55(x91844)),x91841))),f328(f73(f879(x91843),x91843,x91844,f239(x91843)),f328(f176(x91844,x91843),f328(f328(f180(x91844,x91843),f55(x91844)),x91842)))) % 154.70/154.57 [8395]~P107(x83951)+P1(f328(f328(f243(f882(x83951,a870)),f299(x83951,x83952,x83953)),f299(x83951,x83954,x83955)))+~P1(f328(f328(f243(x83951),x83953),x83955))+~P1(f328(f328(f242(x83951),x83954),x83952))+~P1(f328(f328(f242(x83951),x83954),x83955))+~P1(f328(f328(f242(x83951),x83953),x83955)) % 154.70/154.57 [8396]~P107(x83961)+P1(f328(f328(f243(f882(x83961,a870)),f299(x83961,x83962,x83963)),f299(x83961,x83964,x83965)))+~P1(f328(f328(f243(x83961),x83964),x83962))+~P1(f328(f328(f242(x83961),x83963),x83965))+~P1(f328(f328(f242(x83961),x83964),x83965))+~P1(f328(f328(f242(x83961),x83964),x83962)) % 154.70/154.57 [9249]P55(x92492,x92493,x92494,x92491)+E(x92491,f192(f882(x92492,a870)))+~P1(f328(f61(x92492),x92494))+~P1(f328(f61(x92492),x92491))+~P1(f328(f328(x92493,f559(x92491,x92494,x92493,x92492)),x92495))+~P1(f328(f328(f330(x92492),x92495),x92491)) % 154.70/154.57 [9397]~E(x93973,x93975)+~P66(x93971)+~P73(x93971)+~P40(x93973)+E(f328(f328(f6(a1,x93971),x93972),x93973),f328(f328(f6(a1,x93971),x93974),x93975))+P1(f328(f328(f242(a1),f2(a1)),f444(x93972,x93974,x93973,x93975,x93971))) % 154.70/154.57 [9398]~E(x93983,x93985)+~P66(x93981)+~P73(x93981)+~P40(x93983)+E(f328(f328(f9(a1,x93981),x93982),x93983),f328(f328(f9(a1,x93981),x93984),x93985))+P1(f328(f328(f242(a1),f2(a1)),f506(x93982,x93984,x93983,x93985,x93981))) % 154.70/154.57 [9567]~E(x95675,x95673)+~P66(x95671)+~P73(x95671)+~P40(x95675)+~E(f328(x95672,f444(x95674,x95672,x95675,x95673,x95671)),f328(x95674,f444(x95674,x95672,x95675,x95673,x95671)))+E(f328(f328(f6(a1,x95671),x95672),x95673),f328(f328(f6(a1,x95671),x95674),x95675)) % 154.70/154.57 [9568]~E(x95685,x95683)+~P66(x95681)+~P73(x95681)+~P40(x95685)+~E(f328(x95682,f506(x95684,x95682,x95685,x95683,x95681)),f328(x95684,f506(x95684,x95682,x95685,x95683,x95681)))+E(f328(f328(f9(a1,x95681),x95682),x95683),f328(f328(f9(a1,x95681),x95684),x95685)) % 154.70/154.57 [9656]~P81(x96563)+E(f328(x96561,x96562),f2(x96563))+~E(f328(f328(f6(x96564,x96563),x96561),x96565),f2(x96563))+~P1(f328(f61(x96564),x96565))+P1(f328(f328(f330(x96564),f378(x96562,x96561,x96565,x96564,x96563)),x96565))+~P1(f328(f328(f330(x96564),x96562),x96565)) % 154.70/154.57 [9792]~P81(x97923)+E(f328(x97921,x97922),f2(x97923))+~E(f328(f328(f6(x97924,x97923),x97921),x97925),f2(x97923))+~P1(f328(f61(x97924),x97925))+~P1(f328(f328(f330(x97924),x97922),x97925))+~P1(f328(f328(f242(x97923),f2(x97923)),f328(x97921,f378(x97922,x97921,x97925,x97924,x97923)))) % 154.70/154.57 [8312]~P122(x83121)+~P1(f328(f328(f242(x83121),f2(x83121)),x83123))+~P1(f328(f328(f243(x83121),x83123),x83125))+~P1(f328(f328(f243(x83121),x83122),x83124))+~P1(f328(f328(f243(x83121),f2(x83121)),x83124))+P1(f328(f328(f243(x83121),f328(f328(f81(x83121),x83122),x83123)),f328(f328(f81(x83121),x83124),x83125))) % 154.70/154.57 [8313]~P122(x83131)+~P1(f328(f328(f242(x83131),f2(x83131)),x83133))+~P1(f328(f328(f242(x83131),f2(x83131)),x83132))+~P1(f328(f328(f243(x83131),x83133),x83135))+~P1(f328(f328(f243(x83131),x83132),x83134))+P1(f328(f328(f243(x83131),f328(f328(f81(x83131),x83132),x83133)),f328(f328(f81(x83131),x83134),x83135))) % 154.70/154.57 [8314]~P122(x83141)+~P1(f328(f328(f242(x83141),x83142),x83144))+~P1(f328(f328(f242(x83141),f2(x83141)),x83143))+~P1(f328(f328(f243(x83141),x83143),x83145))+~P1(f328(f328(f243(x83141),f2(x83141)),x83142))+P1(f328(f328(f243(x83141),f328(f328(f81(x83141),x83142),x83143)),f328(f328(f81(x83141),x83144),x83145))) % 154.70/154.57 [8315]~P122(x83151)+~P1(f328(f328(f242(x83151),x83153),x83155))+~P1(f328(f328(f242(x83151),f2(x83151)),x83152))+~P1(f328(f328(f243(x83151),x83152),x83154))+~P1(f328(f328(f243(x83151),f2(x83151)),x83153))+P1(f328(f328(f243(x83151),f328(f328(f81(x83151),x83152),x83153)),f328(f328(f81(x83151),x83154),x83155))) % 154.70/154.57 [8316]~P63(x83161)+~P1(f328(f328(f242(x83161),x83162),x83164))+~P1(f328(f328(f243(x83161),x83165),x83163))+~P1(f328(f328(f243(x83161),f2(x83161)),x83165))+~P1(f328(f328(f243(x83161),f2(x83161)),x83162))+P1(f328(f328(f243(x83161),f328(f328(f286(x83161),x83162),x83163)),f328(f328(f286(x83161),x83164),x83165))) % 154.70/154.57 [8317]~P63(x83171)+~P1(f328(f328(f242(x83171),x83175),x83173))+~P1(f328(f328(f242(x83171),f2(x83171)),x83172))+~P1(f328(f328(f243(x83171),x83172),x83174))+~P1(f328(f328(f243(x83171),f2(x83171)),x83175))+P1(f328(f328(f243(x83171),f328(f328(f286(x83171),x83172),x83173)),f328(f328(f286(x83171),x83174),x83175))) % 154.70/154.57 [8318]~P132(x83181)+~P1(f328(f328(f242(x83181),x83183),x83185))+~P1(f328(f328(f242(x83181),x83182),x83184))+~P1(f328(f328(f242(x83181),f2(x83181)),x83183))+~P1(f328(f328(f242(x83181),f2(x83181)),x83184))+P1(f328(f328(f242(x83181),f328(f328(f81(x83181),x83182),x83183)),f328(f328(f81(x83181),x83184),x83185))) % 154.70/154.57 [8319]~P132(x83191)+~P1(f328(f328(f242(x83191),x83193),x83195))+~P1(f328(f328(f242(x83191),x83192),x83194))+~P1(f328(f328(f242(x83191),f2(x83191)),x83193))+~P1(f328(f328(f242(x83191),f2(x83191)),x83192))+P1(f328(f328(f242(x83191),f328(f328(f81(x83191),x83192),x83193)),f328(f328(f81(x83191),x83194),x83195))) % 154.70/154.57 [8320]~P63(x83201)+~P1(f328(f328(f243(x83201),f2(x83201)),x83205))+~P1(f328(f328(f242(x83201),x83205),x83203))+~P1(f328(f328(f242(x83201),x83202),x83204))+~P1(f328(f328(f242(x83201),f2(x83201)),x83202))+P1(f328(f328(f242(x83201),f328(f328(f286(x83201),x83202),x83203)),f328(f328(f286(x83201),x83204),x83205))) % 154.70/154.57 [9696]~P66(x96965)+~P84(x96965)+E(x96961,f192(f882(x96962,a870)))+~P1(f328(f61(x96962),x96961))+P1(f328(f328(f330(x96962),f865(x96963,x96964,x96961,x96962,x96965)),x96961))+P1(f328(f328(f243(x96965),f328(f328(f6(x96962,x96965),x96964),x96961)),f328(f328(f6(x96962,x96965),x96963),x96961))) % 154.70/154.57 [9814]~P66(x98141)+~P82(x98141)+~P1(f328(f61(x98142),x98145))+~P1(f328(f328(f242(x98141),f2(x98141)),f328(x98143,f362(x98143,x98144,x98145,x98142,x98141))))+P1(f328(f328(f242(x98141),f328(f328(f6(x98142,x98141),x98143),x98144)),f328(f328(f6(x98142,x98141),x98143),x98145)))+~P1(f328(f328(f242(f882(x98142,a870)),x98144),x98145)) % 154.70/154.57 [9982]~P66(x99823)+~P84(x99823)+E(x99821,f192(f882(x99822,a870)))+~P1(f328(f61(x99822),x99821))+~P1(f328(f328(f243(x99823),f328(x99824,f865(x99825,x99824,x99821,x99822,x99823))),f328(x99825,f865(x99825,x99824,x99821,x99822,x99823))))+P1(f328(f328(f243(x99823),f328(f328(f6(x99822,x99823),x99824),x99821)),f328(f328(f6(x99822,x99823),x99825),x99821))) % 154.70/154.57 [7028]~P19(x70282,x70285,x70284)+E(x70281,f192(f882(x70282,a870)))+E(x70283,f192(f882(x70282,a870)))+~P1(f328(f61(x70282),x70281))+~P1(f328(f61(x70282),x70283))+E(f328(x70284,f328(f328(f114(f882(x70282,a870)),x70283),x70281)),f328(f328(x70285,f328(x70284,x70283)),f328(x70284,x70281))) % 154.70/154.57 [7615]~P144(x76151,x76154,x76153)+P1(f328(x76151,x76152))+~P1(f328(f328(f243(a1),x76154),f2(a1)))+~P1(f328(f328(f242(a1),x76155),f2(a1)))+~E(x76153,f328(f328(f80(a1),f328(f328(f81(a1),x76154),x76152)),x76155))+~P1(f328(f328(f243(a1),x76154),x76155)) % 154.70/154.57 [7616]~P143(x76161,x76164,x76163)+P1(f328(x76161,x76162))+~P1(f328(f328(f243(a1),x76164),f2(a1)))+~P1(f328(f328(f242(a1),x76162),f2(a1)))+~E(x76163,f328(f328(f80(a1),f328(f328(f81(a1),x76164),x76165)),x76162))+~P1(f328(f328(f243(a1),x76164),x76162)) % 154.70/154.57 [7658]~P144(x76581,x76584,x76583)+P1(f328(x76581,x76582))+~E(x76583,f328(f328(f80(a1),f328(f328(f81(a1),x76584),x76582)),x76585))+~P1(f328(f328(f243(a1),f2(a1)),x76584))+~P1(f328(f328(f242(a1),f2(a1)),x76585))+~P1(f328(f328(f243(a1),x76585),x76584)) % 154.70/154.57 [7659]~P143(x76591,x76594,x76593)+P1(f328(x76591,x76592))+~E(x76593,f328(f328(f80(a1),f328(f328(f81(a1),x76594),x76595)),x76592))+~P1(f328(f328(f243(a1),f2(a1)),x76594))+~P1(f328(f328(f242(a1),f2(a1)),x76592))+~P1(f328(f328(f243(a1),x76592),x76594)) % 154.70/154.57 [8610]P1(f328(f328(x86101,x86102),x86103))+~P1(f328(f328(x86101,f328(f328(f38(a1),x86104),x86105)),f44(a1,x86104,x86105)))+~P1(f328(f328(f243(a1),x86105),f2(a1)))+~P1(f328(f328(f242(a1),x86103),f2(a1)))+~E(x86104,f328(f328(f80(a1),f328(f328(f81(a1),x86105),x86102)),x86103))+~P1(f328(f328(f243(a1),x86105),x86103)) % 154.70/154.57 [8619]P1(f328(f328(x86191,x86192),x86193))+~P1(f328(f328(x86191,f328(f328(f38(a1),x86194),x86195)),f44(a1,x86194,x86195)))+~E(x86194,f328(f328(f80(a1),f328(f328(f81(a1),x86195),x86192)),x86193))+~P1(f328(f328(f243(a1),f2(a1)),x86195))+~P1(f328(f328(f242(a1),f2(a1)),x86193))+~P1(f328(f328(f243(a1),x86193),x86195)) % 154.70/154.57 [8856]E(x88561,x88562)+~P52(x88563,x88565,x88564)+~P1(f328(f328(f330(x88563),x88562),x88565))+~P1(f328(f328(f330(x88563),x88561),x88565))+P1(f328(f328(f330(f881(x88563,x88563)),f328(f328(f263(x88563,x88563),x88561),x88562)),x88564))+P1(f328(f328(f330(f881(x88563,x88563)),f328(f328(f263(x88563,x88563),x88562),x88561)),x88564)) % 154.70/154.57 [9723]~P66(x97235)+~P82(x97235)+~P1(f328(f61(x97231),x97234))+P1(f328(f328(f242(x97235),f328(f328(f6(x97231,x97235),x97232),x97233)),f328(f328(f6(x97231,x97235),x97232),x97234)))+~P1(f328(f328(f242(f882(x97231,a870)),x97233),x97234))+P1(f328(f328(f330(x97231),f362(x97232,x97233,x97234,x97231,x97235)),f328(f328(f22(f882(x97231,a870)),x97234),x97233))) % 154.70/154.57 [9822]E(x98221,f192(f882(x98222,a870)))+~P1(f328(f61(x98222),x98223))+~P1(f328(f61(x98222),x98221))+P1(f328(f328(f330(f881(f882(x98222,a870),f882(x98222,a870))),f328(f328(f263(f882(x98222,a870),f882(x98222,a870)),x98223),x98221)),f319(x98222,x98224)))+~P1(f328(f328(f330(x98222),x98225),x98221))+~P1(f328(f328(f330(f881(x98222,x98222)),f328(f328(f263(x98222,x98222),f561(x98224,x98221,x98223,x98222)),x98225)),x98224)) % 154.70/154.57 [9823]E(x98231,f192(f882(x98232,a870)))+~P1(f328(f61(x98232),x98233))+~P1(f328(f61(x98232),x98231))+P1(f328(f328(f330(f881(f882(x98232,a870),f882(x98232,a870))),f328(f328(f263(f882(x98232,a870),f882(x98232,a870)),x98233),x98231)),f319(x98232,x98234)))+~P1(f328(f328(f330(x98232),x98235),x98231))+~P1(f328(f328(f330(f881(x98232,x98232)),f328(f328(f263(x98232,x98232),f618(x98234,x98231,x98233,x98232)),x98235)),x98234)) % 154.70/154.57 [9986]~P81(x99861)+~E(f328(f328(f6(x99865,x99861),x99862),x99866),x99864)+~P1(f328(f61(x99865),x99866))+P1(f328(f328(f330(x99865),f382(x99863,x99864,x99862,x99866,x99865,x99861)),x99866))+P1(f328(f328(f242(x99861),f328(x99862,x99863)),x99864))+~P1(f328(f328(f330(x99865),x99863),x99866)) % 154.70/154.57 [10033]~P81(x100331)+~E(f328(f328(f6(x100335,x100331),x100332),x100336),x100334)+~P1(f328(f61(x100335),x100336))+~P1(f328(f328(f330(x100335),x100333),x100336))+~P1(f328(f328(f242(x100331),f2(x100331)),f328(x100332,f382(x100333,x100334,x100332,x100336,x100335,x100331))))+P1(f328(f328(f242(x100331),f328(x100332,x100333)),x100334)) % 154.70/154.57 [10147]~E(x101475,x101478)+~E(x101474,x101477)+~P66(x101472)+~P108(x101471)+E(f328(f328(f6(x101471,x101472),x101473),f328(f298(x101471,x101474),x101475)),f328(f328(f6(x101471,x101472),x101476),f328(f298(x101471,x101477),x101478)))+P1(f328(f328(f242(x101471),x101474),f624(x101473,x101476,x101475,x101478,x101474,x101477,x101471,x101472))) % 154.70/154.57 [10164]~E(x101647,x101644)+~E(x101648,x101645)+~P66(x101642)+~P108(x101641)+~E(f328(x101643,f624(x101646,x101643,x101648,x101645,x101647,x101644,x101641,x101642)),f328(x101646,f624(x101646,x101643,x101648,x101645,x101647,x101644,x101641,x101642)))+E(f328(f328(f6(x101641,x101642),x101643),f328(f298(x101641,x101644),x101645)),f328(f328(f6(x101641,x101642),x101646),f328(f298(x101641,x101647),x101648))) % 154.70/154.57 [10166]~E(x101664,x101667)+~E(x101665,x101668)+~P66(x101662)+~P108(x101661)+E(f328(f328(f6(x101661,x101662),x101663),f328(f298(x101661,x101664),x101665)),f328(f328(f6(x101661,x101662),x101666),f328(f298(x101661,x101667),x101668)))+P1(f328(f328(f243(x101661),f624(x101663,x101666,x101665,x101668,x101664,x101667,x101661,x101662)),x101665)) % 154.70/154.57 [9828]~P8(x98285,x98289,x98286)+~P8(x98281,x982810,x98283)+~P15(x98281,x98285,f882(x98282,a870),x98283,x98286,x98288)+~P1(f328(f328(f330(x98285),x98287),x98289))+~P1(f328(f328(f330(x98281),x98284),x982810))+E(f328(f328(f41(x98281,f882(x98282,a870)),f328(f282(x98281,x98281,x98283),f328(f328(f306(x98281),x98284),f192(f882(x98281,a870))))),f328(f328(f8(f882(x98285,f882(x98282,a870)),f882(x98282,a870),x98281),f328(f41(x98285,f882(x98282,a870)),f328(f282(x98285,x98285,x98286),f328(f328(f306(x98285),x98287),f192(f882(x98285,a870)))))),x98288)),f328(f328(x98288,x98284),x98287)) % 154.70/154.57 [5574]~P105(x55743)+~P16(x55743,x55742)+~P16(x55743,x55741)+E(x55741,x55742)+~E(f328(f170(x55743),x55741),f328(f170(x55743),x55742))+~P1(f328(f134(x55743),x55742))+~P1(f328(f134(x55743),x55741)) % 154.70/154.57 [4913]~P134(x49132)+~P128(x49132)+~P129(x49132)+~P112(x49132)+~E(x49133,f2(x49132))+E(x49131,f2(a875))+E(f328(f328(f253(x49132),x49133),x49131),f2(x49132)) % 154.70/154.57 [9125]E(x91251,f2(a875))+~E(x91252,f328(f328(f80(a875),f328(f328(f81(a875),f328(f262(a875,a875),x91253)),x91251)),f328(f266(a875,a875),x91253)))+P1(f328(f47(x91252,x91251),x91253))+~P1(f328(f328(f242(a875),f328(f266(a875,a875),x91253)),f2(a875)))+~P1(f328(f328(f242(a875),f2(a875)),f328(f266(a875,a875),x91253)))+~P1(f328(f328(f243(a875),x91251),f328(f266(a875,a875),x91253)))+~P1(f328(f328(f243(a875),f328(f266(a875,a875),x91253)),x91251)) % 154.70/154.57 [9134]~E(f328(f262(a875,a875),x91343),f2(a875))+~E(x91341,f328(f328(f80(a875),f328(f328(f81(a875),f328(f262(a875,a875),x91343)),x91342)),f328(f266(a875,a875),x91343)))+P1(f328(f47(x91341,x91342),x91343))+~P1(f328(f328(f242(a875),f328(f266(a875,a875),x91343)),f2(a875)))+~P1(f328(f328(f242(a875),f2(a875)),f328(f266(a875,a875),x91343)))+~P1(f328(f328(f243(a875),x91342),f328(f266(a875,a875),x91343)))+~P1(f328(f328(f243(a875),f328(f266(a875,a875),x91343)),x91342)) % 154.70/154.57 [7972]~P70(x79722)+E(x79721,f192(f882(x79722,a870)))+E(x79723,f192(f882(x79722,a870)))+~P1(f328(f61(x79722),x79721))+~P1(f328(f61(x79722),x79723))+~E(f328(f328(f105(f882(x79722,a870)),x79723),x79721),f192(f882(x79722,a870)))+E(f328(f328(f81(x79722),f328(f63(x79722,f81(x79722)),x79723)),f328(f63(x79722,f81(x79722)),x79721)),f328(f63(x79722,f81(x79722)),f328(f328(f114(f882(x79722,a870)),x79723),x79721))) % 154.70/154.57 [7754]E(x77541,f2(a1))+E(f328(f328(f38(a1),x77542),x77541),x77543)+~P1(f328(f328(f242(a1),x77544),f2(a1)))+~E(x77542,f328(f328(f80(a1),f328(f328(f81(a1),x77541),x77543)),x77544))+~P1(f328(f328(f242(a1),f2(a1)),x77544))+~P1(f328(f328(f243(a1),x77544),x77541))+~P1(f328(f328(f243(a1),x77541),x77544)) % 154.70/154.57 [7764]E(f44(a1,x77642,x77641),x77643)+E(x77641,f2(a1))+~P1(f328(f328(f242(a1),x77643),f2(a1)))+~E(x77642,f328(f328(f80(a1),f328(f328(f81(a1),x77641),x77644)),x77643))+~P1(f328(f328(f242(a1),f2(a1)),x77643))+~P1(f328(f328(f243(a1),x77643),x77641))+~P1(f328(f328(f243(a1),x77641),x77643)) % 154.70/154.57 [7667]~P20(x76672,x76675,x76674)+E(x76671,f192(f882(x76672,a870)))+E(x76673,f192(f882(x76672,a870)))+~P1(f328(f61(x76672),x76671))+~P1(f328(f61(x76672),x76673))+~E(f328(f328(f105(f882(x76672,a870)),x76673),x76671),f192(f882(x76672,a870)))+E(f328(x76674,f328(f328(f114(f882(x76672,a870)),x76673),x76671)),f328(f328(x76675,f328(x76674,x76673)),f328(x76674,x76671))) % 154.70/154.57 [9370]~P27(x93703,x93701,x93705,x93704)+~P27(x93701,x93703,x93706,x93702)+E(f328(f37(x93701),x93702),f328(f37(x93703),x93704))+~P1(f328(f61(x93703),x93704))+~P1(f328(f61(x93701),x93702))+~P1(f328(f328(f242(f882(x93703,a870)),f328(f307(x93701,x93703,x93706),x93702)),x93704))+~P1(f328(f328(f242(f882(x93701,a870)),f328(f307(x93703,x93701,x93705),x93704)),x93702)) % 154.70/154.57 [9314]~P1(f328(f328(f243(a1),f328(f328(f80(a1),f328(f328(f81(a1),x93145),x93141)),x93146)),f2(a1)))+~E(f328(f328(f80(a1),f328(f328(f81(a1),x93143),x93142)),x93144),f328(f328(f80(a1),f328(f328(f81(a1),x93145),x93141)),x93146))+~P1(f328(f328(f243(a1),f2(a1)),x93145))+~P1(f328(f328(f242(a1),f2(a1)),x93146))+~P1(f328(f328(f243(a1),x93144),x93143))+~P1(f328(f328(f242(a1),x93145),x93143))+P1(f328(f328(f242(a1),x93141),x93142)) % 154.70/154.57 [9078]~E(f328(f328(f80(a1),f328(f328(f81(a1),x90783),x90781)),x90784),f328(f328(f80(a1),f328(f328(f81(a1),x90785),x90782)),x90786))+~P1(f328(f328(f243(a1),f2(a1)),x90785))+~P1(f328(f328(f242(a1),f2(a1)),x90784))+~P1(f328(f328(f243(a1),x90786),x90785))+~P1(f328(f328(f242(a1),x90785),x90783))+P1(f328(f328(f242(a1),x90781),x90782))+~P1(f328(f328(f242(a1),f2(a1)),f328(f328(f80(a1),f328(f328(f81(a1),x90785),x90782)),x90786))) % 154.70/154.57 [9255]~P126(x92551)+~E(f328(f328(f80(x92551),x92552),x92554),f78(x92551))+~P1(f328(f328(f242(x92551),f2(x92551)),x92554))+~P1(f328(f328(f242(x92551),f2(x92551)),x92552))+~P1(f328(f328(f243(x92551),x92555),x92556))+~P1(f328(f328(f243(x92551),x92553),x92556))+P1(f328(f328(f243(x92551),f328(f328(f80(x92551),f328(f328(f81(x92551),x92552),x92553)),f328(f328(f81(x92551),x92554),x92555))),x92556)) % 154.70/154.57 [9256]~P125(x92561)+~E(f328(f328(f80(x92561),x92562),x92564),f78(x92561))+~P1(f328(f328(f242(x92561),x92565),x92566))+~P1(f328(f328(f242(x92561),x92563),x92566))+~P1(f328(f328(f242(x92561),f2(x92561)),x92564))+~P1(f328(f328(f242(x92561),f2(x92561)),x92562))+P1(f328(f328(f242(x92561),f328(f328(f80(x92561),f328(f328(f81(x92561),x92562),x92563)),f328(f328(f81(x92561),x92564),x92565))),x92566)) % 154.70/154.57 [10078]~P8(x100787,x100786,x100785)+E(x100781,x100782)+~P14(x100787,f882(x100784,a870),x100785,x100783)+E(f328(x100783,f545(x100781,x100782,x100783,x100784,x100785,x100786,x100787)),f328(x100783,f546(x100781,x100782,x100783,x100784,x100785,x100786,x100787)))+~E(f328(f328(f41(x100787,f882(x100784,a870)),x100781),x100783),f328(f328(f41(x100787,f882(x100784,a870)),x100782),x100783))+~P1(f328(f328(f330(f882(x100787,a870)),x100782),f328(f328(f60(x100787),x100786),x100785)))+~P1(f328(f328(f330(f882(x100787,a870)),x100781),f328(f328(f60(x100787),x100786),x100785))) % 154.70/154.57 [10112]~P8(x101123,x101127,x101126)+E(x101121,x101122)+~P14(x101123,f882(x101125,a870),x101126,x101124)+~E(f328(f328(f41(x101123,f882(x101125,a870)),x101121),x101124),f328(f328(f41(x101123,f882(x101125,a870)),x101122),x101124))+P1(f328(f328(f330(x101123),f546(x101121,x101122,x101124,x101125,x101126,x101127,x101123)),x101127))+~P1(f328(f328(f330(f882(x101123,a870)),x101122),f328(f328(f60(x101123),x101127),x101126)))+~P1(f328(f328(f330(f882(x101123,a870)),x101121),f328(f328(f60(x101123),x101127),x101126))) % 154.70/154.57 [10113]~P8(x101133,x101137,x101136)+E(x101131,x101132)+~P14(x101133,f882(x101135,a870),x101136,x101134)+~E(f328(f328(f41(x101133,f882(x101135,a870)),x101131),x101134),f328(f328(f41(x101133,f882(x101135,a870)),x101132),x101134))+P1(f328(f328(f330(x101133),f545(x101131,x101132,x101134,x101135,x101136,x101137,x101133)),x101137))+~P1(f328(f328(f330(f882(x101133,a870)),x101132),f328(f328(f60(x101133),x101137),x101136)))+~P1(f328(f328(f330(f882(x101133,a870)),x101131),f328(f328(f60(x101133),x101137),x101136))) % 154.70/154.57 [10183]E(x101831,x101832)+~P8(x101833,x101836,x101837)+~P14(x101833,f882(x101834,a870),x101837,x101835)+~E(f328(f328(f41(x101833,f882(x101834,a870)),x101831),x101835),f328(f328(f41(x101833,f882(x101834,a870)),x101832),x101835))+~P1(f328(f328(f330(f881(x101833,x101833)),f328(f328(f263(x101833,x101833),f546(x101831,x101832,x101835,x101834,x101837,x101836,x101833)),f545(x101831,x101832,x101835,x101834,x101837,x101836,x101833))),x101837))+~P1(f328(f328(f330(f882(x101833,a870)),x101832),f328(f328(f60(x101833),x101836),x101837)))+~P1(f328(f328(f330(f882(x101833,a870)),x101831),f328(f328(f60(x101833),x101836),x101837))) % 154.70/154.57 [9077]~P8(x90771,x90777,x90774)+~E(x90775,x90776)+~P1(f328(f328(f330(x90771),x90773),x90776))+~P1(f328(f328(f330(x90771),x90772),x90775))+~P1(f328(f328(f330(f882(x90771,a870)),x90776),f328(f328(f60(x90771),x90777),x90774)))+~P1(f328(f328(f330(f882(x90771,a870)),x90775),f328(f328(f60(x90771),x90777),x90774)))+P1(f328(f328(f330(f881(x90771,x90771)),f328(f328(f263(x90771,x90771),x90772),x90773)),x90774)) % 154.70/154.57 [9212]E(x92121,x92122)+~P8(x92123,x92124,x92125)+~P1(f328(f328(f330(x92123),x92126),x92122))+~P1(f328(f328(f330(x92123),x92127),x92121))+~P1(f328(f328(f330(f882(x92123,a870)),x92122),f328(f328(f60(x92123),x92124),x92125)))+~P1(f328(f328(f330(f882(x92123,a870)),x92121),f328(f328(f60(x92123),x92124),x92125)))+~P1(f328(f328(f330(f881(x92123,x92123)),f328(f328(f263(x92123,x92123),x92127),x92126)),x92125)) % 154.70/154.57 [10206]~P8(x102069,x102068,x102067)+~P8(x102061,x1020611,x1020610)+~P15(x102061,x102069,f882(x102066,a870),x1020610,x102067,x102065)+P1(f328(f328(f330(x102061),f548(x102062,x102063,x102064,x102065,x102066,x102067,x102068,x102069,x1020610,x1020611,x102061)),x1020611))+~P1(f328(f328(f330(f882(x102069,a870)),x102063),f328(f328(f60(x102069),x102068),x102067)))+~P1(f328(f328(f330(f882(x102061,a870)),x102064),f328(f328(f60(x102061),x1020611),x1020610)))+P1(f328(f328(f330(f882(x102066,a870)),f328(f328(f41(x102061,f882(x102066,a870)),x102064),f328(f328(f8(f882(x102069,f882(x102066,a870)),f882(x102066,a870),x102061),f328(f41(x102069,f882(x102066,a870)),x102063)),x102065))),x102062)) % 154.70/154.57 [10207]~P8(x1020711,x1020710,x102079)+~P8(x102071,x102078,x102077)+~P15(x1020711,x102071,f882(x102076,a870),x102079,x102077,x102075)+P1(f328(f328(f330(x102071),f549(x102072,x102073,x102074,x102075,x102076,x102077,x102078,x102071,x102079,x1020710,x1020711)),x102078))+~P1(f328(f328(f330(f882(x1020711,a870)),x102074),f328(f328(f60(x1020711),x1020710),x102079)))+~P1(f328(f328(f330(f882(x102071,a870)),x102073),f328(f328(f60(x102071),x102078),x102077)))+P1(f328(f328(f330(f882(x102076,a870)),f328(f328(f41(x1020711,f882(x102076,a870)),x102074),f328(f328(f8(f882(x102071,f882(x102076,a870)),f882(x102076,a870),x1020711),f328(f41(x102071,f882(x102076,a870)),x102073)),x102075))),x102072)) % 154.70/154.57 [10210]~P8(x102102,x102108,x102109)+~P8(x102104,x1021010,x1021011)+~P15(x102102,x102104,f882(x102101,a870),x102109,x1021011,x102106)+~P1(f328(f328(f330(f882(x102102,a870)),x102103),f328(f328(f60(x102102),x102108),x102109)))+~P1(f328(f328(f330(f882(x102104,a870)),x102105),f328(f328(f60(x102104),x1021010),x1021011)))+~P1(f328(f328(f330(f882(x102101,a870)),f328(f328(x102106,f548(x102107,x102105,x102103,x102106,x102101,x1021011,x1021010,x102104,x102109,x102108,x102102)),f549(x102107,x102105,x102103,x102106,x102101,x1021011,x1021010,x102104,x102109,x102108,x102102))),x102107))+P1(f328(f328(f330(f882(x102101,a870)),f328(f328(f41(x102102,f882(x102101,a870)),x102103),f328(f328(f8(f882(x102104,f882(x102101,a870)),f882(x102101,a870),x102102),f328(f41(x102104,f882(x102101,a870)),x102105)),x102106))),x102107)) % 154.70/154.57 [9112]E(x91121,x91122)+~P105(x91124)+~P27(x91123,x91124,x91125,f328(f328(f114(f882(x91123,a870)),f328(f170(x91123),x91121)),f328(f170(x91123),x91122)))+~E(f328(f170(x91123),x91121),f328(f170(x91123),x91122))+~P16(x91124,f328(f328(f151(x91123,x91124),x91125),x91122))+~P16(x91124,f328(f328(f151(x91123,x91124),x91125),x91121))+~P1(f328(f134(x91124),f328(f328(f151(x91123,x91124),x91125),x91122)))+~P1(f328(f134(x91124),f328(f328(f151(x91123,x91124),x91125),x91121))) % 154.70/154.57 %EqnAxiom % 154.70/154.57 [1]E(x11,x11) % 154.70/154.57 [2]E(x22,x21)+~E(x21,x22) % 154.70/154.57 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 154.70/154.57 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 154.70/154.57 [5]~E(x51,x52)+E(f104(x51),f104(x52)) % 154.70/154.57 [6]~E(x61,x62)+E(f22(x61),f22(x62)) % 154.70/154.57 [7]~E(x71,x72)+E(f192(x71),f192(x72)) % 154.70/154.57 [8]~E(x81,x82)+E(f328(x81,x83),f328(x82,x83)) % 154.70/154.57 [9]~E(x91,x92)+E(f328(x93,x91),f328(x93,x92)) % 154.70/154.57 [10]~E(x101,x102)+E(f31(x101),f31(x102)) % 154.70/154.57 [11]~E(x111,x112)+E(f148(x111),f148(x112)) % 154.70/154.57 [12]~E(x121,x122)+E(f105(x121),f105(x122)) % 154.70/154.57 [13]~E(x131,x132)+E(f240(x131),f240(x132)) % 154.70/154.57 [14]~E(x141,x142)+E(f114(x141),f114(x142)) % 154.70/154.57 [15]~E(x151,x152)+E(f241(x151),f241(x152)) % 154.70/154.57 [16]~E(x161,x162)+E(f106(x161),f106(x162)) % 154.70/154.57 [17]~E(x171,x172)+E(f34(x171),f34(x172)) % 154.70/154.57 [18]~E(x181,x182)+E(f84(x181),f84(x182)) % 154.70/154.57 [19]~E(x191,x192)+E(f243(x191),f243(x192)) % 154.70/154.57 [20]~E(x201,x202)+E(f882(x201,x203),f882(x202,x203)) % 154.70/154.57 [21]~E(x211,x212)+E(f882(x213,x211),f882(x213,x212)) % 154.70/154.57 [22]~E(x221,x222)+E(f549(x221,x223,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212),f549(x222,x223,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212)) % 154.70/154.57 [23]~E(x231,x232)+E(f549(x233,x231,x234,x235,x236,x237,x238,x239,x2310,x2311,x2312),f549(x233,x232,x234,x235,x236,x237,x238,x239,x2310,x2311,x2312)) % 154.70/154.57 [24]~E(x241,x242)+E(f549(x243,x244,x241,x245,x246,x247,x248,x249,x2410,x2411,x2412),f549(x243,x244,x242,x245,x246,x247,x248,x249,x2410,x2411,x2412)) % 154.70/154.57 [25]~E(x251,x252)+E(f549(x253,x254,x255,x251,x256,x257,x258,x259,x2510,x2511,x2512),f549(x253,x254,x255,x252,x256,x257,x258,x259,x2510,x2511,x2512)) % 154.70/154.57 [26]~E(x261,x262)+E(f549(x263,x264,x265,x266,x261,x267,x268,x269,x2610,x2611,x2612),f549(x263,x264,x265,x266,x262,x267,x268,x269,x2610,x2611,x2612)) % 154.70/154.57 [27]~E(x271,x272)+E(f549(x273,x274,x275,x276,x277,x271,x278,x279,x2710,x2711,x2712),f549(x273,x274,x275,x276,x277,x272,x278,x279,x2710,x2711,x2712)) % 154.70/154.57 [28]~E(x281,x282)+E(f549(x283,x284,x285,x286,x287,x288,x281,x289,x2810,x2811,x2812),f549(x283,x284,x285,x286,x287,x288,x282,x289,x2810,x2811,x2812)) % 154.70/154.57 [29]~E(x291,x292)+E(f549(x293,x294,x295,x296,x297,x298,x299,x291,x2910,x2911,x2912),f549(x293,x294,x295,x296,x297,x298,x299,x292,x2910,x2911,x2912)) % 154.70/154.57 [30]~E(x301,x302)+E(f549(x303,x304,x305,x306,x307,x308,x309,x3010,x301,x3011,x3012),f549(x303,x304,x305,x306,x307,x308,x309,x3010,x302,x3011,x3012)) % 154.70/154.57 [31]~E(x311,x312)+E(f549(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x311,x3112),f549(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x312,x3112)) % 154.70/154.57 [32]~E(x321,x322)+E(f549(x323,x324,x325,x326,x327,x328,x329,x3210,x3211,x3212,x321),f549(x323,x324,x325,x326,x327,x328,x329,x3210,x3211,x3212,x322)) % 154.70/154.57 [33]~E(x331,x332)+E(f876(x331),f876(x332)) % 154.70/154.57 [34]~E(x341,x342)+E(f78(x341),f78(x342)) % 154.70/154.57 [35]~E(x351,x352)+E(f548(x351,x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512),f548(x352,x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512)) % 154.70/154.57 [36]~E(x361,x362)+E(f548(x363,x361,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612),f548(x363,x362,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612)) % 154.70/154.57 [37]~E(x371,x372)+E(f548(x373,x374,x371,x375,x376,x377,x378,x379,x3710,x3711,x3712),f548(x373,x374,x372,x375,x376,x377,x378,x379,x3710,x3711,x3712)) % 154.70/154.57 [38]~E(x381,x382)+E(f548(x383,x384,x385,x381,x386,x387,x388,x389,x3810,x3811,x3812),f548(x383,x384,x385,x382,x386,x387,x388,x389,x3810,x3811,x3812)) % 154.70/154.57 [39]~E(x391,x392)+E(f548(x393,x394,x395,x396,x391,x397,x398,x399,x3910,x3911,x3912),f548(x393,x394,x395,x396,x392,x397,x398,x399,x3910,x3911,x3912)) % 154.70/154.57 [40]~E(x401,x402)+E(f548(x403,x404,x405,x406,x407,x401,x408,x409,x4010,x4011,x4012),f548(x403,x404,x405,x406,x407,x402,x408,x409,x4010,x4011,x4012)) % 154.70/154.57 [41]~E(x411,x412)+E(f548(x413,x414,x415,x416,x417,x418,x411,x419,x4110,x4111,x4112),f548(x413,x414,x415,x416,x417,x418,x412,x419,x4110,x4111,x4112)) % 154.70/154.57 [42]~E(x421,x422)+E(f548(x423,x424,x425,x426,x427,x428,x429,x421,x4210,x4211,x4212),f548(x423,x424,x425,x426,x427,x428,x429,x422,x4210,x4211,x4212)) % 154.70/154.57 [43]~E(x431,x432)+E(f548(x433,x434,x435,x436,x437,x438,x439,x4310,x431,x4311,x4312),f548(x433,x434,x435,x436,x437,x438,x439,x4310,x432,x4311,x4312)) % 154.70/154.57 [44]~E(x441,x442)+E(f548(x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x441,x4412),f548(x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x442,x4412)) % 154.70/154.57 [45]~E(x451,x452)+E(f548(x453,x454,x455,x456,x457,x458,x459,x4510,x4511,x4512,x451),f548(x453,x454,x455,x456,x457,x458,x459,x4510,x4511,x4512,x452)) % 154.70/154.57 [46]~E(x461,x462)+E(f4(x461),f4(x462)) % 154.70/154.57 [47]~E(x471,x472)+E(f330(x471),f330(x472)) % 154.70/154.57 [48]~E(x481,x482)+E(f251(x481),f251(x482)) % 154.70/154.57 [49]~E(x491,x492)+E(f115(x491),f115(x492)) % 154.70/154.57 [50]~E(x501,x502)+E(f178(x501,x503),f178(x502,x503)) % 154.70/154.57 [51]~E(x511,x512)+E(f178(x513,x511),f178(x513,x512)) % 154.70/154.57 [52]~E(x521,x522)+E(f874(x521),f874(x522)) % 154.70/154.57 [53]~E(x531,x532)+E(f879(x531),f879(x532)) % 154.70/154.57 [54]~E(x541,x542)+E(f242(x541),f242(x542)) % 154.70/154.57 [55]~E(x551,x552)+E(f877(x551),f877(x552)) % 154.70/154.57 [56]~E(x561,x562)+E(f664(x561,x563,x564),f664(x562,x563,x564)) % 154.70/154.57 [57]~E(x571,x572)+E(f664(x573,x571,x574),f664(x573,x572,x574)) % 154.70/154.57 [58]~E(x581,x582)+E(f664(x583,x584,x581),f664(x583,x584,x582)) % 154.70/154.57 [59]~E(x591,x592)+E(f81(x591),f81(x592)) % 154.70/154.57 [60]~E(x601,x602)+E(f881(x601,x603),f881(x602,x603)) % 154.70/154.57 [61]~E(x611,x612)+E(f881(x613,x611),f881(x613,x612)) % 154.70/154.57 [62]~E(x621,x622)+E(f75(x621),f75(x622)) % 154.70/154.57 [63]~E(x631,x632)+E(f79(x631),f79(x632)) % 154.70/154.57 [64]~E(x641,x642)+E(f153(x641,x643,x644,x645),f153(x642,x643,x644,x645)) % 154.70/154.57 [65]~E(x651,x652)+E(f153(x653,x651,x654,x655),f153(x653,x652,x654,x655)) % 154.70/154.57 [66]~E(x661,x662)+E(f153(x663,x664,x661,x665),f153(x663,x664,x662,x665)) % 154.70/154.57 [67]~E(x671,x672)+E(f153(x673,x674,x675,x671),f153(x673,x674,x675,x672)) % 154.70/154.57 [68]~E(x681,x682)+E(f193(x681),f193(x682)) % 154.70/154.57 [69]~E(x691,x692)+E(f117(x691),f117(x692)) % 154.70/154.57 [70]~E(x701,x702)+E(f107(x701),f107(x702)) % 154.70/154.57 [71]~E(x711,x712)+E(f80(x711),f80(x712)) % 154.70/154.57 [72]~E(x721,x722)+E(f306(x721),f306(x722)) % 154.70/154.57 [73]~E(x731,x732)+E(f73(x731,x733,x734,x735),f73(x732,x733,x734,x735)) % 154.70/154.57 [74]~E(x741,x742)+E(f73(x743,x741,x744,x745),f73(x743,x742,x744,x745)) % 154.70/154.57 [75]~E(x751,x752)+E(f73(x753,x754,x751,x755),f73(x753,x754,x752,x755)) % 154.70/154.57 [76]~E(x761,x762)+E(f73(x763,x764,x765,x761),f73(x763,x764,x765,x762)) % 154.70/154.57 [77]~E(x771,x772)+E(f7(x771,x773,x774),f7(x772,x773,x774)) % 154.70/154.57 [78]~E(x781,x782)+E(f7(x783,x781,x784),f7(x783,x782,x784)) % 154.70/154.57 [79]~E(x791,x792)+E(f7(x793,x794,x791),f7(x793,x794,x792)) % 154.70/154.57 [80]~E(x801,x802)+E(f60(x801),f60(x802)) % 154.70/154.57 [81]~E(x811,x812)+E(f61(x811),f61(x812)) % 154.70/154.57 [82]~E(x821,x822)+E(f205(x821),f205(x822)) % 154.70/154.57 [83]~E(x831,x832)+E(f880(x831,x833),f880(x832,x833)) % 154.70/154.57 [84]~E(x841,x842)+E(f880(x843,x841),f880(x843,x842)) % 154.70/154.57 [85]~E(x851,x852)+E(f54(x851,x853,x854),f54(x852,x853,x854)) % 154.70/154.57 [86]~E(x861,x862)+E(f54(x863,x861,x864),f54(x863,x862,x864)) % 154.70/154.57 [87]~E(x871,x872)+E(f54(x873,x874,x871),f54(x873,x874,x872)) % 154.70/154.57 [88]~E(x881,x882)+E(f266(x881,x883),f266(x882,x883)) % 154.70/154.57 [89]~E(x891,x892)+E(f266(x893,x891),f266(x893,x892)) % 154.70/154.57 [90]~E(x901,x902)+E(f8(x901,x903,x904),f8(x902,x903,x904)) % 154.70/154.57 [91]~E(x911,x912)+E(f8(x913,x911,x914),f8(x913,x912,x914)) % 154.70/154.57 [92]~E(x921,x922)+E(f8(x923,x924,x921),f8(x923,x924,x922)) % 154.70/154.57 [93]~E(x931,x932)+E(f163(x931),f163(x932)) % 154.70/154.57 [94]~E(x941,x942)+E(f92(x941),f92(x942)) % 154.70/154.57 [95]~E(x951,x952)+E(f118(x951,x953),f118(x952,x953)) % 154.70/154.57 [96]~E(x961,x962)+E(f118(x963,x961),f118(x963,x962)) % 154.70/154.57 [97]~E(x971,x972)+E(f304(x971,x973),f304(x972,x973)) % 154.70/154.57 [98]~E(x981,x982)+E(f304(x983,x981),f304(x983,x982)) % 154.70/154.57 [99]~E(x991,x992)+E(f543(x991,x993,x994),f543(x992,x993,x994)) % 154.70/154.57 [100]~E(x1001,x1002)+E(f543(x1003,x1001,x1004),f543(x1003,x1002,x1004)) % 154.70/154.57 [101]~E(x1011,x1012)+E(f543(x1013,x1014,x1011),f543(x1013,x1014,x1012)) % 154.70/154.57 [102]~E(x1021,x1022)+E(f77(x1021,x1023,x1024,x1025),f77(x1022,x1023,x1024,x1025)) % 154.70/154.57 [103]~E(x1031,x1032)+E(f77(x1033,x1031,x1034,x1035),f77(x1033,x1032,x1034,x1035)) % 154.70/154.57 [104]~E(x1041,x1042)+E(f77(x1043,x1044,x1041,x1045),f77(x1043,x1044,x1042,x1045)) % 154.70/154.57 [105]~E(x1051,x1052)+E(f77(x1053,x1054,x1055,x1051),f77(x1053,x1054,x1055,x1052)) % 154.70/154.57 [106]~E(x1061,x1062)+E(f16(x1061,x1063),f16(x1062,x1063)) % 154.70/154.57 [107]~E(x1071,x1072)+E(f16(x1073,x1071),f16(x1073,x1072)) % 154.70/154.57 [108]~E(x1081,x1082)+E(f249(x1081),f249(x1082)) % 154.70/154.57 [109]~E(x1091,x1092)+E(f263(x1091,x1093),f263(x1092,x1093)) % 154.70/154.57 [110]~E(x1101,x1102)+E(f263(x1103,x1101),f263(x1103,x1102)) % 154.70/154.57 [111]~E(x1111,x1112)+E(f33(x1111,x1113),f33(x1112,x1113)) % 154.70/154.57 [112]~E(x1121,x1122)+E(f33(x1123,x1121),f33(x1123,x1122)) % 154.70/154.57 [113]~E(x1131,x1132)+E(f286(x1131),f286(x1132)) % 154.70/154.57 [114]~E(x1141,x1142)+E(f170(x1141),f170(x1142)) % 154.70/154.57 [115]~E(x1151,x1152)+E(f134(x1151),f134(x1152)) % 154.70/154.57 [116]~E(x1161,x1162)+E(f396(x1161,x1163,x1164,x1165),f396(x1162,x1163,x1164,x1165)) % 154.70/154.57 [117]~E(x1171,x1172)+E(f396(x1173,x1171,x1174,x1175),f396(x1173,x1172,x1174,x1175)) % 154.70/154.57 [118]~E(x1181,x1182)+E(f396(x1183,x1184,x1181,x1185),f396(x1183,x1184,x1182,x1185)) % 154.70/154.57 [119]~E(x1191,x1192)+E(f396(x1193,x1194,x1195,x1191),f396(x1193,x1194,x1195,x1192)) % 154.70/154.57 [120]~E(x1201,x1202)+E(f9(x1201,x1203),f9(x1202,x1203)) % 154.70/154.57 [121]~E(x1211,x1212)+E(f9(x1213,x1211),f9(x1213,x1212)) % 154.70/154.57 [122]~E(x1221,x1222)+E(f37(x1221),f37(x1222)) % 154.70/154.57 [123]~E(x1231,x1232)+E(f125(x1231),f125(x1232)) % 154.70/154.57 [124]~E(x1241,x1242)+E(f14(x1241,x1243),f14(x1242,x1243)) % 154.70/154.57 [125]~E(x1251,x1252)+E(f14(x1253,x1251),f14(x1253,x1252)) % 154.70/154.57 [126]~E(x1261,x1262)+E(f15(x1261,x1263),f15(x1262,x1263)) % 154.70/154.57 [127]~E(x1271,x1272)+E(f15(x1273,x1271),f15(x1273,x1272)) % 154.70/154.57 [128]~E(x1281,x1282)+E(f397(x1281,x1283,x1284,x1285),f397(x1282,x1283,x1284,x1285)) % 154.70/154.57 [129]~E(x1291,x1292)+E(f397(x1293,x1291,x1294,x1295),f397(x1293,x1292,x1294,x1295)) % 154.70/154.57 [130]~E(x1301,x1302)+E(f397(x1303,x1304,x1301,x1305),f397(x1303,x1304,x1302,x1305)) % 154.70/154.57 [131]~E(x1311,x1312)+E(f397(x1313,x1314,x1315,x1311),f397(x1313,x1314,x1315,x1312)) % 154.70/154.57 [132]~E(x1321,x1322)+E(f787(x1321,x1323,x1324,x1325,x1326),f787(x1322,x1323,x1324,x1325,x1326)) % 154.70/154.57 [133]~E(x1331,x1332)+E(f787(x1333,x1331,x1334,x1335,x1336),f787(x1333,x1332,x1334,x1335,x1336)) % 154.70/154.57 [134]~E(x1341,x1342)+E(f787(x1343,x1344,x1341,x1345,x1346),f787(x1343,x1344,x1342,x1345,x1346)) % 154.70/154.57 [135]~E(x1351,x1352)+E(f787(x1353,x1354,x1355,x1351,x1356),f787(x1353,x1354,x1355,x1352,x1356)) % 154.70/154.57 [136]~E(x1361,x1362)+E(f787(x1363,x1364,x1365,x1366,x1361),f787(x1363,x1364,x1365,x1366,x1362)) % 154.70/154.57 [137]~E(x1371,x1372)+E(f151(x1371,x1373),f151(x1372,x1373)) % 154.70/154.57 [138]~E(x1381,x1382)+E(f151(x1383,x1381),f151(x1383,x1382)) % 154.70/154.57 [139]~E(x1391,x1392)+E(f41(x1391,x1393),f41(x1392,x1393)) % 154.70/154.57 [140]~E(x1401,x1402)+E(f41(x1403,x1401),f41(x1403,x1402)) % 154.70/154.57 [141]~E(x1411,x1412)+E(f149(x1411,x1413),f149(x1412,x1413)) % 154.70/154.57 [142]~E(x1421,x1422)+E(f149(x1423,x1421),f149(x1423,x1422)) % 154.70/154.57 [143]~E(x1431,x1432)+E(f307(x1431,x1433,x1434),f307(x1432,x1433,x1434)) % 154.70/154.57 [144]~E(x1441,x1442)+E(f307(x1443,x1441,x1444),f307(x1443,x1442,x1444)) % 154.70/154.57 [145]~E(x1451,x1452)+E(f307(x1453,x1454,x1451),f307(x1453,x1454,x1452)) % 154.70/154.57 [146]~E(x1461,x1462)+E(f557(x1461,x1463,x1464),f557(x1462,x1463,x1464)) % 154.70/154.57 [147]~E(x1471,x1472)+E(f557(x1473,x1471,x1474),f557(x1473,x1472,x1474)) % 154.70/154.57 [148]~E(x1481,x1482)+E(f557(x1483,x1484,x1481),f557(x1483,x1484,x1482)) % 154.70/154.57 [149]~E(x1491,x1492)+E(f5(x1491),f5(x1492)) % 154.70/154.57 [150]~E(x1501,x1502)+E(f566(x1501,x1503,x1504),f566(x1502,x1503,x1504)) % 154.70/154.57 [151]~E(x1511,x1512)+E(f566(x1513,x1511,x1514),f566(x1513,x1512,x1514)) % 154.70/154.57 [152]~E(x1521,x1522)+E(f566(x1523,x1524,x1521),f566(x1523,x1524,x1522)) % 154.70/154.57 [153]~E(x1531,x1532)+E(f55(x1531),f55(x1532)) % 154.70/154.57 [154]~E(x1541,x1542)+E(f109(x1541),f109(x1542)) % 154.70/154.57 [155]~E(x1551,x1552)+E(f111(x1551),f111(x1552)) % 154.70/154.57 [156]~E(x1561,x1562)+E(f329(x1561),f329(x1562)) % 154.70/154.57 [157]~E(x1571,x1572)+E(f218(x1571,x1573,x1574,x1575,x1576,x1577,x1578),f218(x1572,x1573,x1574,x1575,x1576,x1577,x1578)) % 154.70/154.57 [158]~E(x1581,x1582)+E(f218(x1583,x1581,x1584,x1585,x1586,x1587,x1588),f218(x1583,x1582,x1584,x1585,x1586,x1587,x1588)) % 154.70/154.57 [159]~E(x1591,x1592)+E(f218(x1593,x1594,x1591,x1595,x1596,x1597,x1598),f218(x1593,x1594,x1592,x1595,x1596,x1597,x1598)) % 154.70/154.57 [160]~E(x1601,x1602)+E(f218(x1603,x1604,x1605,x1601,x1606,x1607,x1608),f218(x1603,x1604,x1605,x1602,x1606,x1607,x1608)) % 154.70/154.57 [161]~E(x1611,x1612)+E(f218(x1613,x1614,x1615,x1616,x1611,x1617,x1618),f218(x1613,x1614,x1615,x1616,x1612,x1617,x1618)) % 154.70/154.57 [162]~E(x1621,x1622)+E(f218(x1623,x1624,x1625,x1626,x1627,x1621,x1628),f218(x1623,x1624,x1625,x1626,x1627,x1622,x1628)) % 154.70/154.57 [163]~E(x1631,x1632)+E(f218(x1633,x1634,x1635,x1636,x1637,x1638,x1631),f218(x1633,x1634,x1635,x1636,x1637,x1638,x1632)) % 154.70/154.57 [164]~E(x1641,x1642)+E(f44(x1641,x1643,x1644),f44(x1642,x1643,x1644)) % 154.70/154.57 [165]~E(x1651,x1652)+E(f44(x1653,x1651,x1654),f44(x1653,x1652,x1654)) % 154.70/154.57 [166]~E(x1661,x1662)+E(f44(x1663,x1664,x1661),f44(x1663,x1664,x1662)) % 154.70/154.57 [167]~E(x1671,x1672)+E(f156(x1671,x1673),f156(x1672,x1673)) % 154.70/154.57 [168]~E(x1681,x1682)+E(f156(x1683,x1681),f156(x1683,x1682)) % 154.70/154.57 [169]~E(x1691,x1692)+E(f139(x1691,x1693,x1694,x1695),f139(x1692,x1693,x1694,x1695)) % 154.70/154.57 [170]~E(x1701,x1702)+E(f139(x1703,x1701,x1704,x1705),f139(x1703,x1702,x1704,x1705)) % 154.70/154.57 [171]~E(x1711,x1712)+E(f139(x1713,x1714,x1711,x1715),f139(x1713,x1714,x1712,x1715)) % 154.70/154.57 [172]~E(x1721,x1722)+E(f139(x1723,x1724,x1725,x1721),f139(x1723,x1724,x1725,x1722)) % 154.70/154.57 [173]~E(x1731,x1732)+E(f42(x1731,x1733),f42(x1732,x1733)) % 154.70/154.57 [174]~E(x1741,x1742)+E(f42(x1743,x1741),f42(x1743,x1742)) % 154.70/154.57 [175]~E(x1751,x1752)+E(f175(x1751,x1753,x1754),f175(x1752,x1753,x1754)) % 154.70/154.57 [176]~E(x1761,x1762)+E(f175(x1763,x1761,x1764),f175(x1763,x1762,x1764)) % 154.70/154.57 [177]~E(x1771,x1772)+E(f175(x1773,x1774,x1771),f175(x1773,x1774,x1772)) % 154.70/154.57 [178]~E(x1781,x1782)+E(f248(x1781),f248(x1782)) % 154.70/154.57 [179]~E(x1791,x1792)+E(f166(x1791),f166(x1792)) % 154.70/154.57 [180]~E(x1801,x1802)+E(f691(x1801),f691(x1802)) % 154.70/154.57 [181]~E(x1811,x1812)+E(f262(x1811,x1813),f262(x1812,x1813)) % 154.70/154.57 [182]~E(x1821,x1822)+E(f262(x1823,x1821),f262(x1823,x1822)) % 154.70/154.57 [183]~E(x1831,x1832)+E(f162(x1831),f162(x1832)) % 154.70/154.57 [184]~E(x1841,x1842)+E(f64(x1841,x1843,x1844),f64(x1842,x1843,x1844)) % 154.70/154.57 [185]~E(x1851,x1852)+E(f64(x1853,x1851,x1854),f64(x1853,x1852,x1854)) % 154.70/154.57 [186]~E(x1861,x1862)+E(f64(x1863,x1864,x1861),f64(x1863,x1864,x1862)) % 154.70/154.57 [187]~E(x1871,x1872)+E(f189(x1871,x1873,x1874,x1875),f189(x1872,x1873,x1874,x1875)) % 154.70/154.57 [188]~E(x1881,x1882)+E(f189(x1883,x1881,x1884,x1885),f189(x1883,x1882,x1884,x1885)) % 154.70/154.57 [189]~E(x1891,x1892)+E(f189(x1893,x1894,x1891,x1895),f189(x1893,x1894,x1892,x1895)) % 154.70/154.57 [190]~E(x1901,x1902)+E(f189(x1903,x1904,x1905,x1901),f189(x1903,x1904,x1905,x1902)) % 154.70/154.57 [191]~E(x1911,x1912)+E(f517(x1911,x1913,x1914,x1915),f517(x1912,x1913,x1914,x1915)) % 154.70/154.57 [192]~E(x1921,x1922)+E(f517(x1923,x1921,x1924,x1925),f517(x1923,x1922,x1924,x1925)) % 154.70/154.57 [193]~E(x1931,x1932)+E(f517(x1933,x1934,x1931,x1935),f517(x1933,x1934,x1932,x1935)) % 154.70/154.57 [194]~E(x1941,x1942)+E(f517(x1943,x1944,x1945,x1941),f517(x1943,x1944,x1945,x1942)) % 154.70/154.57 [195]~E(x1951,x1952)+E(f253(x1951),f253(x1952)) % 154.70/154.57 [196]~E(x1961,x1962)+E(f6(x1961,x1963),f6(x1962,x1963)) % 154.70/154.57 [197]~E(x1971,x1972)+E(f6(x1973,x1971),f6(x1973,x1972)) % 154.70/154.57 [198]~E(x1981,x1982)+E(f239(x1981),f239(x1982)) % 154.70/154.57 [199]~E(x1991,x1992)+E(f265(x1991,x1993),f265(x1992,x1993)) % 154.70/154.57 [200]~E(x2001,x2002)+E(f265(x2003,x2001),f265(x2003,x2002)) % 154.70/154.57 [201]~E(x2011,x2012)+E(f415(x2011,x2013,x2014,x2015),f415(x2012,x2013,x2014,x2015)) % 154.70/154.57 [202]~E(x2021,x2022)+E(f415(x2023,x2021,x2024,x2025),f415(x2023,x2022,x2024,x2025)) % 154.70/154.57 [203]~E(x2031,x2032)+E(f415(x2033,x2034,x2031,x2035),f415(x2033,x2034,x2032,x2035)) % 154.70/154.57 [204]~E(x2041,x2042)+E(f415(x2043,x2044,x2045,x2041),f415(x2043,x2044,x2045,x2042)) % 154.70/154.57 [205]~E(x2051,x2052)+E(f12(x2051,x2053,x2054),f12(x2052,x2053,x2054)) % 154.70/154.57 [206]~E(x2061,x2062)+E(f12(x2063,x2061,x2064),f12(x2063,x2062,x2064)) % 154.70/154.57 [207]~E(x2071,x2072)+E(f12(x2073,x2074,x2071),f12(x2073,x2074,x2072)) % 154.70/154.57 [208]~E(x2081,x2082)+E(f39(x2081,x2083),f39(x2082,x2083)) % 154.70/154.57 [209]~E(x2091,x2092)+E(f39(x2093,x2091),f39(x2093,x2092)) % 154.70/154.57 [210]~E(x2101,x2102)+E(f402(x2101,x2103,x2104,x2105),f402(x2102,x2103,x2104,x2105)) % 154.70/154.57 [211]~E(x2111,x2112)+E(f402(x2113,x2111,x2114,x2115),f402(x2113,x2112,x2114,x2115)) % 154.70/154.57 [212]~E(x2121,x2122)+E(f402(x2123,x2124,x2121,x2125),f402(x2123,x2124,x2122,x2125)) % 154.70/154.57 [213]~E(x2131,x2132)+E(f402(x2133,x2134,x2135,x2131),f402(x2133,x2134,x2135,x2132)) % 154.70/154.57 [214]~E(x2141,x2142)+E(f298(x2141,x2143),f298(x2142,x2143)) % 154.70/154.57 [215]~E(x2151,x2152)+E(f298(x2153,x2151),f298(x2153,x2152)) % 154.70/154.57 [216]~E(x2161,x2162)+E(f98(x2161,x2163,x2164,x2165),f98(x2162,x2163,x2164,x2165)) % 154.70/154.57 [217]~E(x2171,x2172)+E(f98(x2173,x2171,x2174,x2175),f98(x2173,x2172,x2174,x2175)) % 154.70/154.57 [218]~E(x2181,x2182)+E(f98(x2183,x2184,x2181,x2185),f98(x2183,x2184,x2182,x2185)) % 154.70/154.57 [219]~E(x2191,x2192)+E(f98(x2193,x2194,x2195,x2191),f98(x2193,x2194,x2195,x2192)) % 154.70/154.57 [220]~E(x2201,x2202)+E(f144(x2201,x2203),f144(x2202,x2203)) % 154.70/154.57 [221]~E(x2211,x2212)+E(f144(x2213,x2211),f144(x2213,x2212)) % 154.70/154.57 [222]~E(x2221,x2222)+E(f100(x2221),f100(x2222)) % 154.70/154.57 [223]~E(x2231,x2232)+E(f285(x2231,x2233,x2234),f285(x2232,x2233,x2234)) % 154.70/154.57 [224]~E(x2241,x2242)+E(f285(x2243,x2241,x2244),f285(x2243,x2242,x2244)) % 154.70/154.57 [225]~E(x2251,x2252)+E(f285(x2253,x2254,x2251),f285(x2253,x2254,x2252)) % 154.70/154.57 [226]~E(x2261,x2262)+E(f165(x2261),f165(x2262)) % 154.70/154.57 [227]~E(x2271,x2272)+E(f403(x2271,x2273,x2274,x2275),f403(x2272,x2273,x2274,x2275)) % 154.70/154.57 [228]~E(x2281,x2282)+E(f403(x2283,x2281,x2284,x2285),f403(x2283,x2282,x2284,x2285)) % 154.70/154.57 [229]~E(x2291,x2292)+E(f403(x2293,x2294,x2291,x2295),f403(x2293,x2294,x2292,x2295)) % 154.70/154.57 [230]~E(x2301,x2302)+E(f403(x2303,x2304,x2305,x2301),f403(x2303,x2304,x2305,x2302)) % 154.70/154.57 [231]~E(x2311,x2312)+E(f267(x2311,x2313,x2314),f267(x2312,x2313,x2314)) % 154.70/154.57 [232]~E(x2321,x2322)+E(f267(x2323,x2321,x2324),f267(x2323,x2322,x2324)) % 154.70/154.57 [233]~E(x2331,x2332)+E(f267(x2333,x2334,x2331),f267(x2333,x2334,x2332)) % 154.70/154.57 [234]~E(x2341,x2342)+E(f256(x2341,x2343),f256(x2342,x2343)) % 154.70/154.57 [235]~E(x2351,x2352)+E(f256(x2353,x2351),f256(x2353,x2352)) % 154.70/154.57 [236]~E(x2361,x2362)+E(f260(x2361,x2363),f260(x2362,x2363)) % 154.70/154.57 [237]~E(x2371,x2372)+E(f260(x2373,x2371),f260(x2373,x2372)) % 154.70/154.57 [238]~E(x2381,x2382)+E(f133(x2381,x2383),f133(x2382,x2383)) % 154.70/154.57 [239]~E(x2391,x2392)+E(f133(x2393,x2391),f133(x2393,x2392)) % 154.70/154.57 [240]~E(x2401,x2402)+E(f317(x2401,x2403),f317(x2402,x2403)) % 154.70/154.57 [241]~E(x2411,x2412)+E(f317(x2413,x2411),f317(x2413,x2412)) % 154.70/154.57 [242]~E(x2421,x2422)+E(f135(x2421),f135(x2422)) % 154.70/154.57 [243]~E(x2431,x2432)+E(f173(x2431),f173(x2432)) % 154.70/154.57 [244]~E(x2441,x2442)+E(f813(x2441,x2443,x2444),f813(x2442,x2443,x2444)) % 154.70/154.57 [245]~E(x2451,x2452)+E(f813(x2453,x2451,x2454),f813(x2453,x2452,x2454)) % 154.70/154.57 [246]~E(x2461,x2462)+E(f813(x2463,x2464,x2461),f813(x2463,x2464,x2462)) % 154.70/154.57 [247]~E(x2471,x2472)+E(f180(x2471,x2473),f180(x2472,x2473)) % 154.70/154.57 [248]~E(x2481,x2482)+E(f180(x2483,x2481),f180(x2483,x2482)) % 154.70/154.57 [249]~E(x2491,x2492)+E(f862(x2491,x2493,x2494),f862(x2492,x2493,x2494)) % 154.70/154.57 [250]~E(x2501,x2502)+E(f862(x2503,x2501,x2504),f862(x2503,x2502,x2504)) % 154.70/154.57 [251]~E(x2511,x2512)+E(f862(x2513,x2514,x2511),f862(x2513,x2514,x2512)) % 154.70/154.57 [252]~E(x2521,x2522)+E(f264(x2521,x2523,x2524,x2525,x2526),f264(x2522,x2523,x2524,x2525,x2526)) % 154.70/154.57 [253]~E(x2531,x2532)+E(f264(x2533,x2531,x2534,x2535,x2536),f264(x2533,x2532,x2534,x2535,x2536)) % 154.70/154.57 [254]~E(x2541,x2542)+E(f264(x2543,x2544,x2541,x2545,x2546),f264(x2543,x2544,x2542,x2545,x2546)) % 154.70/154.57 [255]~E(x2551,x2552)+E(f264(x2553,x2554,x2555,x2551,x2556),f264(x2553,x2554,x2555,x2552,x2556)) % 154.70/154.57 [256]~E(x2561,x2562)+E(f264(x2563,x2564,x2565,x2566,x2561),f264(x2563,x2564,x2565,x2566,x2562)) % 154.70/154.57 [257]~E(x2571,x2572)+E(f421(x2571,x2573),f421(x2572,x2573)) % 154.70/154.57 [258]~E(x2581,x2582)+E(f421(x2583,x2581),f421(x2583,x2582)) % 154.70/154.57 [259]~E(x2591,x2592)+E(f282(x2591,x2593,x2594),f282(x2592,x2593,x2594)) % 154.70/154.57 [260]~E(x2601,x2602)+E(f282(x2603,x2601,x2604),f282(x2603,x2602,x2604)) % 154.70/154.57 [261]~E(x2611,x2612)+E(f282(x2613,x2614,x2611),f282(x2613,x2614,x2612)) % 154.70/154.57 [262]~E(x2621,x2622)+E(f398(x2621,x2623,x2624,x2625),f398(x2622,x2623,x2624,x2625)) % 154.70/154.57 [263]~E(x2631,x2632)+E(f398(x2633,x2631,x2634,x2635),f398(x2633,x2632,x2634,x2635)) % 154.70/154.57 [264]~E(x2641,x2642)+E(f398(x2643,x2644,x2641,x2645),f398(x2643,x2644,x2642,x2645)) % 154.70/154.57 [265]~E(x2651,x2652)+E(f398(x2653,x2654,x2655,x2651),f398(x2653,x2654,x2655,x2652)) % 154.70/154.57 [266]~E(x2661,x2662)+E(f268(x2661,x2663,x2664,x2665,x2666,x2667),f268(x2662,x2663,x2664,x2665,x2666,x2667)) % 154.70/154.57 [267]~E(x2671,x2672)+E(f268(x2673,x2671,x2674,x2675,x2676,x2677),f268(x2673,x2672,x2674,x2675,x2676,x2677)) % 154.70/154.57 [268]~E(x2681,x2682)+E(f268(x2683,x2684,x2681,x2685,x2686,x2687),f268(x2683,x2684,x2682,x2685,x2686,x2687)) % 154.70/154.57 [269]~E(x2691,x2692)+E(f268(x2693,x2694,x2695,x2691,x2696,x2697),f268(x2693,x2694,x2695,x2692,x2696,x2697)) % 154.70/154.57 [270]~E(x2701,x2702)+E(f268(x2703,x2704,x2705,x2706,x2701,x2707),f268(x2703,x2704,x2705,x2706,x2702,x2707)) % 154.70/154.57 [271]~E(x2711,x2712)+E(f268(x2713,x2714,x2715,x2716,x2717,x2711),f268(x2713,x2714,x2715,x2716,x2717,x2712)) % 154.70/154.57 [272]~E(x2721,x2722)+E(f754(x2721,x2723,x2724,x2725,x2726),f754(x2722,x2723,x2724,x2725,x2726)) % 154.70/154.57 [273]~E(x2731,x2732)+E(f754(x2733,x2731,x2734,x2735,x2736),f754(x2733,x2732,x2734,x2735,x2736)) % 154.70/154.57 [274]~E(x2741,x2742)+E(f754(x2743,x2744,x2741,x2745,x2746),f754(x2743,x2744,x2742,x2745,x2746)) % 154.70/154.57 [275]~E(x2751,x2752)+E(f754(x2753,x2754,x2755,x2751,x2756),f754(x2753,x2754,x2755,x2752,x2756)) % 154.70/154.57 [276]~E(x2761,x2762)+E(f754(x2763,x2764,x2765,x2766,x2761),f754(x2763,x2764,x2765,x2766,x2762)) % 154.70/154.57 [277]~E(x2771,x2772)+E(f299(x2771,x2773,x2774),f299(x2772,x2773,x2774)) % 154.70/154.57 [278]~E(x2781,x2782)+E(f299(x2783,x2781,x2784),f299(x2783,x2782,x2784)) % 154.70/154.57 [279]~E(x2791,x2792)+E(f299(x2793,x2794,x2791),f299(x2793,x2794,x2792)) % 154.70/154.57 [280]~E(x2801,x2802)+E(f195(x2801),f195(x2802)) % 154.70/154.57 [281]~E(x2811,x2812)+E(f219(x2811),f219(x2812)) % 154.70/154.57 [282]~E(x2821,x2822)+E(f119(x2821),f119(x2822)) % 154.70/154.57 [283]~E(x2831,x2832)+E(f87(x2831),f87(x2832)) % 154.70/154.57 [284]~E(x2841,x2842)+E(f668(x2841,x2843,x2844),f668(x2842,x2843,x2844)) % 154.70/154.57 [285]~E(x2851,x2852)+E(f668(x2853,x2851,x2854),f668(x2853,x2852,x2854)) % 154.70/154.57 [286]~E(x2861,x2862)+E(f668(x2863,x2864,x2861),f668(x2863,x2864,x2862)) % 154.70/154.57 [287]~E(x2871,x2872)+E(f738(x2871,x2873,x2874,x2875,x2876),f738(x2872,x2873,x2874,x2875,x2876)) % 154.70/154.57 [288]~E(x2881,x2882)+E(f738(x2883,x2881,x2884,x2885,x2886),f738(x2883,x2882,x2884,x2885,x2886)) % 154.70/154.57 [289]~E(x2891,x2892)+E(f738(x2893,x2894,x2891,x2895,x2896),f738(x2893,x2894,x2892,x2895,x2896)) % 154.70/154.57 [290]~E(x2901,x2902)+E(f738(x2903,x2904,x2905,x2901,x2906),f738(x2903,x2904,x2905,x2902,x2906)) % 154.70/154.57 [291]~E(x2911,x2912)+E(f738(x2913,x2914,x2915,x2916,x2911),f738(x2913,x2914,x2915,x2916,x2912)) % 154.70/154.57 [292]~E(x2921,x2922)+E(f822(x2921,x2923,x2924),f822(x2922,x2923,x2924)) % 154.70/154.57 [293]~E(x2931,x2932)+E(f822(x2933,x2931,x2934),f822(x2933,x2932,x2934)) % 154.70/154.57 [294]~E(x2941,x2942)+E(f822(x2943,x2944,x2941),f822(x2943,x2944,x2942)) % 154.70/154.57 [295]~E(x2951,x2952)+E(f38(x2951),f38(x2952)) % 154.70/154.57 [296]~E(x2961,x2962)+E(f82(x2961,x2963),f82(x2962,x2963)) % 154.70/154.57 [297]~E(x2971,x2972)+E(f82(x2973,x2971),f82(x2973,x2972)) % 154.70/154.57 [298]~E(x2981,x2982)+E(f458(x2981,x2983,x2984),f458(x2982,x2983,x2984)) % 154.70/154.57 [299]~E(x2991,x2992)+E(f458(x2993,x2991,x2994),f458(x2993,x2992,x2994)) % 154.70/154.57 [300]~E(x3001,x3002)+E(f458(x3003,x3004,x3001),f458(x3003,x3004,x3002)) % 154.70/154.57 [301]~E(x3011,x3012)+E(f168(x3011,x3013,x3014),f168(x3012,x3013,x3014)) % 154.70/154.57 [302]~E(x3021,x3022)+E(f168(x3023,x3021,x3024),f168(x3023,x3022,x3024)) % 154.70/154.57 [303]~E(x3031,x3032)+E(f168(x3033,x3034,x3031),f168(x3033,x3034,x3032)) % 154.70/154.57 [304]~E(x3041,x3042)+E(f48(x3041,x3043),f48(x3042,x3043)) % 154.70/154.57 [305]~E(x3051,x3052)+E(f48(x3053,x3051),f48(x3053,x3052)) % 154.70/154.57 [306]~E(x3061,x3062)+E(f235(x3061),f235(x3062)) % 154.70/154.57 [307]~E(x3071,x3072)+E(f43(x3071),f43(x3072)) % 154.70/154.57 [308]~E(x3081,x3082)+E(f146(x3081,x3083,x3084,x3085,x3086),f146(x3082,x3083,x3084,x3085,x3086)) % 154.70/154.57 [309]~E(x3091,x3092)+E(f146(x3093,x3091,x3094,x3095,x3096),f146(x3093,x3092,x3094,x3095,x3096)) % 154.70/154.57 [310]~E(x3101,x3102)+E(f146(x3103,x3104,x3101,x3105,x3106),f146(x3103,x3104,x3102,x3105,x3106)) % 154.70/154.57 [311]~E(x3111,x3112)+E(f146(x3113,x3114,x3115,x3111,x3116),f146(x3113,x3114,x3115,x3112,x3116)) % 154.70/154.57 [312]~E(x3121,x3122)+E(f146(x3123,x3124,x3125,x3126,x3121),f146(x3123,x3124,x3125,x3126,x3122)) % 154.70/154.57 [313]~E(x3131,x3132)+E(f32(x3131,x3133),f32(x3132,x3133)) % 154.70/154.57 [314]~E(x3141,x3142)+E(f32(x3143,x3141),f32(x3143,x3142)) % 154.70/154.57 [315]~E(x3151,x3152)+E(f169(x3151),f169(x3152)) % 154.70/154.57 [316]~E(x3161,x3162)+E(f380(x3161,x3163,x3164,x3165),f380(x3162,x3163,x3164,x3165)) % 154.70/154.57 [317]~E(x3171,x3172)+E(f380(x3173,x3171,x3174,x3175),f380(x3173,x3172,x3174,x3175)) % 154.70/154.57 [318]~E(x3181,x3182)+E(f380(x3183,x3184,x3181,x3185),f380(x3183,x3184,x3182,x3185)) % 154.70/154.57 [319]~E(x3191,x3192)+E(f380(x3193,x3194,x3195,x3191),f380(x3193,x3194,x3195,x3192)) % 154.70/154.57 [320]~E(x3201,x3202)+E(f10(x3201,x3203),f10(x3202,x3203)) % 154.70/154.57 [321]~E(x3211,x3212)+E(f10(x3213,x3211),f10(x3213,x3212)) % 154.70/154.57 [322]~E(x3221,x3222)+E(f280(x3221,x3223,x3224,x3225),f280(x3222,x3223,x3224,x3225)) % 154.70/154.57 [323]~E(x3231,x3232)+E(f280(x3233,x3231,x3234,x3235),f280(x3233,x3232,x3234,x3235)) % 154.70/154.57 [324]~E(x3241,x3242)+E(f280(x3243,x3244,x3241,x3245),f280(x3243,x3244,x3242,x3245)) % 154.70/154.57 [325]~E(x3251,x3252)+E(f280(x3253,x3254,x3255,x3251),f280(x3253,x3254,x3255,x3252)) % 154.70/154.57 [326]~E(x3261,x3262)+E(f49(x3261,x3263),f49(x3262,x3263)) % 154.70/154.57 [327]~E(x3271,x3272)+E(f49(x3273,x3271),f49(x3273,x3272)) % 154.70/154.57 [328]~E(x3281,x3282)+E(f138(x3281),f138(x3282)) % 154.70/154.57 [329]~E(x3291,x3292)+E(f18(x3291,x3293,x3294),f18(x3292,x3293,x3294)) % 154.70/154.57 [330]~E(x3301,x3302)+E(f18(x3303,x3301,x3304),f18(x3303,x3302,x3304)) % 154.70/154.57 [331]~E(x3311,x3312)+E(f18(x3313,x3314,x3311),f18(x3313,x3314,x3312)) % 154.70/154.57 [332]~E(x3321,x3322)+E(f524(x3321,x3323,x3324),f524(x3322,x3323,x3324)) % 154.70/154.57 [333]~E(x3331,x3332)+E(f524(x3333,x3331,x3334),f524(x3333,x3332,x3334)) % 154.70/154.57 [334]~E(x3341,x3342)+E(f524(x3343,x3344,x3341),f524(x3343,x3344,x3342)) % 154.70/154.57 [335]~E(x3351,x3352)+E(f823(x3351,x3353,x3354),f823(x3352,x3353,x3354)) % 154.70/154.57 [336]~E(x3361,x3362)+E(f823(x3363,x3361,x3364),f823(x3363,x3362,x3364)) % 154.70/154.57 [337]~E(x3371,x3372)+E(f823(x3373,x3374,x3371),f823(x3373,x3374,x3372)) % 154.70/154.57 [338]~E(x3381,x3382)+E(f450(x3381,x3383,x3384),f450(x3382,x3383,x3384)) % 154.70/154.57 [339]~E(x3391,x3392)+E(f450(x3393,x3391,x3394),f450(x3393,x3392,x3394)) % 154.70/154.57 [340]~E(x3401,x3402)+E(f450(x3403,x3404,x3401),f450(x3403,x3404,x3402)) % 154.70/154.57 [341]~E(x3411,x3412)+E(f11(x3411,x3413),f11(x3412,x3413)) % 154.70/154.57 [342]~E(x3421,x3422)+E(f11(x3423,x3421),f11(x3423,x3422)) % 154.70/154.57 [343]~E(x3431,x3432)+E(f624(x3431,x3433,x3434,x3435,x3436,x3437,x3438,x3439),f624(x3432,x3433,x3434,x3435,x3436,x3437,x3438,x3439)) % 154.70/154.57 [344]~E(x3441,x3442)+E(f624(x3443,x3441,x3444,x3445,x3446,x3447,x3448,x3449),f624(x3443,x3442,x3444,x3445,x3446,x3447,x3448,x3449)) % 154.70/154.57 [345]~E(x3451,x3452)+E(f624(x3453,x3454,x3451,x3455,x3456,x3457,x3458,x3459),f624(x3453,x3454,x3452,x3455,x3456,x3457,x3458,x3459)) % 154.70/154.57 [346]~E(x3461,x3462)+E(f624(x3463,x3464,x3465,x3461,x3466,x3467,x3468,x3469),f624(x3463,x3464,x3465,x3462,x3466,x3467,x3468,x3469)) % 154.70/154.57 [347]~E(x3471,x3472)+E(f624(x3473,x3474,x3475,x3476,x3471,x3477,x3478,x3479),f624(x3473,x3474,x3475,x3476,x3472,x3477,x3478,x3479)) % 154.70/154.57 [348]~E(x3481,x3482)+E(f624(x3483,x3484,x3485,x3486,x3487,x3481,x3488,x3489),f624(x3483,x3484,x3485,x3486,x3487,x3482,x3488,x3489)) % 154.70/154.57 [349]~E(x3491,x3492)+E(f624(x3493,x3494,x3495,x3496,x3497,x3498,x3491,x3499),f624(x3493,x3494,x3495,x3496,x3497,x3498,x3492,x3499)) % 154.70/154.57 [350]~E(x3501,x3502)+E(f624(x3503,x3504,x3505,x3506,x3507,x3508,x3509,x3501),f624(x3503,x3504,x3505,x3506,x3507,x3508,x3509,x3502)) % 154.70/154.57 [351]~E(x3511,x3512)+E(f176(x3511,x3513),f176(x3512,x3513)) % 154.70/154.57 [352]~E(x3521,x3522)+E(f176(x3523,x3521),f176(x3523,x3522)) % 154.70/154.57 [353]~E(x3531,x3532)+E(f95(x3531,x3533,x3534),f95(x3532,x3533,x3534)) % 154.70/154.57 [354]~E(x3541,x3542)+E(f95(x3543,x3541,x3544),f95(x3543,x3542,x3544)) % 154.70/154.57 [355]~E(x3551,x3552)+E(f95(x3553,x3554,x3551),f95(x3553,x3554,x3552)) % 154.70/154.57 [356]~E(x3561,x3562)+E(f315(x3561,x3563,x3564,x3565),f315(x3562,x3563,x3564,x3565)) % 154.70/154.57 [357]~E(x3571,x3572)+E(f315(x3573,x3571,x3574,x3575),f315(x3573,x3572,x3574,x3575)) % 154.70/154.57 [358]~E(x3581,x3582)+E(f315(x3583,x3584,x3581,x3585),f315(x3583,x3584,x3582,x3585)) % 154.70/154.57 [359]~E(x3591,x3592)+E(f315(x3593,x3594,x3595,x3591),f315(x3593,x3594,x3595,x3592)) % 154.70/154.57 [360]~E(x3601,x3602)+E(f319(x3601,x3603),f319(x3602,x3603)) % 154.70/154.57 [361]~E(x3611,x3612)+E(f319(x3613,x3611),f319(x3613,x3612)) % 154.70/154.57 [362]~E(x3621,x3622)+E(f348(x3621,x3623,x3624,x3625),f348(x3622,x3623,x3624,x3625)) % 154.70/154.57 [363]~E(x3631,x3632)+E(f348(x3633,x3631,x3634,x3635),f348(x3633,x3632,x3634,x3635)) % 154.70/154.57 [364]~E(x3641,x3642)+E(f348(x3643,x3644,x3641,x3645),f348(x3643,x3644,x3642,x3645)) % 154.70/154.57 [365]~E(x3651,x3652)+E(f348(x3653,x3654,x3655,x3651),f348(x3653,x3654,x3655,x3652)) % 154.70/154.57 [366]~E(x3661,x3662)+E(f321(x3661,x3663),f321(x3662,x3663)) % 154.70/154.57 [367]~E(x3671,x3672)+E(f321(x3673,x3671),f321(x3673,x3672)) % 154.70/154.57 [368]~E(x3681,x3682)+E(f30(x3681,x3683,x3684),f30(x3682,x3683,x3684)) % 154.70/154.57 [369]~E(x3691,x3692)+E(f30(x3693,x3691,x3694),f30(x3693,x3692,x3694)) % 154.70/154.57 [370]~E(x3701,x3702)+E(f30(x3703,x3704,x3701),f30(x3703,x3704,x3702)) % 154.70/154.57 [371]~E(x3711,x3712)+E(f563(x3711,x3713,x3714),f563(x3712,x3713,x3714)) % 154.70/154.57 [372]~E(x3721,x3722)+E(f563(x3723,x3721,x3724),f563(x3723,x3722,x3724)) % 154.70/154.57 [373]~E(x3731,x3732)+E(f563(x3733,x3734,x3731),f563(x3733,x3734,x3732)) % 154.70/154.57 [374]~E(x3741,x3742)+E(f812(x3741,x3743,x3744),f812(x3742,x3743,x3744)) % 154.70/154.57 [375]~E(x3751,x3752)+E(f812(x3753,x3751,x3754),f812(x3753,x3752,x3754)) % 154.70/154.57 [376]~E(x3761,x3762)+E(f812(x3763,x3764,x3761),f812(x3763,x3764,x3762)) % 154.70/154.57 [377]~E(x3771,x3772)+E(f120(x3771,x3773,x3774),f120(x3772,x3773,x3774)) % 154.70/154.57 [378]~E(x3781,x3782)+E(f120(x3783,x3781,x3784),f120(x3783,x3782,x3784)) % 154.70/154.57 [379]~E(x3791,x3792)+E(f120(x3793,x3794,x3791),f120(x3793,x3794,x3792)) % 154.70/154.57 [380]~E(x3801,x3802)+E(f58(x3801),f58(x3802)) % 154.70/154.57 [381]~E(x3811,x3812)+E(f137(x3811,x3813,x3814),f137(x3812,x3813,x3814)) % 154.70/154.57 [382]~E(x3821,x3822)+E(f137(x3823,x3821,x3824),f137(x3823,x3822,x3824)) % 154.70/154.57 [383]~E(x3831,x3832)+E(f137(x3833,x3834,x3831),f137(x3833,x3834,x3832)) % 154.70/154.57 [384]~E(x3841,x3842)+E(f91(x3841),f91(x3842)) % 154.70/154.57 [385]~E(x3851,x3852)+E(f140(x3851,x3853),f140(x3852,x3853)) % 154.70/154.57 [386]~E(x3861,x3862)+E(f140(x3863,x3861),f140(x3863,x3862)) % 154.70/154.57 [387]~E(x3871,x3872)+E(f814(x3871,x3873,x3874),f814(x3872,x3873,x3874)) % 154.70/154.57 [388]~E(x3881,x3882)+E(f814(x3883,x3881,x3884),f814(x3883,x3882,x3884)) % 154.70/154.57 [389]~E(x3891,x3892)+E(f814(x3893,x3894,x3891),f814(x3893,x3894,x3892)) % 154.70/154.57 [390]~E(x3901,x3902)+E(f237(x3901,x3903,x3904,x3905),f237(x3902,x3903,x3904,x3905)) % 154.70/154.57 [391]~E(x3911,x3912)+E(f237(x3913,x3911,x3914,x3915),f237(x3913,x3912,x3914,x3915)) % 154.70/154.57 [392]~E(x3921,x3922)+E(f237(x3923,x3924,x3921,x3925),f237(x3923,x3924,x3922,x3925)) % 154.70/154.57 [393]~E(x3931,x3932)+E(f237(x3933,x3934,x3935,x3931),f237(x3933,x3934,x3935,x3932)) % 154.70/154.57 [394]~E(x3941,x3942)+E(f748(x3941,x3943,x3944),f748(x3942,x3943,x3944)) % 154.70/154.57 [395]~E(x3951,x3952)+E(f748(x3953,x3951,x3954),f748(x3953,x3952,x3954)) % 154.70/154.57 [396]~E(x3961,x3962)+E(f748(x3963,x3964,x3961),f748(x3963,x3964,x3962)) % 154.70/154.57 [397]~E(x3971,x3972)+E(f113(x3971),f113(x3972)) % 154.70/154.57 [398]~E(x3981,x3982)+E(f465(x3981,x3983,x3984,x3985,x3986,x3987),f465(x3982,x3983,x3984,x3985,x3986,x3987)) % 154.70/154.57 [399]~E(x3991,x3992)+E(f465(x3993,x3991,x3994,x3995,x3996,x3997),f465(x3993,x3992,x3994,x3995,x3996,x3997)) % 154.70/154.57 [400]~E(x4001,x4002)+E(f465(x4003,x4004,x4001,x4005,x4006,x4007),f465(x4003,x4004,x4002,x4005,x4006,x4007)) % 154.70/154.57 [401]~E(x4011,x4012)+E(f465(x4013,x4014,x4015,x4011,x4016,x4017),f465(x4013,x4014,x4015,x4012,x4016,x4017)) % 154.70/154.57 [402]~E(x4021,x4022)+E(f465(x4023,x4024,x4025,x4026,x4021,x4027),f465(x4023,x4024,x4025,x4026,x4022,x4027)) % 154.70/154.57 [403]~E(x4031,x4032)+E(f465(x4033,x4034,x4035,x4036,x4037,x4031),f465(x4033,x4034,x4035,x4036,x4037,x4032)) % 154.70/154.57 [404]~E(x4041,x4042)+E(f141(x4041,x4043),f141(x4042,x4043)) % 154.70/154.57 [405]~E(x4051,x4052)+E(f141(x4053,x4051),f141(x4053,x4052)) % 154.70/154.57 [406]~E(x4061,x4062)+E(f313(x4061),f313(x4062)) % 154.70/154.57 [407]~E(x4071,x4072)+E(f157(x4071,x4073),f157(x4072,x4073)) % 154.70/154.57 [408]~E(x4081,x4082)+E(f157(x4083,x4081),f157(x4083,x4082)) % 154.70/154.57 [409]~E(x4091,x4092)+E(f85(x4091,x4093),f85(x4092,x4093)) % 154.70/154.57 [410]~E(x4101,x4102)+E(f85(x4103,x4101),f85(x4103,x4102)) % 154.70/154.57 [411]~E(x4111,x4112)+E(f88(x4111),f88(x4112)) % 154.70/154.57 [412]~E(x4121,x4122)+E(f90(x4121,x4123),f90(x4122,x4123)) % 154.70/154.57 [413]~E(x4131,x4132)+E(f90(x4133,x4131),f90(x4133,x4132)) % 154.70/154.57 [414]~E(x4141,x4142)+E(f177(x4141,x4143),f177(x4142,x4143)) % 154.70/154.57 [415]~E(x4151,x4152)+E(f177(x4153,x4151),f177(x4153,x4152)) % 154.70/154.57 [416]~E(x4161,x4162)+E(f150(x4161,x4163),f150(x4162,x4163)) % 154.70/154.57 [417]~E(x4171,x4172)+E(f150(x4173,x4171),f150(x4173,x4172)) % 154.70/154.57 [418]~E(x4181,x4182)+E(f52(x4181,x4183),f52(x4182,x4183)) % 154.70/154.57 [419]~E(x4191,x4192)+E(f52(x4193,x4191),f52(x4193,x4192)) % 154.70/154.57 [420]~E(x4201,x4202)+E(f670(x4201,x4203,x4204,x4205,x4206),f670(x4202,x4203,x4204,x4205,x4206)) % 154.70/154.57 [421]~E(x4211,x4212)+E(f670(x4213,x4211,x4214,x4215,x4216),f670(x4213,x4212,x4214,x4215,x4216)) % 154.70/154.57 [422]~E(x4221,x4222)+E(f670(x4223,x4224,x4221,x4225,x4226),f670(x4223,x4224,x4222,x4225,x4226)) % 154.70/154.57 [423]~E(x4231,x4232)+E(f670(x4233,x4234,x4235,x4231,x4236),f670(x4233,x4234,x4235,x4232,x4236)) % 154.70/154.57 [424]~E(x4241,x4242)+E(f670(x4243,x4244,x4245,x4246,x4241),f670(x4243,x4244,x4245,x4246,x4242)) % 154.70/154.57 [425]~E(x4251,x4252)+E(f695(x4251,x4253,x4254,x4255,x4256),f695(x4252,x4253,x4254,x4255,x4256)) % 154.70/154.57 [426]~E(x4261,x4262)+E(f695(x4263,x4261,x4264,x4265,x4266),f695(x4263,x4262,x4264,x4265,x4266)) % 154.70/154.57 [427]~E(x4271,x4272)+E(f695(x4273,x4274,x4271,x4275,x4276),f695(x4273,x4274,x4272,x4275,x4276)) % 154.70/154.57 [428]~E(x4281,x4282)+E(f695(x4283,x4284,x4285,x4281,x4286),f695(x4283,x4284,x4285,x4282,x4286)) % 154.70/154.57 [429]~E(x4291,x4292)+E(f695(x4293,x4294,x4295,x4296,x4291),f695(x4293,x4294,x4295,x4296,x4292)) % 154.70/154.57 [430]~E(x4301,x4302)+E(f484(x4301,x4303),f484(x4302,x4303)) % 154.70/154.57 [431]~E(x4311,x4312)+E(f484(x4313,x4311),f484(x4313,x4312)) % 154.70/154.57 [432]~E(x4321,x4322)+E(f820(x4321,x4323,x4324),f820(x4322,x4323,x4324)) % 154.70/154.57 [433]~E(x4331,x4332)+E(f820(x4333,x4331,x4334),f820(x4333,x4332,x4334)) % 154.70/154.57 [434]~E(x4341,x4342)+E(f820(x4343,x4344,x4341),f820(x4343,x4344,x4342)) % 154.70/154.57 [435]~E(x4351,x4352)+E(f13(x4351,x4353,x4354),f13(x4352,x4353,x4354)) % 154.70/154.57 [436]~E(x4361,x4362)+E(f13(x4363,x4361,x4364),f13(x4363,x4362,x4364)) % 154.70/154.57 [437]~E(x4371,x4372)+E(f13(x4373,x4374,x4371),f13(x4373,x4374,x4372)) % 154.70/154.57 [438]~E(x4381,x4382)+E(f618(x4381,x4383,x4384,x4385),f618(x4382,x4383,x4384,x4385)) % 154.70/154.57 [439]~E(x4391,x4392)+E(f618(x4393,x4391,x4394,x4395),f618(x4393,x4392,x4394,x4395)) % 154.70/154.57 [440]~E(x4401,x4402)+E(f618(x4403,x4404,x4401,x4405),f618(x4403,x4404,x4402,x4405)) % 154.70/154.57 [441]~E(x4411,x4412)+E(f618(x4413,x4414,x4415,x4411),f618(x4413,x4414,x4415,x4412)) % 154.70/154.57 [442]~E(x4421,x4422)+E(f725(x4421,x4423,x4424,x4425,x4426),f725(x4422,x4423,x4424,x4425,x4426)) % 154.70/154.57 [443]~E(x4431,x4432)+E(f725(x4433,x4431,x4434,x4435,x4436),f725(x4433,x4432,x4434,x4435,x4436)) % 154.70/154.57 [444]~E(x4441,x4442)+E(f725(x4443,x4444,x4441,x4445,x4446),f725(x4443,x4444,x4442,x4445,x4446)) % 154.70/154.57 [445]~E(x4451,x4452)+E(f725(x4453,x4454,x4455,x4451,x4456),f725(x4453,x4454,x4455,x4452,x4456)) % 154.70/154.57 [446]~E(x4461,x4462)+E(f725(x4463,x4464,x4465,x4466,x4461),f725(x4463,x4464,x4465,x4466,x4462)) % 154.70/154.57 [447]~E(x4471,x4472)+E(f174(x4471,x4473,x4474),f174(x4472,x4473,x4474)) % 154.70/154.57 [448]~E(x4481,x4482)+E(f174(x4483,x4481,x4484),f174(x4483,x4482,x4484)) % 154.70/154.57 [449]~E(x4491,x4492)+E(f174(x4493,x4494,x4491),f174(x4493,x4494,x4492)) % 154.70/154.57 [450]~E(x4501,x4502)+E(f86(x4501,x4503),f86(x4502,x4503)) % 154.70/154.57 [451]~E(x4511,x4512)+E(f86(x4513,x4511),f86(x4513,x4512)) % 154.70/154.57 [452]~E(x4521,x4522)+E(f305(x4521),f305(x4522)) % 154.70/154.57 [453]~E(x4531,x4532)+E(f852(x4531,x4533,x4534),f852(x4532,x4533,x4534)) % 154.70/154.57 [454]~E(x4541,x4542)+E(f852(x4543,x4541,x4544),f852(x4543,x4542,x4544)) % 154.70/154.57 [455]~E(x4551,x4552)+E(f852(x4553,x4554,x4551),f852(x4553,x4554,x4552)) % 154.70/154.57 [456]~E(x4561,x4562)+E(f167(x4561,x4563,x4564),f167(x4562,x4563,x4564)) % 154.70/154.57 [457]~E(x4571,x4572)+E(f167(x4573,x4571,x4574),f167(x4573,x4572,x4574)) % 154.70/154.57 [458]~E(x4581,x4582)+E(f167(x4583,x4584,x4581),f167(x4583,x4584,x4582)) % 154.70/154.57 [459]~E(x4591,x4592)+E(f752(x4591,x4593),f752(x4592,x4593)) % 154.70/154.57 [460]~E(x4601,x4602)+E(f752(x4603,x4601),f752(x4603,x4602)) % 154.70/154.57 [461]~E(x4611,x4612)+E(f320(x4611,x4613,x4614,x4615),f320(x4612,x4613,x4614,x4615)) % 154.70/154.57 [462]~E(x4621,x4622)+E(f320(x4623,x4621,x4624,x4625),f320(x4623,x4622,x4624,x4625)) % 154.70/154.57 [463]~E(x4631,x4632)+E(f320(x4633,x4634,x4631,x4635),f320(x4633,x4634,x4632,x4635)) % 154.70/154.57 [464]~E(x4641,x4642)+E(f320(x4643,x4644,x4645,x4641),f320(x4643,x4644,x4645,x4642)) % 154.70/154.57 [465]~E(x4651,x4652)+E(f57(x4651),f57(x4652)) % 154.70/154.57 [466]~E(x4661,x4662)+E(f154(x4661,x4663),f154(x4662,x4663)) % 154.70/154.57 [467]~E(x4671,x4672)+E(f154(x4673,x4671),f154(x4673,x4672)) % 154.70/154.57 [468]~E(x4681,x4682)+E(f182(x4681,x4683,x4684),f182(x4682,x4683,x4684)) % 154.70/154.57 [469]~E(x4691,x4692)+E(f182(x4693,x4691,x4694),f182(x4693,x4692,x4694)) % 154.70/154.57 [470]~E(x4701,x4702)+E(f182(x4703,x4704,x4701),f182(x4703,x4704,x4702)) % 154.70/154.57 [471]~E(x4711,x4712)+E(f152(x4711,x4713,x4714),f152(x4712,x4713,x4714)) % 154.70/154.57 [472]~E(x4721,x4722)+E(f152(x4723,x4721,x4724),f152(x4723,x4722,x4724)) % 154.70/154.57 [473]~E(x4731,x4732)+E(f152(x4733,x4734,x4731),f152(x4733,x4734,x4732)) % 154.70/154.57 [474]~E(x4741,x4742)+E(f805(x4741,x4743,x4744,x4745),f805(x4742,x4743,x4744,x4745)) % 154.70/154.57 [475]~E(x4751,x4752)+E(f805(x4753,x4751,x4754,x4755),f805(x4753,x4752,x4754,x4755)) % 154.70/154.57 [476]~E(x4761,x4762)+E(f805(x4763,x4764,x4761,x4765),f805(x4763,x4764,x4762,x4765)) % 154.70/154.57 [477]~E(x4771,x4772)+E(f805(x4773,x4774,x4775,x4771),f805(x4773,x4774,x4775,x4772)) % 154.70/154.57 [478]~E(x4781,x4782)+E(f145(x4781,x4783,x4784),f145(x4782,x4783,x4784)) % 154.70/154.57 [479]~E(x4791,x4792)+E(f145(x4793,x4791,x4794),f145(x4793,x4792,x4794)) % 154.70/154.57 [480]~E(x4801,x4802)+E(f145(x4803,x4804,x4801),f145(x4803,x4804,x4802)) % 154.70/154.57 [481]~E(x4811,x4812)+E(f221(x4811,x4813),f221(x4812,x4813)) % 154.70/154.57 [482]~E(x4821,x4822)+E(f221(x4823,x4821),f221(x4823,x4822)) % 154.70/154.57 [483]~E(x4831,x4832)+E(f202(x4831,x4833,x4834,x4835),f202(x4832,x4833,x4834,x4835)) % 154.70/154.57 [484]~E(x4841,x4842)+E(f202(x4843,x4841,x4844,x4845),f202(x4843,x4842,x4844,x4845)) % 154.70/154.57 [485]~E(x4851,x4852)+E(f202(x4853,x4854,x4851,x4855),f202(x4853,x4854,x4852,x4855)) % 154.70/154.57 [486]~E(x4861,x4862)+E(f202(x4863,x4864,x4865,x4861),f202(x4863,x4864,x4865,x4862)) % 154.70/154.57 [487]~E(x4871,x4872)+E(f379(x4871,x4873,x4874),f379(x4872,x4873,x4874)) % 154.70/154.57 [488]~E(x4881,x4882)+E(f379(x4883,x4881,x4884),f379(x4883,x4882,x4884)) % 154.70/154.57 [489]~E(x4891,x4892)+E(f379(x4893,x4894,x4891),f379(x4893,x4894,x4892)) % 154.70/154.57 [490]~E(x4901,x4902)+E(f179(x4901),f179(x4902)) % 154.70/154.57 [491]~E(x4911,x4912)+E(f636(x4911,x4913),f636(x4912,x4913)) % 154.70/154.57 [492]~E(x4921,x4922)+E(f636(x4923,x4921),f636(x4923,x4922)) % 154.70/154.57 [493]~E(x4931,x4932)+E(f65(x4931,x4933,x4934),f65(x4932,x4933,x4934)) % 154.70/154.57 [494]~E(x4941,x4942)+E(f65(x4943,x4941,x4944),f65(x4943,x4942,x4944)) % 154.70/154.57 [495]~E(x4951,x4952)+E(f65(x4953,x4954,x4951),f65(x4953,x4954,x4952)) % 154.70/154.57 [496]~E(x4961,x4962)+E(f252(x4961,x4963,x4964),f252(x4962,x4963,x4964)) % 154.70/154.57 [497]~E(x4971,x4972)+E(f252(x4973,x4971,x4974),f252(x4973,x4972,x4974)) % 154.70/154.57 [498]~E(x4981,x4982)+E(f252(x4983,x4984,x4981),f252(x4983,x4984,x4982)) % 154.70/154.57 [499]~E(x4991,x4992)+E(f829(x4991,x4993,x4994,x4995,x4996),f829(x4992,x4993,x4994,x4995,x4996)) % 154.70/154.57 [500]~E(x5001,x5002)+E(f829(x5003,x5001,x5004,x5005,x5006),f829(x5003,x5002,x5004,x5005,x5006)) % 154.70/154.57 [501]~E(x5011,x5012)+E(f829(x5013,x5014,x5011,x5015,x5016),f829(x5013,x5014,x5012,x5015,x5016)) % 154.70/154.57 [502]~E(x5021,x5022)+E(f829(x5023,x5024,x5025,x5021,x5026),f829(x5023,x5024,x5025,x5022,x5026)) % 154.70/154.57 [503]~E(x5031,x5032)+E(f829(x5033,x5034,x5035,x5036,x5031),f829(x5033,x5034,x5035,x5036,x5032)) % 154.70/154.57 [504]~E(x5041,x5042)+E(f303(x5041),f303(x5042)) % 154.70/154.57 [505]~E(x5051,x5052)+E(f316(x5051,x5053),f316(x5052,x5053)) % 154.70/154.57 [506]~E(x5061,x5062)+E(f316(x5063,x5061),f316(x5063,x5062)) % 154.70/154.57 [507]~E(x5071,x5072)+E(f378(x5071,x5073,x5074,x5075,x5076),f378(x5072,x5073,x5074,x5075,x5076)) % 154.70/154.57 [508]~E(x5081,x5082)+E(f378(x5083,x5081,x5084,x5085,x5086),f378(x5083,x5082,x5084,x5085,x5086)) % 154.70/154.57 [509]~E(x5091,x5092)+E(f378(x5093,x5094,x5091,x5095,x5096),f378(x5093,x5094,x5092,x5095,x5096)) % 154.70/154.57 [510]~E(x5101,x5102)+E(f378(x5103,x5104,x5105,x5101,x5106),f378(x5103,x5104,x5105,x5102,x5106)) % 154.70/154.57 [511]~E(x5111,x5112)+E(f378(x5113,x5114,x5115,x5116,x5111),f378(x5113,x5114,x5115,x5116,x5112)) % 154.70/154.57 [512]~E(x5121,x5122)+E(f300(x5121),f300(x5122)) % 154.70/154.57 [513]~E(x5131,x5132)+E(f757(x5131,x5133),f757(x5132,x5133)) % 154.70/154.57 [514]~E(x5141,x5142)+E(f757(x5143,x5141),f757(x5143,x5142)) % 154.70/154.57 [515]~E(x5151,x5152)+E(f821(x5151,x5153,x5154),f821(x5152,x5153,x5154)) % 154.70/154.57 [516]~E(x5161,x5162)+E(f821(x5163,x5161,x5164),f821(x5163,x5162,x5164)) % 154.70/154.57 [517]~E(x5171,x5172)+E(f821(x5173,x5174,x5171),f821(x5173,x5174,x5172)) % 154.70/154.57 [518]~E(x5181,x5182)+E(f187(x5181,x5183),f187(x5182,x5183)) % 154.70/154.57 [519]~E(x5191,x5192)+E(f187(x5193,x5191),f187(x5193,x5192)) % 154.70/154.57 [520]~E(x5201,x5202)+E(f865(x5201,x5203,x5204,x5205,x5206),f865(x5202,x5203,x5204,x5205,x5206)) % 154.70/154.57 [521]~E(x5211,x5212)+E(f865(x5213,x5211,x5214,x5215,x5216),f865(x5213,x5212,x5214,x5215,x5216)) % 154.70/154.57 [522]~E(x5221,x5222)+E(f865(x5223,x5224,x5221,x5225,x5226),f865(x5223,x5224,x5222,x5225,x5226)) % 154.70/154.57 [523]~E(x5231,x5232)+E(f865(x5233,x5234,x5235,x5231,x5236),f865(x5233,x5234,x5235,x5232,x5236)) % 154.70/154.57 [524]~E(x5241,x5242)+E(f865(x5243,x5244,x5245,x5246,x5241),f865(x5243,x5244,x5245,x5246,x5242)) % 154.70/154.57 [525]~E(x5251,x5252)+E(f800(x5251,x5253,x5254),f800(x5252,x5253,x5254)) % 154.70/154.57 [526]~E(x5261,x5262)+E(f800(x5263,x5261,x5264),f800(x5263,x5262,x5264)) % 154.70/154.57 [527]~E(x5271,x5272)+E(f800(x5273,x5274,x5271),f800(x5273,x5274,x5272)) % 154.70/154.57 [528]~E(x5281,x5282)+E(f225(x5281,x5283),f225(x5282,x5283)) % 154.70/154.57 [529]~E(x5291,x5292)+E(f225(x5293,x5291),f225(x5293,x5292)) % 154.70/154.57 [530]~E(x5301,x5302)+E(f729(x5301,x5303),f729(x5302,x5303)) % 154.70/154.57 [531]~E(x5311,x5312)+E(f729(x5313,x5311),f729(x5313,x5312)) % 154.70/154.57 [532]~E(x5321,x5322)+E(f536(x5321,x5323,x5324),f536(x5322,x5323,x5324)) % 154.70/154.57 [533]~E(x5331,x5332)+E(f536(x5333,x5331,x5334),f536(x5333,x5332,x5334)) % 154.70/154.57 [534]~E(x5341,x5342)+E(f536(x5343,x5344,x5341),f536(x5343,x5344,x5342)) % 154.70/154.57 [535]~E(x5351,x5352)+E(f250(x5351),f250(x5352)) % 154.70/154.57 [536]~E(x5361,x5362)+E(f186(x5361,x5363,x5364,x5365),f186(x5362,x5363,x5364,x5365)) % 154.70/154.57 [537]~E(x5371,x5372)+E(f186(x5373,x5371,x5374,x5375),f186(x5373,x5372,x5374,x5375)) % 154.70/154.57 [538]~E(x5381,x5382)+E(f186(x5383,x5384,x5381,x5385),f186(x5383,x5384,x5382,x5385)) % 154.70/154.57 [539]~E(x5391,x5392)+E(f186(x5393,x5394,x5395,x5391),f186(x5393,x5394,x5395,x5392)) % 154.70/154.57 [540]~E(x5401,x5402)+E(f223(x5401,x5403),f223(x5402,x5403)) % 154.70/154.57 [541]~E(x5411,x5412)+E(f223(x5413,x5411),f223(x5413,x5412)) % 154.70/154.57 [542]~E(x5421,x5422)+E(f827(x5421,x5423,x5424),f827(x5422,x5423,x5424)) % 154.70/154.57 [543]~E(x5431,x5432)+E(f827(x5433,x5431,x5434),f827(x5433,x5432,x5434)) % 154.70/154.57 [544]~E(x5441,x5442)+E(f827(x5443,x5444,x5441),f827(x5443,x5444,x5442)) % 154.70/154.57 [545]~E(x5451,x5452)+E(f355(x5451,x5453,x5454,x5455),f355(x5452,x5453,x5454,x5455)) % 154.70/154.57 [546]~E(x5461,x5462)+E(f355(x5463,x5461,x5464,x5465),f355(x5463,x5462,x5464,x5465)) % 154.70/154.57 [547]~E(x5471,x5472)+E(f355(x5473,x5474,x5471,x5475),f355(x5473,x5474,x5472,x5475)) % 154.70/154.57 [548]~E(x5481,x5482)+E(f355(x5483,x5484,x5485,x5481),f355(x5483,x5484,x5485,x5482)) % 154.70/154.57 [549]~E(x5491,x5492)+E(f831(x5491,x5493,x5494,x5495),f831(x5492,x5493,x5494,x5495)) % 154.70/154.57 [550]~E(x5501,x5502)+E(f831(x5503,x5501,x5504,x5505),f831(x5503,x5502,x5504,x5505)) % 154.70/154.57 [551]~E(x5511,x5512)+E(f831(x5513,x5514,x5511,x5515),f831(x5513,x5514,x5512,x5515)) % 154.70/154.57 [552]~E(x5521,x5522)+E(f831(x5523,x5524,x5525,x5521),f831(x5523,x5524,x5525,x5522)) % 154.70/154.57 [553]~E(x5531,x5532)+E(f308(x5531,x5533,x5534),f308(x5532,x5533,x5534)) % 154.70/154.57 [554]~E(x5541,x5542)+E(f308(x5543,x5541,x5544),f308(x5543,x5542,x5544)) % 154.70/154.57 [555]~E(x5551,x5552)+E(f308(x5553,x5554,x5551),f308(x5553,x5554,x5552)) % 154.70/154.57 [556]~E(x5561,x5562)+E(f395(x5561,x5563,x5564),f395(x5562,x5563,x5564)) % 154.70/154.57 [557]~E(x5571,x5572)+E(f395(x5573,x5571,x5574),f395(x5573,x5572,x5574)) % 154.70/154.57 [558]~E(x5581,x5582)+E(f395(x5583,x5584,x5581),f395(x5583,x5584,x5582)) % 154.70/154.57 [559]~E(x5591,x5592)+E(f59(x5591,x5593,x5594,x5595),f59(x5592,x5593,x5594,x5595)) % 154.70/154.57 [560]~E(x5601,x5602)+E(f59(x5603,x5601,x5604,x5605),f59(x5603,x5602,x5604,x5605)) % 154.70/154.57 [561]~E(x5611,x5612)+E(f59(x5613,x5614,x5611,x5615),f59(x5613,x5614,x5612,x5615)) % 154.70/154.57 [562]~E(x5621,x5622)+E(f59(x5623,x5624,x5625,x5621),f59(x5623,x5624,x5625,x5622)) % 154.70/154.57 [563]~E(x5631,x5632)+E(f337(x5631),f337(x5632)) % 154.70/154.57 [564]~E(x5641,x5642)+E(f222(x5641,x5643),f222(x5642,x5643)) % 154.70/154.57 [565]~E(x5651,x5652)+E(f222(x5653,x5651),f222(x5653,x5652)) % 154.70/154.57 [566]~E(x5661,x5662)+E(f53(x5661,x5663),f53(x5662,x5663)) % 154.70/154.57 [567]~E(x5671,x5672)+E(f53(x5673,x5671),f53(x5673,x5672)) % 154.70/154.57 [568]~E(x5681,x5682)+E(f283(x5681,x5683),f283(x5682,x5683)) % 154.70/154.57 [569]~E(x5691,x5692)+E(f283(x5693,x5691),f283(x5693,x5692)) % 154.70/154.57 [570]~E(x5701,x5702)+E(f799(x5701,x5703,x5704),f799(x5702,x5703,x5704)) % 154.70/154.57 [571]~E(x5711,x5712)+E(f799(x5713,x5711,x5714),f799(x5713,x5712,x5714)) % 154.70/154.57 [572]~E(x5721,x5722)+E(f799(x5723,x5724,x5721),f799(x5723,x5724,x5722)) % 154.70/154.57 [573]~E(x5731,x5732)+E(f47(x5731,x5733),f47(x5732,x5733)) % 154.70/154.57 [574]~E(x5741,x5742)+E(f47(x5743,x5741),f47(x5743,x5742)) % 154.70/154.57 [575]~E(x5751,x5752)+E(f234(x5751,x5753),f234(x5752,x5753)) % 154.70/154.57 [576]~E(x5761,x5762)+E(f234(x5763,x5761),f234(x5763,x5762)) % 154.70/154.57 [577]~E(x5771,x5772)+E(f811(x5771,x5773,x5774),f811(x5772,x5773,x5774)) % 154.70/154.57 [578]~E(x5781,x5782)+E(f811(x5783,x5781,x5784),f811(x5783,x5782,x5784)) % 154.70/154.57 [579]~E(x5791,x5792)+E(f811(x5793,x5794,x5791),f811(x5793,x5794,x5792)) % 154.70/154.57 [580]~E(x5801,x5802)+E(f537(x5801,x5803,x5804),f537(x5802,x5803,x5804)) % 154.70/154.57 [581]~E(x5811,x5812)+E(f537(x5813,x5811,x5814),f537(x5813,x5812,x5814)) % 154.70/154.57 [582]~E(x5821,x5822)+E(f537(x5823,x5824,x5821),f537(x5823,x5824,x5822)) % 154.70/154.57 [583]~E(x5831,x5832)+E(f269(x5831,x5833,x5834,x5835),f269(x5832,x5833,x5834,x5835)) % 154.70/154.57 [584]~E(x5841,x5842)+E(f269(x5843,x5841,x5844,x5845),f269(x5843,x5842,x5844,x5845)) % 154.70/154.57 [585]~E(x5851,x5852)+E(f269(x5853,x5854,x5851,x5855),f269(x5853,x5854,x5852,x5855)) % 154.70/154.57 [586]~E(x5861,x5862)+E(f269(x5863,x5864,x5865,x5861),f269(x5863,x5864,x5865,x5862)) % 154.70/154.57 [587]~E(x5871,x5872)+E(f767(x5871,x5873),f767(x5872,x5873)) % 154.70/154.57 [588]~E(x5881,x5882)+E(f767(x5883,x5881),f767(x5883,x5882)) % 154.70/154.57 [589]~E(x5891,x5892)+E(f632(x5891,x5893),f632(x5892,x5893)) % 154.70/154.57 [590]~E(x5901,x5902)+E(f632(x5903,x5901),f632(x5903,x5902)) % 154.70/154.57 [591]~E(x5911,x5912)+E(f371(x5911,x5913),f371(x5912,x5913)) % 154.70/154.57 [592]~E(x5921,x5922)+E(f371(x5923,x5921),f371(x5923,x5922)) % 154.70/154.57 [593]~E(x5931,x5932)+E(f480(x5931,x5933),f480(x5932,x5933)) % 154.70/154.57 [594]~E(x5941,x5942)+E(f480(x5943,x5941),f480(x5943,x5942)) % 154.70/154.57 [595]~E(x5951,x5952)+E(f674(x5951,x5953,x5954,x5955),f674(x5952,x5953,x5954,x5955)) % 154.70/154.57 [596]~E(x5961,x5962)+E(f674(x5963,x5961,x5964,x5965),f674(x5963,x5962,x5964,x5965)) % 154.70/154.57 [597]~E(x5971,x5972)+E(f674(x5973,x5974,x5971,x5975),f674(x5973,x5974,x5972,x5975)) % 154.70/154.57 [598]~E(x5981,x5982)+E(f674(x5983,x5984,x5985,x5981),f674(x5983,x5984,x5985,x5982)) % 154.70/154.57 [599]~E(x5991,x5992)+E(f40(x5991,x5993),f40(x5992,x5993)) % 154.70/154.57 [600]~E(x6001,x6002)+E(f40(x6003,x6001),f40(x6003,x6002)) % 154.70/154.57 [601]~E(x6011,x6012)+E(f567(x6011,x6013,x6014,x6015),f567(x6012,x6013,x6014,x6015)) % 154.70/154.57 [602]~E(x6021,x6022)+E(f567(x6023,x6021,x6024,x6025),f567(x6023,x6022,x6024,x6025)) % 154.70/154.57 [603]~E(x6031,x6032)+E(f567(x6033,x6034,x6031,x6035),f567(x6033,x6034,x6032,x6035)) % 154.70/154.57 [604]~E(x6041,x6042)+E(f567(x6043,x6044,x6045,x6041),f567(x6043,x6044,x6045,x6042)) % 154.70/154.57 [605]~E(x6051,x6052)+E(f155(x6051,x6053),f155(x6052,x6053)) % 154.70/154.57 [606]~E(x6061,x6062)+E(f155(x6063,x6061),f155(x6063,x6062)) % 154.70/154.57 [607]~E(x6071,x6072)+E(f405(x6071,x6073,x6074),f405(x6072,x6073,x6074)) % 154.70/154.57 [608]~E(x6081,x6082)+E(f405(x6083,x6081,x6084),f405(x6083,x6082,x6084)) % 154.70/154.57 [609]~E(x6091,x6092)+E(f405(x6093,x6094,x6091),f405(x6093,x6094,x6092)) % 154.70/154.57 [610]~E(x6101,x6102)+E(f230(x6101,x6103,x6104),f230(x6102,x6103,x6104)) % 154.70/154.57 [611]~E(x6111,x6112)+E(f230(x6113,x6111,x6114),f230(x6113,x6112,x6114)) % 154.70/154.57 [612]~E(x6121,x6122)+E(f230(x6123,x6124,x6121),f230(x6123,x6124,x6122)) % 154.70/154.57 [613]~E(x6131,x6132)+E(f72(x6131,x6133),f72(x6132,x6133)) % 154.70/154.57 [614]~E(x6141,x6142)+E(f72(x6143,x6141),f72(x6143,x6142)) % 154.70/154.57 [615]~E(x6151,x6152)+E(f830(x6151,x6153,x6154,x6155),f830(x6152,x6153,x6154,x6155)) % 154.70/154.57 [616]~E(x6161,x6162)+E(f830(x6163,x6161,x6164,x6165),f830(x6163,x6162,x6164,x6165)) % 154.70/154.57 [617]~E(x6171,x6172)+E(f830(x6173,x6174,x6171,x6175),f830(x6173,x6174,x6172,x6175)) % 154.70/154.57 [618]~E(x6181,x6182)+E(f830(x6183,x6184,x6185,x6181),f830(x6183,x6184,x6185,x6182)) % 154.70/154.57 [619]~E(x6191,x6192)+E(f473(x6191,x6193,x6194,x6195),f473(x6192,x6193,x6194,x6195)) % 154.70/154.57 [620]~E(x6201,x6202)+E(f473(x6203,x6201,x6204,x6205),f473(x6203,x6202,x6204,x6205)) % 154.70/154.57 [621]~E(x6211,x6212)+E(f473(x6213,x6214,x6211,x6215),f473(x6213,x6214,x6212,x6215)) % 154.70/154.57 [622]~E(x6221,x6222)+E(f473(x6223,x6224,x6225,x6221),f473(x6223,x6224,x6225,x6222)) % 154.70/154.57 [623]~E(x6231,x6232)+E(f494(x6231,x6233,x6234),f494(x6232,x6233,x6234)) % 154.70/154.57 [624]~E(x6241,x6242)+E(f494(x6243,x6241,x6244),f494(x6243,x6242,x6244)) % 154.70/154.57 [625]~E(x6251,x6252)+E(f494(x6253,x6254,x6251),f494(x6253,x6254,x6252)) % 154.70/154.57 [626]~E(x6261,x6262)+E(f375(x6261,x6263),f375(x6262,x6263)) % 154.70/154.57 [627]~E(x6271,x6272)+E(f375(x6273,x6271),f375(x6273,x6272)) % 154.70/154.57 [628]~E(x6281,x6282)+E(f507(x6281,x6283,x6284),f507(x6282,x6283,x6284)) % 154.70/154.57 [629]~E(x6291,x6292)+E(f507(x6293,x6291,x6294),f507(x6293,x6292,x6294)) % 154.70/154.57 [630]~E(x6301,x6302)+E(f507(x6303,x6304,x6301),f507(x6303,x6304,x6302)) % 154.70/154.57 [631]~E(x6311,x6312)+E(f158(x6311,x6313),f158(x6312,x6313)) % 154.70/154.57 [632]~E(x6321,x6322)+E(f158(x6323,x6321),f158(x6323,x6322)) % 154.70/154.57 [633]~E(x6331,x6332)+E(f297(x6331),f297(x6332)) % 154.70/154.57 [634]~E(x6341,x6342)+E(f690(x6341,x6343),f690(x6342,x6343)) % 154.70/154.57 [635]~E(x6351,x6352)+E(f690(x6353,x6351),f690(x6353,x6352)) % 154.70/154.57 [636]~E(x6361,x6362)+E(f685(x6361,x6363),f685(x6362,x6363)) % 154.70/154.57 [637]~E(x6371,x6372)+E(f685(x6373,x6371),f685(x6373,x6372)) % 154.70/154.57 [638]~E(x6381,x6382)+E(f290(x6381,x6383,x6384),f290(x6382,x6383,x6384)) % 154.70/154.57 [639]~E(x6391,x6392)+E(f290(x6393,x6391,x6394),f290(x6393,x6392,x6394)) % 154.70/154.57 [640]~E(x6401,x6402)+E(f290(x6403,x6404,x6401),f290(x6403,x6404,x6402)) % 154.70/154.57 [641]~E(x6411,x6412)+E(f147(x6411,x6413,x6414,x6415),f147(x6412,x6413,x6414,x6415)) % 154.70/154.57 [642]~E(x6421,x6422)+E(f147(x6423,x6421,x6424,x6425),f147(x6423,x6422,x6424,x6425)) % 154.70/154.57 [643]~E(x6431,x6432)+E(f147(x6433,x6434,x6431,x6435),f147(x6433,x6434,x6432,x6435)) % 154.70/154.57 [644]~E(x6441,x6442)+E(f147(x6443,x6444,x6445,x6441),f147(x6443,x6444,x6445,x6442)) % 154.70/154.57 [645]~E(x6451,x6452)+E(f687(x6451,x6453,x6454,x6455),f687(x6452,x6453,x6454,x6455)) % 154.70/154.57 [646]~E(x6461,x6462)+E(f687(x6463,x6461,x6464,x6465),f687(x6463,x6462,x6464,x6465)) % 154.70/154.57 [647]~E(x6471,x6472)+E(f687(x6473,x6474,x6471,x6475),f687(x6473,x6474,x6472,x6475)) % 154.70/154.57 [648]~E(x6481,x6482)+E(f687(x6483,x6484,x6485,x6481),f687(x6483,x6484,x6485,x6482)) % 154.70/154.57 [649]~E(x6491,x6492)+E(f449(x6491,x6493,x6494),f449(x6492,x6493,x6494)) % 154.70/154.57 [650]~E(x6501,x6502)+E(f449(x6503,x6501,x6504),f449(x6503,x6502,x6504)) % 154.70/154.57 [651]~E(x6511,x6512)+E(f449(x6513,x6514,x6511),f449(x6513,x6514,x6512)) % 154.70/154.57 [652]~E(x6521,x6522)+E(f512(x6521,x6523,x6524),f512(x6522,x6523,x6524)) % 154.70/154.57 [653]~E(x6531,x6532)+E(f512(x6533,x6531,x6534),f512(x6533,x6532,x6534)) % 154.70/154.57 [654]~E(x6541,x6542)+E(f512(x6543,x6544,x6541),f512(x6543,x6544,x6542)) % 154.70/154.57 [655]~E(x6551,x6552)+E(f824(x6551,x6553,x6554),f824(x6552,x6553,x6554)) % 154.70/154.57 [656]~E(x6561,x6562)+E(f824(x6563,x6561,x6564),f824(x6563,x6562,x6564)) % 154.70/154.57 [657]~E(x6571,x6572)+E(f824(x6573,x6574,x6571),f824(x6573,x6574,x6572)) % 154.70/154.57 [658]~E(x6581,x6582)+E(f289(x6581,x6583,x6584),f289(x6582,x6583,x6584)) % 154.70/154.57 [659]~E(x6591,x6592)+E(f289(x6593,x6591,x6594),f289(x6593,x6592,x6594)) % 154.70/154.57 [660]~E(x6601,x6602)+E(f289(x6603,x6604,x6601),f289(x6603,x6604,x6602)) % 154.70/154.57 [661]~E(x6611,x6612)+E(f164(x6611,x6613,x6614),f164(x6612,x6613,x6614)) % 154.70/154.57 [662]~E(x6621,x6622)+E(f164(x6623,x6621,x6624),f164(x6623,x6622,x6624)) % 154.70/154.57 [663]~E(x6631,x6632)+E(f164(x6633,x6634,x6631),f164(x6633,x6634,x6632)) % 154.70/154.57 [664]~E(x6641,x6642)+E(f464(x6641,x6643,x6644,x6645,x6646,x6647),f464(x6642,x6643,x6644,x6645,x6646,x6647)) % 154.70/154.57 [665]~E(x6651,x6652)+E(f464(x6653,x6651,x6654,x6655,x6656,x6657),f464(x6653,x6652,x6654,x6655,x6656,x6657)) % 154.70/154.57 [666]~E(x6661,x6662)+E(f464(x6663,x6664,x6661,x6665,x6666,x6667),f464(x6663,x6664,x6662,x6665,x6666,x6667)) % 154.70/154.57 [667]~E(x6671,x6672)+E(f464(x6673,x6674,x6675,x6671,x6676,x6677),f464(x6673,x6674,x6675,x6672,x6676,x6677)) % 154.70/154.57 [668]~E(x6681,x6682)+E(f464(x6683,x6684,x6685,x6686,x6681,x6687),f464(x6683,x6684,x6685,x6686,x6682,x6687)) % 154.70/154.57 [669]~E(x6691,x6692)+E(f464(x6693,x6694,x6695,x6696,x6697,x6691),f464(x6693,x6694,x6695,x6696,x6697,x6692)) % 154.70/154.57 [670]~E(x6701,x6702)+E(f819(x6701,x6703,x6704),f819(x6702,x6703,x6704)) % 154.70/154.57 [671]~E(x6711,x6712)+E(f819(x6713,x6711,x6714),f819(x6713,x6712,x6714)) % 154.70/154.57 [672]~E(x6721,x6722)+E(f819(x6723,x6724,x6721),f819(x6723,x6724,x6722)) % 154.70/154.57 [673]~E(x6731,x6732)+E(f185(x6731,x6733,x6734,x6735,x6736),f185(x6732,x6733,x6734,x6735,x6736)) % 154.70/154.57 [674]~E(x6741,x6742)+E(f185(x6743,x6741,x6744,x6745,x6746),f185(x6743,x6742,x6744,x6745,x6746)) % 154.70/154.57 [675]~E(x6751,x6752)+E(f185(x6753,x6754,x6751,x6755,x6756),f185(x6753,x6754,x6752,x6755,x6756)) % 154.70/154.57 [676]~E(x6761,x6762)+E(f185(x6763,x6764,x6765,x6761,x6766),f185(x6763,x6764,x6765,x6762,x6766)) % 154.70/154.57 [677]~E(x6771,x6772)+E(f185(x6773,x6774,x6775,x6776,x6771),f185(x6773,x6774,x6775,x6776,x6772)) % 154.70/154.57 [678]~E(x6781,x6782)+E(f207(x6781,x6783),f207(x6782,x6783)) % 154.70/154.57 [679]~E(x6791,x6792)+E(f207(x6793,x6791),f207(x6793,x6792)) % 154.70/154.57 [680]~E(x6801,x6802)+E(f301(x6801,x6803,x6804),f301(x6802,x6803,x6804)) % 154.70/154.57 [681]~E(x6811,x6812)+E(f301(x6813,x6811,x6814),f301(x6813,x6812,x6814)) % 154.70/154.57 [682]~E(x6821,x6822)+E(f301(x6823,x6824,x6821),f301(x6823,x6824,x6822)) % 154.70/154.57 [683]~E(x6831,x6832)+E(f686(x6831,x6833,x6834,x6835),f686(x6832,x6833,x6834,x6835)) % 154.70/154.57 [684]~E(x6841,x6842)+E(f686(x6843,x6841,x6844,x6845),f686(x6843,x6842,x6844,x6845)) % 154.70/154.57 [685]~E(x6851,x6852)+E(f686(x6853,x6854,x6851,x6855),f686(x6853,x6854,x6852,x6855)) % 154.70/154.57 [686]~E(x6861,x6862)+E(f686(x6863,x6864,x6865,x6861),f686(x6863,x6864,x6865,x6862)) % 154.70/154.57 [687]~E(x6871,x6872)+E(f527(x6871,x6873,x6874,x6875),f527(x6872,x6873,x6874,x6875)) % 154.70/154.57 [688]~E(x6881,x6882)+E(f527(x6883,x6881,x6884,x6885),f527(x6883,x6882,x6884,x6885)) % 154.70/154.57 [689]~E(x6891,x6892)+E(f527(x6893,x6894,x6891,x6895),f527(x6893,x6894,x6892,x6895)) % 154.70/154.57 [690]~E(x6901,x6902)+E(f527(x6903,x6904,x6905,x6901),f527(x6903,x6904,x6905,x6902)) % 154.70/154.57 [691]~E(x6911,x6912)+E(f761(x6911,x6913),f761(x6912,x6913)) % 154.70/154.57 [692]~E(x6921,x6922)+E(f761(x6923,x6921),f761(x6923,x6922)) % 154.70/154.57 [693]~E(x6931,x6932)+E(f136(x6931,x6933),f136(x6932,x6933)) % 154.70/154.57 [694]~E(x6941,x6942)+E(f136(x6943,x6941),f136(x6943,x6942)) % 154.70/154.57 [695]~E(x6951,x6952)+E(f697(x6951,x6953,x6954,x6955,x6956),f697(x6952,x6953,x6954,x6955,x6956)) % 154.70/154.57 [696]~E(x6961,x6962)+E(f697(x6963,x6961,x6964,x6965,x6966),f697(x6963,x6962,x6964,x6965,x6966)) % 154.70/154.57 [697]~E(x6971,x6972)+E(f697(x6973,x6974,x6971,x6975,x6976),f697(x6973,x6974,x6972,x6975,x6976)) % 154.70/154.57 [698]~E(x6981,x6982)+E(f697(x6983,x6984,x6985,x6981,x6986),f697(x6983,x6984,x6985,x6982,x6986)) % 154.70/154.57 [699]~E(x6991,x6992)+E(f697(x6993,x6994,x6995,x6996,x6991),f697(x6993,x6994,x6995,x6996,x6992)) % 154.70/154.57 [700]~E(x7001,x7002)+E(f96(x7001,x7003,x7004,x7005),f96(x7002,x7003,x7004,x7005)) % 154.70/154.57 [701]~E(x7011,x7012)+E(f96(x7013,x7011,x7014,x7015),f96(x7013,x7012,x7014,x7015)) % 154.70/154.57 [702]~E(x7021,x7022)+E(f96(x7023,x7024,x7021,x7025),f96(x7023,x7024,x7022,x7025)) % 154.70/154.57 [703]~E(x7031,x7032)+E(f96(x7033,x7034,x7035,x7031),f96(x7033,x7034,x7035,x7032)) % 154.70/154.57 [704]~E(x7041,x7042)+E(f654(x7041,x7043),f654(x7042,x7043)) % 154.70/154.57 [705]~E(x7051,x7052)+E(f654(x7053,x7051),f654(x7053,x7052)) % 154.70/154.57 [706]~E(x7061,x7062)+E(f531(x7061,x7063),f531(x7062,x7063)) % 154.70/154.57 [707]~E(x7071,x7072)+E(f531(x7073,x7071),f531(x7073,x7072)) % 154.70/154.57 [708]~E(x7081,x7082)+E(f412(x7081,x7083,x7084),f412(x7082,x7083,x7084)) % 154.70/154.57 [709]~E(x7091,x7092)+E(f412(x7093,x7091,x7094),f412(x7093,x7092,x7094)) % 154.70/154.57 [710]~E(x7101,x7102)+E(f412(x7103,x7104,x7101),f412(x7103,x7104,x7102)) % 154.70/154.57 [711]~E(x7111,x7112)+E(f587(x7111,x7113,x7114,x7115,x7116,x7117,x7118,x7119),f587(x7112,x7113,x7114,x7115,x7116,x7117,x7118,x7119)) % 154.70/154.57 [712]~E(x7121,x7122)+E(f587(x7123,x7121,x7124,x7125,x7126,x7127,x7128,x7129),f587(x7123,x7122,x7124,x7125,x7126,x7127,x7128,x7129)) % 154.70/154.57 [713]~E(x7131,x7132)+E(f587(x7133,x7134,x7131,x7135,x7136,x7137,x7138,x7139),f587(x7133,x7134,x7132,x7135,x7136,x7137,x7138,x7139)) % 154.70/154.57 [714]~E(x7141,x7142)+E(f587(x7143,x7144,x7145,x7141,x7146,x7147,x7148,x7149),f587(x7143,x7144,x7145,x7142,x7146,x7147,x7148,x7149)) % 154.70/154.57 [715]~E(x7151,x7152)+E(f587(x7153,x7154,x7155,x7156,x7151,x7157,x7158,x7159),f587(x7153,x7154,x7155,x7156,x7152,x7157,x7158,x7159)) % 154.70/154.57 [716]~E(x7161,x7162)+E(f587(x7163,x7164,x7165,x7166,x7167,x7161,x7168,x7169),f587(x7163,x7164,x7165,x7166,x7167,x7162,x7168,x7169)) % 154.70/154.57 [717]~E(x7171,x7172)+E(f587(x7173,x7174,x7175,x7176,x7177,x7178,x7171,x7179),f587(x7173,x7174,x7175,x7176,x7177,x7178,x7172,x7179)) % 154.70/154.57 [718]~E(x7181,x7182)+E(f587(x7183,x7184,x7185,x7186,x7187,x7188,x7189,x7181),f587(x7183,x7184,x7185,x7186,x7187,x7188,x7189,x7182)) % 154.70/154.57 [719]~E(x7191,x7192)+E(f206(x7191,x7193),f206(x7192,x7193)) % 154.70/154.57 [720]~E(x7201,x7202)+E(f206(x7203,x7201),f206(x7203,x7202)) % 154.70/154.57 [721]~E(x7211,x7212)+E(f620(x7211,x7213,x7214),f620(x7212,x7213,x7214)) % 154.70/154.57 [722]~E(x7221,x7222)+E(f620(x7223,x7221,x7224),f620(x7223,x7222,x7224)) % 154.70/154.57 [723]~E(x7231,x7232)+E(f620(x7233,x7234,x7231),f620(x7233,x7234,x7232)) % 154.70/154.57 [724]~E(x7241,x7242)+E(f583(x7241,x7243,x7244,x7245),f583(x7242,x7243,x7244,x7245)) % 154.70/154.57 [725]~E(x7251,x7252)+E(f583(x7253,x7251,x7254,x7255),f583(x7253,x7252,x7254,x7255)) % 154.70/154.57 [726]~E(x7261,x7262)+E(f583(x7263,x7264,x7261,x7265),f583(x7263,x7264,x7262,x7265)) % 154.70/154.57 [727]~E(x7271,x7272)+E(f583(x7273,x7274,x7275,x7271),f583(x7273,x7274,x7275,x7272)) % 154.70/154.57 [728]~E(x7281,x7282)+E(f554(x7281,x7283),f554(x7282,x7283)) % 154.70/154.57 [729]~E(x7291,x7292)+E(f554(x7293,x7291),f554(x7293,x7292)) % 154.70/154.57 [730]~E(x7301,x7302)+E(f616(x7301,x7303,x7304,x7305,x7306,x7307),f616(x7302,x7303,x7304,x7305,x7306,x7307)) % 154.70/154.57 [731]~E(x7311,x7312)+E(f616(x7313,x7311,x7314,x7315,x7316,x7317),f616(x7313,x7312,x7314,x7315,x7316,x7317)) % 154.70/154.57 [732]~E(x7321,x7322)+E(f616(x7323,x7324,x7321,x7325,x7326,x7327),f616(x7323,x7324,x7322,x7325,x7326,x7327)) % 154.70/154.57 [733]~E(x7331,x7332)+E(f616(x7333,x7334,x7335,x7331,x7336,x7337),f616(x7333,x7334,x7335,x7332,x7336,x7337)) % 154.70/154.57 [734]~E(x7341,x7342)+E(f616(x7343,x7344,x7345,x7346,x7341,x7347),f616(x7343,x7344,x7345,x7346,x7342,x7347)) % 154.70/154.57 [735]~E(x7351,x7352)+E(f616(x7353,x7354,x7355,x7356,x7357,x7351),f616(x7353,x7354,x7355,x7356,x7357,x7352)) % 154.70/154.57 [736]~E(x7361,x7362)+E(f593(x7361),f593(x7362)) % 154.70/154.57 [737]~E(x7371,x7372)+E(f217(x7371,x7373,x7374,x7375),f217(x7372,x7373,x7374,x7375)) % 154.70/154.57 [738]~E(x7381,x7382)+E(f217(x7383,x7381,x7384,x7385),f217(x7383,x7382,x7384,x7385)) % 154.70/154.57 [739]~E(x7391,x7392)+E(f217(x7393,x7394,x7391,x7395),f217(x7393,x7394,x7392,x7395)) % 154.70/154.57 [740]~E(x7401,x7402)+E(f217(x7403,x7404,x7405,x7401),f217(x7403,x7404,x7405,x7402)) % 154.70/154.57 [741]~E(x7411,x7412)+E(f741(x7411,x7413,x7414),f741(x7412,x7413,x7414)) % 154.70/154.57 [742]~E(x7421,x7422)+E(f741(x7423,x7421,x7424),f741(x7423,x7422,x7424)) % 154.70/154.57 [743]~E(x7431,x7432)+E(f741(x7433,x7434,x7431),f741(x7433,x7434,x7432)) % 154.70/154.57 [744]~E(x7441,x7442)+E(f245(x7441,x7443),f245(x7442,x7443)) % 154.70/154.57 [745]~E(x7451,x7452)+E(f245(x7453,x7451),f245(x7453,x7452)) % 154.70/154.57 [746]~E(x7461,x7462)+E(f183(x7461,x7463,x7464,x7465),f183(x7462,x7463,x7464,x7465)) % 154.70/154.57 [747]~E(x7471,x7472)+E(f183(x7473,x7471,x7474,x7475),f183(x7473,x7472,x7474,x7475)) % 154.70/154.57 [748]~E(x7481,x7482)+E(f183(x7483,x7484,x7481,x7485),f183(x7483,x7484,x7482,x7485)) % 154.70/154.57 [749]~E(x7491,x7492)+E(f183(x7493,x7494,x7495,x7491),f183(x7493,x7494,x7495,x7492)) % 154.70/154.57 [750]~E(x7501,x7502)+E(f652(x7501,x7503,x7504,x7505,x7506),f652(x7502,x7503,x7504,x7505,x7506)) % 154.70/154.57 [751]~E(x7511,x7512)+E(f652(x7513,x7511,x7514,x7515,x7516),f652(x7513,x7512,x7514,x7515,x7516)) % 154.70/154.57 [752]~E(x7521,x7522)+E(f652(x7523,x7524,x7521,x7525,x7526),f652(x7523,x7524,x7522,x7525,x7526)) % 154.70/154.57 [753]~E(x7531,x7532)+E(f652(x7533,x7534,x7535,x7531,x7536),f652(x7533,x7534,x7535,x7532,x7536)) % 154.70/154.57 [754]~E(x7541,x7542)+E(f652(x7543,x7544,x7545,x7546,x7541),f652(x7543,x7544,x7545,x7546,x7542)) % 154.70/154.57 [755]~E(x7551,x7552)+E(f127(x7551,x7553,x7554),f127(x7552,x7553,x7554)) % 154.70/154.57 [756]~E(x7561,x7562)+E(f127(x7563,x7561,x7564),f127(x7563,x7562,x7564)) % 154.70/154.57 [757]~E(x7571,x7572)+E(f127(x7573,x7574,x7571),f127(x7573,x7574,x7572)) % 154.70/154.57 [758]~E(x7581,x7582)+E(f46(x7581,x7583),f46(x7582,x7583)) % 154.70/154.57 [759]~E(x7591,x7592)+E(f46(x7593,x7591),f46(x7593,x7592)) % 154.70/154.57 [760]~E(x7601,x7602)+E(f621(x7601,x7603,x7604,x7605,x7606,x7607,x7608,x7609),f621(x7602,x7603,x7604,x7605,x7606,x7607,x7608,x7609)) % 154.70/154.57 [761]~E(x7611,x7612)+E(f621(x7613,x7611,x7614,x7615,x7616,x7617,x7618,x7619),f621(x7613,x7612,x7614,x7615,x7616,x7617,x7618,x7619)) % 154.70/154.57 [762]~E(x7621,x7622)+E(f621(x7623,x7624,x7621,x7625,x7626,x7627,x7628,x7629),f621(x7623,x7624,x7622,x7625,x7626,x7627,x7628,x7629)) % 154.70/154.57 [763]~E(x7631,x7632)+E(f621(x7633,x7634,x7635,x7631,x7636,x7637,x7638,x7639),f621(x7633,x7634,x7635,x7632,x7636,x7637,x7638,x7639)) % 154.70/154.57 [764]~E(x7641,x7642)+E(f621(x7643,x7644,x7645,x7646,x7641,x7647,x7648,x7649),f621(x7643,x7644,x7645,x7646,x7642,x7647,x7648,x7649)) % 154.70/154.57 [765]~E(x7651,x7652)+E(f621(x7653,x7654,x7655,x7656,x7657,x7651,x7658,x7659),f621(x7653,x7654,x7655,x7656,x7657,x7652,x7658,x7659)) % 154.70/154.57 [766]~E(x7661,x7662)+E(f621(x7663,x7664,x7665,x7666,x7667,x7668,x7661,x7669),f621(x7663,x7664,x7665,x7666,x7667,x7668,x7662,x7669)) % 154.70/154.57 [767]~E(x7671,x7672)+E(f621(x7673,x7674,x7675,x7676,x7677,x7678,x7679,x7671),f621(x7673,x7674,x7675,x7676,x7677,x7678,x7679,x7672)) % 154.70/154.57 [768]~E(x7681,x7682)+E(f846(x7681,x7683,x7684,x7685,x7686,x7687,x7688),f846(x7682,x7683,x7684,x7685,x7686,x7687,x7688)) % 154.70/154.57 [769]~E(x7691,x7692)+E(f846(x7693,x7691,x7694,x7695,x7696,x7697,x7698),f846(x7693,x7692,x7694,x7695,x7696,x7697,x7698)) % 154.70/154.57 [770]~E(x7701,x7702)+E(f846(x7703,x7704,x7701,x7705,x7706,x7707,x7708),f846(x7703,x7704,x7702,x7705,x7706,x7707,x7708)) % 154.70/154.57 [771]~E(x7711,x7712)+E(f846(x7713,x7714,x7715,x7711,x7716,x7717,x7718),f846(x7713,x7714,x7715,x7712,x7716,x7717,x7718)) % 154.70/154.57 [772]~E(x7721,x7722)+E(f846(x7723,x7724,x7725,x7726,x7721,x7727,x7728),f846(x7723,x7724,x7725,x7726,x7722,x7727,x7728)) % 154.70/154.57 [773]~E(x7731,x7732)+E(f846(x7733,x7734,x7735,x7736,x7737,x7731,x7738),f846(x7733,x7734,x7735,x7736,x7737,x7732,x7738)) % 154.70/154.57 [774]~E(x7741,x7742)+E(f846(x7743,x7744,x7745,x7746,x7747,x7748,x7741),f846(x7743,x7744,x7745,x7746,x7747,x7748,x7742)) % 154.70/154.57 [775]~E(x7751,x7752)+E(f259(x7751,x7753),f259(x7752,x7753)) % 154.70/154.57 [776]~E(x7761,x7762)+E(f259(x7763,x7761),f259(x7763,x7762)) % 154.70/154.57 [777]~E(x7771,x7772)+E(f63(x7771,x7773),f63(x7772,x7773)) % 154.70/154.57 [778]~E(x7781,x7782)+E(f63(x7783,x7781),f63(x7783,x7782)) % 154.70/154.57 [779]~E(x7791,x7792)+E(f228(x7791,x7793,x7794),f228(x7792,x7793,x7794)) % 154.70/154.57 [780]~E(x7801,x7802)+E(f228(x7803,x7801,x7804),f228(x7803,x7802,x7804)) % 154.70/154.57 [781]~E(x7811,x7812)+E(f228(x7813,x7814,x7811),f228(x7813,x7814,x7812)) % 154.70/154.57 [782]~E(x7821,x7822)+E(f723(x7821,x7823,x7824),f723(x7822,x7823,x7824)) % 154.70/154.57 [783]~E(x7831,x7832)+E(f723(x7833,x7831,x7834),f723(x7833,x7832,x7834)) % 154.70/154.57 [784]~E(x7841,x7842)+E(f723(x7843,x7844,x7841),f723(x7843,x7844,x7842)) % 154.70/154.57 [785]~E(x7851,x7852)+E(f261(x7851,x7853),f261(x7852,x7853)) % 154.70/154.57 [786]~E(x7861,x7862)+E(f261(x7863,x7861),f261(x7863,x7862)) % 154.70/154.57 [787]~E(x7871,x7872)+E(f678(x7871,x7873,x7874),f678(x7872,x7873,x7874)) % 154.70/154.57 [788]~E(x7881,x7882)+E(f678(x7883,x7881,x7884),f678(x7883,x7882,x7884)) % 154.70/154.57 [789]~E(x7891,x7892)+E(f678(x7893,x7894,x7891),f678(x7893,x7894,x7892)) % 154.70/154.57 [790]~E(x7901,x7902)+E(f753(x7901,x7903,x7904),f753(x7902,x7903,x7904)) % 154.70/154.57 [791]~E(x7911,x7912)+E(f753(x7913,x7911,x7914),f753(x7913,x7912,x7914)) % 154.70/154.57 [792]~E(x7921,x7922)+E(f753(x7923,x7924,x7921),f753(x7923,x7924,x7922)) % 154.70/154.57 [793]~E(x7931,x7932)+E(f302(x7931,x7933,x7934),f302(x7932,x7933,x7934)) % 154.70/154.57 [794]~E(x7941,x7942)+E(f302(x7943,x7941,x7944),f302(x7943,x7942,x7944)) % 154.70/154.57 [795]~E(x7951,x7952)+E(f302(x7953,x7954,x7951),f302(x7953,x7954,x7952)) % 154.70/154.57 [796]~E(x7961,x7962)+E(f628(x7961,x7963,x7964),f628(x7962,x7963,x7964)) % 154.70/154.57 [797]~E(x7971,x7972)+E(f628(x7973,x7971,x7974),f628(x7973,x7972,x7974)) % 154.70/154.57 [798]~E(x7981,x7982)+E(f628(x7983,x7984,x7981),f628(x7983,x7984,x7982)) % 154.70/154.57 [799]~E(x7991,x7992)+E(f142(x7991,x7993),f142(x7992,x7993)) % 154.70/154.57 [800]~E(x8001,x8002)+E(f142(x8003,x8001),f142(x8003,x8002)) % 154.70/154.57 [801]~E(x8011,x8012)+E(f472(x8011,x8013,x8014),f472(x8012,x8013,x8014)) % 154.70/154.57 [802]~E(x8021,x8022)+E(f472(x8023,x8021,x8024),f472(x8023,x8022,x8024)) % 154.70/154.57 [803]~E(x8031,x8032)+E(f472(x8033,x8034,x8031),f472(x8033,x8034,x8032)) % 154.70/154.57 [804]~E(x8041,x8042)+E(f194(x8041,x8043,x8044,x8045),f194(x8042,x8043,x8044,x8045)) % 154.70/154.57 [805]~E(x8051,x8052)+E(f194(x8053,x8051,x8054,x8055),f194(x8053,x8052,x8054,x8055)) % 154.70/154.57 [806]~E(x8061,x8062)+E(f194(x8063,x8064,x8061,x8065),f194(x8063,x8064,x8062,x8065)) % 154.70/154.57 [807]~E(x8071,x8072)+E(f194(x8073,x8074,x8075,x8071),f194(x8073,x8074,x8075,x8072)) % 154.70/154.57 [808]~E(x8081,x8082)+E(f858(x8081,x8083,x8084),f858(x8082,x8083,x8084)) % 154.70/154.57 [809]~E(x8091,x8092)+E(f858(x8093,x8091,x8094),f858(x8093,x8092,x8094)) % 154.70/154.57 [810]~E(x8101,x8102)+E(f858(x8103,x8104,x8101),f858(x8103,x8104,x8102)) % 154.70/154.57 [811]~E(x8111,x8112)+E(f739(x8111,x8113,x8114,x8115,x8116),f739(x8112,x8113,x8114,x8115,x8116)) % 154.70/154.57 [812]~E(x8121,x8122)+E(f739(x8123,x8121,x8124,x8125,x8126),f739(x8123,x8122,x8124,x8125,x8126)) % 154.70/154.57 [813]~E(x8131,x8132)+E(f739(x8133,x8134,x8131,x8135,x8136),f739(x8133,x8134,x8132,x8135,x8136)) % 154.70/154.57 [814]~E(x8141,x8142)+E(f739(x8143,x8144,x8145,x8141,x8146),f739(x8143,x8144,x8145,x8142,x8146)) % 154.70/154.57 [815]~E(x8151,x8152)+E(f739(x8153,x8154,x8155,x8156,x8151),f739(x8153,x8154,x8155,x8156,x8152)) % 154.70/154.57 [816]~E(x8161,x8162)+E(f732(x8161,x8163,x8164),f732(x8162,x8163,x8164)) % 154.70/154.57 [817]~E(x8171,x8172)+E(f732(x8173,x8171,x8174),f732(x8173,x8172,x8174)) % 154.70/154.57 [818]~E(x8181,x8182)+E(f732(x8183,x8184,x8181),f732(x8183,x8184,x8182)) % 154.70/154.57 [819]~E(x8191,x8192)+E(f172(x8191,x8193,x8194),f172(x8192,x8193,x8194)) % 154.70/154.57 [820]~E(x8201,x8202)+E(f172(x8203,x8201,x8204),f172(x8203,x8202,x8204)) % 154.70/154.57 [821]~E(x8211,x8212)+E(f172(x8213,x8214,x8211),f172(x8213,x8214,x8212)) % 154.70/154.57 [822]~E(x8221,x8222)+E(f452(x8221,x8223),f452(x8222,x8223)) % 154.70/154.57 [823]~E(x8231,x8232)+E(f452(x8233,x8231),f452(x8233,x8232)) % 154.70/154.57 [824]~E(x8241,x8242)+E(f274(x8241,x8243),f274(x8242,x8243)) % 154.70/154.57 [825]~E(x8251,x8252)+E(f274(x8253,x8251),f274(x8253,x8252)) % 154.70/154.57 [826]~E(x8261,x8262)+E(f419(x8261,x8263,x8264,x8265),f419(x8262,x8263,x8264,x8265)) % 154.70/154.57 [827]~E(x8271,x8272)+E(f419(x8273,x8271,x8274,x8275),f419(x8273,x8272,x8274,x8275)) % 154.70/154.57 [828]~E(x8281,x8282)+E(f419(x8283,x8284,x8281,x8285),f419(x8283,x8284,x8282,x8285)) % 154.70/154.57 [829]~E(x8291,x8292)+E(f419(x8293,x8294,x8295,x8291),f419(x8293,x8294,x8295,x8292)) % 154.70/154.57 [830]~E(x8301,x8302)+E(f613(x8301,x8303,x8304),f613(x8302,x8303,x8304)) % 154.70/154.57 [831]~E(x8311,x8312)+E(f613(x8313,x8311,x8314),f613(x8313,x8312,x8314)) % 154.70/154.57 [832]~E(x8321,x8322)+E(f613(x8323,x8324,x8321),f613(x8323,x8324,x8322)) % 154.70/154.57 [833]~E(x8331,x8332)+E(f640(x8331,x8333,x8334,x8335,x8336),f640(x8332,x8333,x8334,x8335,x8336)) % 154.70/154.57 [834]~E(x8341,x8342)+E(f640(x8343,x8341,x8344,x8345,x8346),f640(x8343,x8342,x8344,x8345,x8346)) % 154.70/154.57 [835]~E(x8351,x8352)+E(f640(x8353,x8354,x8351,x8355,x8356),f640(x8353,x8354,x8352,x8355,x8356)) % 154.70/154.57 [836]~E(x8361,x8362)+E(f640(x8363,x8364,x8365,x8361,x8366),f640(x8363,x8364,x8365,x8362,x8366)) % 154.70/154.57 [837]~E(x8371,x8372)+E(f640(x8373,x8374,x8375,x8376,x8371),f640(x8373,x8374,x8375,x8376,x8372)) % 154.70/154.57 [838]~E(x8381,x8382)+E(f143(x8381,x8383),f143(x8382,x8383)) % 154.70/154.57 [839]~E(x8391,x8392)+E(f143(x8393,x8391),f143(x8393,x8392)) % 154.70/154.57 [840]~E(x8401,x8402)+E(f816(x8401,x8403,x8404,x8405),f816(x8402,x8403,x8404,x8405)) % 154.70/154.57 [841]~E(x8411,x8412)+E(f816(x8413,x8411,x8414,x8415),f816(x8413,x8412,x8414,x8415)) % 154.70/154.57 [842]~E(x8421,x8422)+E(f816(x8423,x8424,x8421,x8425),f816(x8423,x8424,x8422,x8425)) % 154.70/154.57 [843]~E(x8431,x8432)+E(f816(x8433,x8434,x8435,x8431),f816(x8433,x8434,x8435,x8432)) % 154.70/154.57 [844]~E(x8441,x8442)+E(f658(x8441,x8443,x8444,x8445,x8446),f658(x8442,x8443,x8444,x8445,x8446)) % 154.70/154.57 [845]~E(x8451,x8452)+E(f658(x8453,x8451,x8454,x8455,x8456),f658(x8453,x8452,x8454,x8455,x8456)) % 154.70/154.57 [846]~E(x8461,x8462)+E(f658(x8463,x8464,x8461,x8465,x8466),f658(x8463,x8464,x8462,x8465,x8466)) % 154.70/154.57 [847]~E(x8471,x8472)+E(f658(x8473,x8474,x8475,x8471,x8476),f658(x8473,x8474,x8475,x8472,x8476)) % 154.70/154.57 [848]~E(x8481,x8482)+E(f658(x8483,x8484,x8485,x8486,x8481),f658(x8483,x8484,x8485,x8486,x8482)) % 154.70/154.57 [849]~E(x8491,x8492)+E(f411(x8491,x8493),f411(x8492,x8493)) % 154.70/154.57 [850]~E(x8501,x8502)+E(f411(x8503,x8501),f411(x8503,x8502)) % 154.70/154.57 [851]~E(x8511,x8512)+E(f344(x8511,x8513,x8514,x8515),f344(x8512,x8513,x8514,x8515)) % 154.70/154.57 [852]~E(x8521,x8522)+E(f344(x8523,x8521,x8524,x8525),f344(x8523,x8522,x8524,x8525)) % 154.70/154.57 [853]~E(x8531,x8532)+E(f344(x8533,x8534,x8531,x8535),f344(x8533,x8534,x8532,x8535)) % 154.70/154.57 [854]~E(x8541,x8542)+E(f344(x8543,x8544,x8545,x8541),f344(x8543,x8544,x8545,x8542)) % 154.70/154.57 [855]~E(x8551,x8552)+E(f190(x8551),f190(x8552)) % 154.70/154.57 [856]~E(x8561,x8562)+E(f765(x8561,x8563,x8564,x8565),f765(x8562,x8563,x8564,x8565)) % 154.70/154.57 [857]~E(x8571,x8572)+E(f765(x8573,x8571,x8574,x8575),f765(x8573,x8572,x8574,x8575)) % 154.70/154.57 [858]~E(x8581,x8582)+E(f765(x8583,x8584,x8581,x8585),f765(x8583,x8584,x8582,x8585)) % 154.70/154.57 [859]~E(x8591,x8592)+E(f765(x8593,x8594,x8595,x8591),f765(x8593,x8594,x8595,x8592)) % 154.70/154.57 [860]~E(x8601,x8602)+E(f279(x8601,x8603),f279(x8602,x8603)) % 154.70/154.57 [861]~E(x8611,x8612)+E(f279(x8613,x8611),f279(x8613,x8612)) % 154.70/154.57 [862]~E(x8621,x8622)+E(f864(x8621,x8623,x8624,x8625),f864(x8622,x8623,x8624,x8625)) % 154.70/154.57 [863]~E(x8631,x8632)+E(f864(x8633,x8631,x8634,x8635),f864(x8633,x8632,x8634,x8635)) % 154.70/154.57 [864]~E(x8641,x8642)+E(f864(x8643,x8644,x8641,x8645),f864(x8643,x8644,x8642,x8645)) % 154.70/154.57 [865]~E(x8651,x8652)+E(f864(x8653,x8654,x8655,x8651),f864(x8653,x8654,x8655,x8652)) % 154.70/154.57 [866]~E(x8661,x8662)+E(f388(x8661,x8663,x8664),f388(x8662,x8663,x8664)) % 154.70/154.57 [867]~E(x8671,x8672)+E(f388(x8673,x8671,x8674),f388(x8673,x8672,x8674)) % 154.70/154.57 [868]~E(x8681,x8682)+E(f388(x8683,x8684,x8681),f388(x8683,x8684,x8682)) % 154.70/154.57 [869]~E(x8691,x8692)+E(f745(x8691,x8693),f745(x8692,x8693)) % 154.70/154.57 [870]~E(x8701,x8702)+E(f745(x8703,x8701),f745(x8703,x8702)) % 154.70/154.57 [871]~E(x8711,x8712)+E(f441(x8711,x8713,x8714),f441(x8712,x8713,x8714)) % 154.70/154.57 [872]~E(x8721,x8722)+E(f441(x8723,x8721,x8724),f441(x8723,x8722,x8724)) % 154.70/154.57 [873]~E(x8731,x8732)+E(f441(x8733,x8734,x8731),f441(x8733,x8734,x8732)) % 154.70/154.57 [874]~E(x8741,x8742)+E(f271(x8741,x8743,x8744,x8745,x8746),f271(x8742,x8743,x8744,x8745,x8746)) % 154.70/154.57 [875]~E(x8751,x8752)+E(f271(x8753,x8751,x8754,x8755,x8756),f271(x8753,x8752,x8754,x8755,x8756)) % 154.70/154.57 [876]~E(x8761,x8762)+E(f271(x8763,x8764,x8761,x8765,x8766),f271(x8763,x8764,x8762,x8765,x8766)) % 154.70/154.57 [877]~E(x8771,x8772)+E(f271(x8773,x8774,x8775,x8771,x8776),f271(x8773,x8774,x8775,x8772,x8776)) % 154.70/154.57 [878]~E(x8781,x8782)+E(f271(x8783,x8784,x8785,x8786,x8781),f271(x8783,x8784,x8785,x8786,x8782)) % 154.70/154.57 [879]~E(x8791,x8792)+E(f660(x8791,x8793,x8794,x8795,x8796,x8797),f660(x8792,x8793,x8794,x8795,x8796,x8797)) % 154.70/154.57 [880]~E(x8801,x8802)+E(f660(x8803,x8801,x8804,x8805,x8806,x8807),f660(x8803,x8802,x8804,x8805,x8806,x8807)) % 154.70/154.57 [881]~E(x8811,x8812)+E(f660(x8813,x8814,x8811,x8815,x8816,x8817),f660(x8813,x8814,x8812,x8815,x8816,x8817)) % 154.70/154.57 [882]~E(x8821,x8822)+E(f660(x8823,x8824,x8825,x8821,x8826,x8827),f660(x8823,x8824,x8825,x8822,x8826,x8827)) % 154.70/154.57 [883]~E(x8831,x8832)+E(f660(x8833,x8834,x8835,x8836,x8831,x8837),f660(x8833,x8834,x8835,x8836,x8832,x8837)) % 154.70/154.57 [884]~E(x8841,x8842)+E(f660(x8843,x8844,x8845,x8846,x8847,x8841),f660(x8843,x8844,x8845,x8846,x8847,x8842)) % 154.70/154.57 [885]~E(x8851,x8852)+E(f196(x8851,x8853),f196(x8852,x8853)) % 154.70/154.57 [886]~E(x8861,x8862)+E(f196(x8863,x8861),f196(x8863,x8862)) % 154.70/154.57 [887]~E(x8871,x8872)+E(f847(x8871,x8873,x8874,x8875,x8876),f847(x8872,x8873,x8874,x8875,x8876)) % 154.70/154.57 [888]~E(x8881,x8882)+E(f847(x8883,x8881,x8884,x8885,x8886),f847(x8883,x8882,x8884,x8885,x8886)) % 154.70/154.57 [889]~E(x8891,x8892)+E(f847(x8893,x8894,x8891,x8895,x8896),f847(x8893,x8894,x8892,x8895,x8896)) % 154.70/154.57 [890]~E(x8901,x8902)+E(f847(x8903,x8904,x8905,x8901,x8906),f847(x8903,x8904,x8905,x8902,x8906)) % 154.70/154.57 [891]~E(x8911,x8912)+E(f847(x8913,x8914,x8915,x8916,x8911),f847(x8913,x8914,x8915,x8916,x8912)) % 154.70/154.57 [892]~E(x8921,x8922)+E(f122(x8921,x8923),f122(x8922,x8923)) % 154.70/154.57 [893]~E(x8931,x8932)+E(f122(x8933,x8931),f122(x8933,x8932)) % 154.70/154.57 [894]~E(x8941,x8942)+E(f657(x8941,x8943),f657(x8942,x8943)) % 154.70/154.57 [895]~E(x8951,x8952)+E(f657(x8953,x8951),f657(x8953,x8952)) % 154.70/154.57 [896]~E(x8961,x8962)+E(f121(x8961,x8963,x8964),f121(x8962,x8963,x8964)) % 154.70/154.57 [897]~E(x8971,x8972)+E(f121(x8973,x8971,x8974),f121(x8973,x8972,x8974)) % 154.70/154.57 [898]~E(x8981,x8982)+E(f121(x8983,x8984,x8981),f121(x8983,x8984,x8982)) % 154.70/154.57 [899]~E(x8991,x8992)+E(f734(x8991,x8993),f734(x8992,x8993)) % 154.70/154.57 [900]~E(x9001,x9002)+E(f734(x9003,x9001),f734(x9003,x9002)) % 154.70/154.57 [901]~E(x9011,x9012)+E(f66(x9011,x9013,x9014,x9015,x9016),f66(x9012,x9013,x9014,x9015,x9016)) % 154.70/154.57 [902]~E(x9021,x9022)+E(f66(x9023,x9021,x9024,x9025,x9026),f66(x9023,x9022,x9024,x9025,x9026)) % 154.70/154.57 [903]~E(x9031,x9032)+E(f66(x9033,x9034,x9031,x9035,x9036),f66(x9033,x9034,x9032,x9035,x9036)) % 154.70/154.57 [904]~E(x9041,x9042)+E(f66(x9043,x9044,x9045,x9041,x9046),f66(x9043,x9044,x9045,x9042,x9046)) % 154.70/154.57 [905]~E(x9051,x9052)+E(f66(x9053,x9054,x9055,x9056,x9051),f66(x9053,x9054,x9055,x9056,x9052)) % 154.70/154.57 [906]~E(x9061,x9062)+E(f768(x9061,x9063),f768(x9062,x9063)) % 154.70/154.57 [907]~E(x9071,x9072)+E(f768(x9073,x9071),f768(x9073,x9072)) % 154.70/154.57 [908]~E(x9081,x9082)+E(f399(x9081,x9083,x9084,x9085),f399(x9082,x9083,x9084,x9085)) % 154.70/154.57 [909]~E(x9091,x9092)+E(f399(x9093,x9091,x9094,x9095),f399(x9093,x9092,x9094,x9095)) % 154.70/154.57 [910]~E(x9101,x9102)+E(f399(x9103,x9104,x9101,x9105),f399(x9103,x9104,x9102,x9105)) % 154.70/154.57 [911]~E(x9111,x9112)+E(f399(x9113,x9114,x9115,x9111),f399(x9113,x9114,x9115,x9112)) % 154.70/154.57 [912]~E(x9121,x9122)+E(f417(x9121,x9123,x9124,x9125),f417(x9122,x9123,x9124,x9125)) % 154.70/154.57 [913]~E(x9131,x9132)+E(f417(x9133,x9131,x9134,x9135),f417(x9133,x9132,x9134,x9135)) % 154.70/154.57 [914]~E(x9141,x9142)+E(f417(x9143,x9144,x9141,x9145),f417(x9143,x9144,x9142,x9145)) % 154.70/154.57 [915]~E(x9151,x9152)+E(f417(x9153,x9154,x9155,x9151),f417(x9153,x9154,x9155,x9152)) % 154.70/154.57 [916]~E(x9161,x9162)+E(f603(x9161,x9163,x9164,x9165,x9166),f603(x9162,x9163,x9164,x9165,x9166)) % 154.70/154.57 [917]~E(x9171,x9172)+E(f603(x9173,x9171,x9174,x9175,x9176),f603(x9173,x9172,x9174,x9175,x9176)) % 154.70/154.57 [918]~E(x9181,x9182)+E(f603(x9183,x9184,x9181,x9185,x9186),f603(x9183,x9184,x9182,x9185,x9186)) % 154.70/154.57 [919]~E(x9191,x9192)+E(f603(x9193,x9194,x9195,x9191,x9196),f603(x9193,x9194,x9195,x9192,x9196)) % 154.70/154.57 [920]~E(x9201,x9202)+E(f603(x9203,x9204,x9205,x9206,x9201),f603(x9203,x9204,x9205,x9206,x9202)) % 154.70/154.57 [921]~E(x9211,x9212)+E(f254(x9211,x9213,x9214),f254(x9212,x9213,x9214)) % 154.70/154.57 [922]~E(x9221,x9222)+E(f254(x9223,x9221,x9224),f254(x9223,x9222,x9224)) % 154.70/154.57 [923]~E(x9231,x9232)+E(f254(x9233,x9234,x9231),f254(x9233,x9234,x9232)) % 154.70/154.57 [924]~E(x9241,x9242)+E(f209(x9241),f209(x9242)) % 154.70/154.57 [925]~E(x9251,x9252)+E(f477(x9251,x9253,x9254),f477(x9252,x9253,x9254)) % 154.70/154.57 [926]~E(x9261,x9262)+E(f477(x9263,x9261,x9264),f477(x9263,x9262,x9264)) % 154.70/154.57 [927]~E(x9271,x9272)+E(f477(x9273,x9274,x9271),f477(x9273,x9274,x9272)) % 154.70/154.57 [928]~E(x9281,x9282)+E(f281(x9281),f281(x9282)) % 154.70/154.57 [929]~E(x9291,x9292)+E(f542(x9291,x9293,x9294),f542(x9292,x9293,x9294)) % 154.70/154.57 [930]~E(x9301,x9302)+E(f542(x9303,x9301,x9304),f542(x9303,x9302,x9304)) % 154.70/154.57 [931]~E(x9311,x9312)+E(f542(x9313,x9314,x9311),f542(x9313,x9314,x9312)) % 154.70/154.57 [932]~E(x9321,x9322)+E(f580(x9321,x9323,x9324,x9325,x9326),f580(x9322,x9323,x9324,x9325,x9326)) % 154.70/154.57 [933]~E(x9331,x9332)+E(f580(x9333,x9331,x9334,x9335,x9336),f580(x9333,x9332,x9334,x9335,x9336)) % 154.70/154.57 [934]~E(x9341,x9342)+E(f580(x9343,x9344,x9341,x9345,x9346),f580(x9343,x9344,x9342,x9345,x9346)) % 154.70/154.57 [935]~E(x9351,x9352)+E(f580(x9353,x9354,x9355,x9351,x9356),f580(x9353,x9354,x9355,x9352,x9356)) % 154.70/154.57 [936]~E(x9361,x9362)+E(f580(x9363,x9364,x9365,x9366,x9361),f580(x9363,x9364,x9365,x9366,x9362)) % 154.70/154.57 [937]~E(x9371,x9372)+E(f826(x9371,x9373,x9374),f826(x9372,x9373,x9374)) % 154.70/154.57 [938]~E(x9381,x9382)+E(f826(x9383,x9381,x9384),f826(x9383,x9382,x9384)) % 154.70/154.57 [939]~E(x9391,x9392)+E(f826(x9393,x9394,x9391),f826(x9393,x9394,x9392)) % 154.70/154.57 [940]~E(x9401,x9402)+E(f702(x9401,x9403,x9404,x9405),f702(x9402,x9403,x9404,x9405)) % 154.70/154.57 [941]~E(x9411,x9412)+E(f702(x9413,x9411,x9414,x9415),f702(x9413,x9412,x9414,x9415)) % 154.70/154.57 [942]~E(x9421,x9422)+E(f702(x9423,x9424,x9421,x9425),f702(x9423,x9424,x9422,x9425)) % 154.70/154.57 [943]~E(x9431,x9432)+E(f702(x9433,x9434,x9435,x9431),f702(x9433,x9434,x9435,x9432)) % 154.70/154.57 [944]~E(x9441,x9442)+E(f322(x9441,x9443,x9444),f322(x9442,x9443,x9444)) % 154.70/154.57 [945]~E(x9451,x9452)+E(f322(x9453,x9451,x9454),f322(x9453,x9452,x9454)) % 154.70/154.57 [946]~E(x9461,x9462)+E(f322(x9463,x9464,x9461),f322(x9463,x9464,x9462)) % 154.70/154.57 [947]~E(x9471,x9472)+E(f679(x9471,x9473,x9474,x9475),f679(x9472,x9473,x9474,x9475)) % 154.70/154.57 [948]~E(x9481,x9482)+E(f679(x9483,x9481,x9484,x9485),f679(x9483,x9482,x9484,x9485)) % 154.70/154.57 [949]~E(x9491,x9492)+E(f679(x9493,x9494,x9491,x9495),f679(x9493,x9494,x9492,x9495)) % 154.70/154.57 [950]~E(x9501,x9502)+E(f679(x9503,x9504,x9505,x9501),f679(x9503,x9504,x9505,x9502)) % 154.70/154.57 [951]~E(x9511,x9512)+E(f582(x9511,x9513,x9514,x9515,x9516),f582(x9512,x9513,x9514,x9515,x9516)) % 154.70/154.57 [952]~E(x9521,x9522)+E(f582(x9523,x9521,x9524,x9525,x9526),f582(x9523,x9522,x9524,x9525,x9526)) % 154.70/154.57 [953]~E(x9531,x9532)+E(f582(x9533,x9534,x9531,x9535,x9536),f582(x9533,x9534,x9532,x9535,x9536)) % 154.70/154.57 [954]~E(x9541,x9542)+E(f582(x9543,x9544,x9545,x9541,x9546),f582(x9543,x9544,x9545,x9542,x9546)) % 154.70/154.57 [955]~E(x9551,x9552)+E(f582(x9553,x9554,x9555,x9556,x9551),f582(x9553,x9554,x9555,x9556,x9552)) % 154.70/154.57 [956]~E(x9561,x9562)+E(f310(x9561,x9563,x9564),f310(x9562,x9563,x9564)) % 154.70/154.57 [957]~E(x9571,x9572)+E(f310(x9573,x9571,x9574),f310(x9573,x9572,x9574)) % 154.70/154.57 [958]~E(x9581,x9582)+E(f310(x9583,x9584,x9581),f310(x9583,x9584,x9582)) % 154.70/154.57 [959]~E(x9591,x9592)+E(f797(x9591,x9593),f797(x9592,x9593)) % 154.70/154.57 [960]~E(x9601,x9602)+E(f797(x9603,x9601),f797(x9603,x9602)) % 154.70/154.57 [961]~E(x9611,x9612)+E(f856(x9611,x9613,x9614,x9615,x9616),f856(x9612,x9613,x9614,x9615,x9616)) % 154.70/154.57 [962]~E(x9621,x9622)+E(f856(x9623,x9621,x9624,x9625,x9626),f856(x9623,x9622,x9624,x9625,x9626)) % 154.70/154.57 [963]~E(x9631,x9632)+E(f856(x9633,x9634,x9631,x9635,x9636),f856(x9633,x9634,x9632,x9635,x9636)) % 154.70/154.57 [964]~E(x9641,x9642)+E(f856(x9643,x9644,x9645,x9641,x9646),f856(x9643,x9644,x9645,x9642,x9646)) % 154.70/154.57 [965]~E(x9651,x9652)+E(f856(x9653,x9654,x9655,x9656,x9651),f856(x9653,x9654,x9655,x9656,x9652)) % 154.70/154.57 [966]~E(x9661,x9662)+E(f737(x9661,x9663,x9664,x9665,x9666),f737(x9662,x9663,x9664,x9665,x9666)) % 154.70/154.57 [967]~E(x9671,x9672)+E(f737(x9673,x9671,x9674,x9675,x9676),f737(x9673,x9672,x9674,x9675,x9676)) % 154.70/154.57 [968]~E(x9681,x9682)+E(f737(x9683,x9684,x9681,x9685,x9686),f737(x9683,x9684,x9682,x9685,x9686)) % 154.70/154.57 [969]~E(x9691,x9692)+E(f737(x9693,x9694,x9695,x9691,x9696),f737(x9693,x9694,x9695,x9692,x9696)) % 154.70/154.57 [970]~E(x9701,x9702)+E(f737(x9703,x9704,x9705,x9706,x9701),f737(x9703,x9704,x9705,x9706,x9702)) % 154.70/154.57 [971]~E(x9711,x9712)+E(f656(x9711,x9713,x9714,x9715),f656(x9712,x9713,x9714,x9715)) % 154.70/154.57 [972]~E(x9721,x9722)+E(f656(x9723,x9721,x9724,x9725),f656(x9723,x9722,x9724,x9725)) % 154.70/154.57 [973]~E(x9731,x9732)+E(f656(x9733,x9734,x9731,x9735),f656(x9733,x9734,x9732,x9735)) % 154.70/154.57 [974]~E(x9741,x9742)+E(f656(x9743,x9744,x9745,x9741),f656(x9743,x9744,x9745,x9742)) % 154.70/154.57 [975]~E(x9751,x9752)+E(f671(x9751,x9753,x9754,x9755,x9756),f671(x9752,x9753,x9754,x9755,x9756)) % 154.70/154.57 [976]~E(x9761,x9762)+E(f671(x9763,x9761,x9764,x9765,x9766),f671(x9763,x9762,x9764,x9765,x9766)) % 154.70/154.57 [977]~E(x9771,x9772)+E(f671(x9773,x9774,x9771,x9775,x9776),f671(x9773,x9774,x9772,x9775,x9776)) % 154.70/154.57 [978]~E(x9781,x9782)+E(f671(x9783,x9784,x9785,x9781,x9786),f671(x9783,x9784,x9785,x9782,x9786)) % 154.70/154.57 [979]~E(x9791,x9792)+E(f671(x9793,x9794,x9795,x9796,x9791),f671(x9793,x9794,x9795,x9796,x9792)) % 154.70/154.57 [980]~E(x9801,x9802)+E(f422(x9801,x9803),f422(x9802,x9803)) % 154.70/154.57 [981]~E(x9811,x9812)+E(f422(x9813,x9811),f422(x9813,x9812)) % 154.70/154.57 [982]~E(x9821,x9822)+E(f855(x9821,x9823,x9824,x9825,x9826),f855(x9822,x9823,x9824,x9825,x9826)) % 154.70/154.57 [983]~E(x9831,x9832)+E(f855(x9833,x9831,x9834,x9835,x9836),f855(x9833,x9832,x9834,x9835,x9836)) % 154.70/154.57 [984]~E(x9841,x9842)+E(f855(x9843,x9844,x9841,x9845,x9846),f855(x9843,x9844,x9842,x9845,x9846)) % 154.70/154.57 [985]~E(x9851,x9852)+E(f855(x9853,x9854,x9855,x9851,x9856),f855(x9853,x9854,x9855,x9852,x9856)) % 154.70/154.57 [986]~E(x9861,x9862)+E(f855(x9863,x9864,x9865,x9866,x9861),f855(x9863,x9864,x9865,x9866,x9862)) % 154.70/154.57 [987]~E(x9871,x9872)+E(f611(x9871,x9873),f611(x9872,x9873)) % 154.70/154.57 [988]~E(x9881,x9882)+E(f611(x9883,x9881),f611(x9883,x9882)) % 154.70/154.57 [989]~E(x9891,x9892)+E(f215(x9891),f215(x9892)) % 154.70/154.57 [990]~E(x9901,x9902)+E(f29(x9901,x9903,x9904),f29(x9902,x9903,x9904)) % 154.70/154.57 [991]~E(x9911,x9912)+E(f29(x9913,x9911,x9914),f29(x9913,x9912,x9914)) % 154.70/154.57 [992]~E(x9921,x9922)+E(f29(x9923,x9924,x9921),f29(x9923,x9924,x9922)) % 154.70/154.57 [993]~E(x9931,x9932)+E(f645(x9931,x9933,x9934,x9935,x9936),f645(x9932,x9933,x9934,x9935,x9936)) % 154.70/154.57 [994]~E(x9941,x9942)+E(f645(x9943,x9941,x9944,x9945,x9946),f645(x9943,x9942,x9944,x9945,x9946)) % 154.70/154.57 [995]~E(x9951,x9952)+E(f645(x9953,x9954,x9951,x9955,x9956),f645(x9953,x9954,x9952,x9955,x9956)) % 154.70/154.57 [996]~E(x9961,x9962)+E(f645(x9963,x9964,x9965,x9961,x9966),f645(x9963,x9964,x9965,x9962,x9966)) % 154.70/154.57 [997]~E(x9971,x9972)+E(f645(x9973,x9974,x9975,x9976,x9971),f645(x9973,x9974,x9975,x9976,x9972)) % 154.70/154.57 [998]~E(x9981,x9982)+E(f338(x9981),f338(x9982)) % 154.70/154.57 [999]~E(x9991,x9992)+E(f17(x9991,x9993,x9994,x9995),f17(x9992,x9993,x9994,x9995)) % 154.70/154.57 [1000]~E(x10001,x10002)+E(f17(x10003,x10001,x10004,x10005),f17(x10003,x10002,x10004,x10005)) % 154.70/154.57 [1001]~E(x10011,x10012)+E(f17(x10013,x10014,x10011,x10015),f17(x10013,x10014,x10012,x10015)) % 154.70/154.57 [1002]~E(x10021,x10022)+E(f17(x10023,x10024,x10025,x10021),f17(x10023,x10024,x10025,x10022)) % 154.70/154.57 [1003]~E(x10031,x10032)+E(f347(x10031,x10033,x10034,x10035,x10036),f347(x10032,x10033,x10034,x10035,x10036)) % 154.70/154.57 [1004]~E(x10041,x10042)+E(f347(x10043,x10041,x10044,x10045,x10046),f347(x10043,x10042,x10044,x10045,x10046)) % 154.70/154.57 [1005]~E(x10051,x10052)+E(f347(x10053,x10054,x10051,x10055,x10056),f347(x10053,x10054,x10052,x10055,x10056)) % 154.70/154.57 [1006]~E(x10061,x10062)+E(f347(x10063,x10064,x10065,x10061,x10066),f347(x10063,x10064,x10065,x10062,x10066)) % 154.70/154.57 [1007]~E(x10071,x10072)+E(f347(x10073,x10074,x10075,x10076,x10071),f347(x10073,x10074,x10075,x10076,x10072)) % 154.70/154.57 [1008]~E(x10081,x10082)+E(f698(x10081,x10083,x10084,x10085,x10086),f698(x10082,x10083,x10084,x10085,x10086)) % 154.70/154.57 [1009]~E(x10091,x10092)+E(f698(x10093,x10091,x10094,x10095,x10096),f698(x10093,x10092,x10094,x10095,x10096)) % 154.70/154.57 [1010]~E(x10101,x10102)+E(f698(x10103,x10104,x10101,x10105,x10106),f698(x10103,x10104,x10102,x10105,x10106)) % 154.70/154.57 [1011]~E(x10111,x10112)+E(f698(x10113,x10114,x10115,x10111,x10116),f698(x10113,x10114,x10115,x10112,x10116)) % 154.70/154.57 [1012]~E(x10121,x10122)+E(f698(x10123,x10124,x10125,x10126,x10121),f698(x10123,x10124,x10125,x10126,x10122)) % 154.70/154.57 [1013]~E(x10131,x10132)+E(f715(x10131,x10133,x10134,x10135,x10136),f715(x10132,x10133,x10134,x10135,x10136)) % 154.70/154.57 [1014]~E(x10141,x10142)+E(f715(x10143,x10141,x10144,x10145,x10146),f715(x10143,x10142,x10144,x10145,x10146)) % 154.70/154.57 [1015]~E(x10151,x10152)+E(f715(x10153,x10154,x10151,x10155,x10156),f715(x10153,x10154,x10152,x10155,x10156)) % 154.70/154.57 [1016]~E(x10161,x10162)+E(f715(x10163,x10164,x10165,x10161,x10166),f715(x10163,x10164,x10165,x10162,x10166)) % 154.70/154.57 [1017]~E(x10171,x10172)+E(f715(x10173,x10174,x10175,x10176,x10171),f715(x10173,x10174,x10175,x10176,x10172)) % 154.70/154.57 [1018]~E(x10181,x10182)+E(f762(x10181,x10183),f762(x10182,x10183)) % 154.70/154.57 [1019]~E(x10191,x10192)+E(f762(x10193,x10191),f762(x10193,x10192)) % 154.70/154.57 [1020]~E(x10201,x10202)+E(f791(x10201,x10203,x10204,x10205),f791(x10202,x10203,x10204,x10205)) % 154.70/154.57 [1021]~E(x10211,x10212)+E(f791(x10213,x10211,x10214,x10215),f791(x10213,x10212,x10214,x10215)) % 154.70/154.57 [1022]~E(x10221,x10222)+E(f791(x10223,x10224,x10221,x10225),f791(x10223,x10224,x10222,x10225)) % 154.70/154.57 [1023]~E(x10231,x10232)+E(f791(x10233,x10234,x10235,x10231),f791(x10233,x10234,x10235,x10232)) % 154.70/154.57 [1024]~E(x10241,x10242)+E(f443(x10241,x10243,x10244,x10245),f443(x10242,x10243,x10244,x10245)) % 154.70/154.57 [1025]~E(x10251,x10252)+E(f443(x10253,x10251,x10254,x10255),f443(x10253,x10252,x10254,x10255)) % 154.70/154.57 [1026]~E(x10261,x10262)+E(f443(x10263,x10264,x10261,x10265),f443(x10263,x10264,x10262,x10265)) % 154.70/154.57 [1027]~E(x10271,x10272)+E(f443(x10273,x10274,x10275,x10271),f443(x10273,x10274,x10275,x10272)) % 154.70/154.57 [1028]~E(x10281,x10282)+E(f238(x10281,x10283,x10284,x10285,x10286),f238(x10282,x10283,x10284,x10285,x10286)) % 154.70/154.57 [1029]~E(x10291,x10292)+E(f238(x10293,x10291,x10294,x10295,x10296),f238(x10293,x10292,x10294,x10295,x10296)) % 154.70/154.57 [1030]~E(x10301,x10302)+E(f238(x10303,x10304,x10301,x10305,x10306),f238(x10303,x10304,x10302,x10305,x10306)) % 154.70/154.57 [1031]~E(x10311,x10312)+E(f238(x10313,x10314,x10315,x10311,x10316),f238(x10313,x10314,x10315,x10312,x10316)) % 154.70/154.57 [1032]~E(x10321,x10322)+E(f238(x10323,x10324,x10325,x10326,x10321),f238(x10323,x10324,x10325,x10326,x10322)) % 154.70/154.57 [1033]~E(x10331,x10332)+E(f860(x10331,x10333,x10334,x10335),f860(x10332,x10333,x10334,x10335)) % 154.70/154.57 [1034]~E(x10341,x10342)+E(f860(x10343,x10341,x10344,x10345),f860(x10343,x10342,x10344,x10345)) % 154.70/154.57 [1035]~E(x10351,x10352)+E(f860(x10353,x10354,x10351,x10355),f860(x10353,x10354,x10352,x10355)) % 154.70/154.57 [1036]~E(x10361,x10362)+E(f860(x10363,x10364,x10365,x10361),f860(x10363,x10364,x10365,x10362)) % 154.70/154.57 [1037]~E(x10371,x10372)+E(f571(x10371,x10373,x10374),f571(x10372,x10373,x10374)) % 154.70/154.57 [1038]~E(x10381,x10382)+E(f571(x10383,x10381,x10384),f571(x10383,x10382,x10384)) % 154.70/154.57 [1039]~E(x10391,x10392)+E(f571(x10393,x10394,x10391),f571(x10393,x10394,x10392)) % 154.70/154.57 [1040]~E(x10401,x10402)+E(f693(x10401,x10403,x10404,x10405),f693(x10402,x10403,x10404,x10405)) % 154.70/154.57 [1041]~E(x10411,x10412)+E(f693(x10413,x10411,x10414,x10415),f693(x10413,x10412,x10414,x10415)) % 154.70/154.57 [1042]~E(x10421,x10422)+E(f693(x10423,x10424,x10421,x10425),f693(x10423,x10424,x10422,x10425)) % 154.70/154.57 [1043]~E(x10431,x10432)+E(f693(x10433,x10434,x10435,x10431),f693(x10433,x10434,x10435,x10432)) % 154.70/154.57 [1044]~E(x10441,x10442)+E(f535(x10441,x10443,x10444),f535(x10442,x10443,x10444)) % 154.70/154.57 [1045]~E(x10451,x10452)+E(f535(x10453,x10451,x10454),f535(x10453,x10452,x10454)) % 154.70/154.57 [1046]~E(x10461,x10462)+E(f535(x10463,x10464,x10461),f535(x10463,x10464,x10462)) % 154.70/154.57 [1047]~E(x10471,x10472)+E(f667(x10471,x10473,x10474,x10475),f667(x10472,x10473,x10474,x10475)) % 154.70/154.57 [1048]~E(x10481,x10482)+E(f667(x10483,x10481,x10484,x10485),f667(x10483,x10482,x10484,x10485)) % 154.70/154.57 [1049]~E(x10491,x10492)+E(f667(x10493,x10494,x10491,x10495),f667(x10493,x10494,x10492,x10495)) % 154.70/154.57 [1050]~E(x10501,x10502)+E(f667(x10503,x10504,x10505,x10501),f667(x10503,x10504,x10505,x10502)) % 154.70/154.57 [1051]~E(x10511,x10512)+E(f184(x10511,x10513,x10514),f184(x10512,x10513,x10514)) % 154.70/154.57 [1052]~E(x10521,x10522)+E(f184(x10523,x10521,x10524),f184(x10523,x10522,x10524)) % 154.70/154.57 [1053]~E(x10531,x10532)+E(f184(x10533,x10534,x10531),f184(x10533,x10534,x10532)) % 154.70/154.57 [1054]~E(x10541,x10542)+E(f575(x10541,x10543,x10544,x10545,x10546,x10547),f575(x10542,x10543,x10544,x10545,x10546,x10547)) % 154.70/154.57 [1055]~E(x10551,x10552)+E(f575(x10553,x10551,x10554,x10555,x10556,x10557),f575(x10553,x10552,x10554,x10555,x10556,x10557)) % 154.70/154.57 [1056]~E(x10561,x10562)+E(f575(x10563,x10564,x10561,x10565,x10566,x10567),f575(x10563,x10564,x10562,x10565,x10566,x10567)) % 154.70/154.57 [1057]~E(x10571,x10572)+E(f575(x10573,x10574,x10575,x10571,x10576,x10577),f575(x10573,x10574,x10575,x10572,x10576,x10577)) % 154.70/154.57 [1058]~E(x10581,x10582)+E(f575(x10583,x10584,x10585,x10586,x10581,x10587),f575(x10583,x10584,x10585,x10586,x10582,x10587)) % 154.70/154.57 [1059]~E(x10591,x10592)+E(f575(x10593,x10594,x10595,x10596,x10597,x10591),f575(x10593,x10594,x10595,x10596,x10597,x10592)) % 154.70/154.57 [1060]~E(x10601,x10602)+E(f404(x10601,x10603,x10604,x10605,x10606,x10607),f404(x10602,x10603,x10604,x10605,x10606,x10607)) % 154.70/154.57 [1061]~E(x10611,x10612)+E(f404(x10613,x10611,x10614,x10615,x10616,x10617),f404(x10613,x10612,x10614,x10615,x10616,x10617)) % 154.70/154.57 [1062]~E(x10621,x10622)+E(f404(x10623,x10624,x10621,x10625,x10626,x10627),f404(x10623,x10624,x10622,x10625,x10626,x10627)) % 154.70/154.57 [1063]~E(x10631,x10632)+E(f404(x10633,x10634,x10635,x10631,x10636,x10637),f404(x10633,x10634,x10635,x10632,x10636,x10637)) % 154.70/154.57 [1064]~E(x10641,x10642)+E(f404(x10643,x10644,x10645,x10646,x10641,x10647),f404(x10643,x10644,x10645,x10646,x10642,x10647)) % 154.70/154.57 [1065]~E(x10651,x10652)+E(f404(x10653,x10654,x10655,x10656,x10657,x10651),f404(x10653,x10654,x10655,x10656,x10657,x10652)) % 154.70/154.57 [1066]~E(x10661,x10662)+E(f803(x10661,x10663,x10664),f803(x10662,x10663,x10664)) % 154.70/154.57 [1067]~E(x10671,x10672)+E(f803(x10673,x10671,x10674),f803(x10673,x10672,x10674)) % 154.70/154.57 [1068]~E(x10681,x10682)+E(f803(x10683,x10684,x10681),f803(x10683,x10684,x10682)) % 154.70/154.57 [1069]~E(x10691,x10692)+E(f588(x10691,x10693,x10694,x10695,x10696,x10697,x10698,x10699),f588(x10692,x10693,x10694,x10695,x10696,x10697,x10698,x10699)) % 154.70/154.57 [1070]~E(x10701,x10702)+E(f588(x10703,x10701,x10704,x10705,x10706,x10707,x10708,x10709),f588(x10703,x10702,x10704,x10705,x10706,x10707,x10708,x10709)) % 154.70/154.57 [1071]~E(x10711,x10712)+E(f588(x10713,x10714,x10711,x10715,x10716,x10717,x10718,x10719),f588(x10713,x10714,x10712,x10715,x10716,x10717,x10718,x10719)) % 154.70/154.57 [1072]~E(x10721,x10722)+E(f588(x10723,x10724,x10725,x10721,x10726,x10727,x10728,x10729),f588(x10723,x10724,x10725,x10722,x10726,x10727,x10728,x10729)) % 154.70/154.57 [1073]~E(x10731,x10732)+E(f588(x10733,x10734,x10735,x10736,x10731,x10737,x10738,x10739),f588(x10733,x10734,x10735,x10736,x10732,x10737,x10738,x10739)) % 154.70/154.57 [1074]~E(x10741,x10742)+E(f588(x10743,x10744,x10745,x10746,x10747,x10741,x10748,x10749),f588(x10743,x10744,x10745,x10746,x10747,x10742,x10748,x10749)) % 154.70/154.57 [1075]~E(x10751,x10752)+E(f588(x10753,x10754,x10755,x10756,x10757,x10758,x10751,x10759),f588(x10753,x10754,x10755,x10756,x10757,x10758,x10752,x10759)) % 154.70/154.57 [1076]~E(x10761,x10762)+E(f588(x10763,x10764,x10765,x10766,x10767,x10768,x10769,x10761),f588(x10763,x10764,x10765,x10766,x10767,x10768,x10769,x10762)) % 154.70/154.57 [1077]~E(x10771,x10772)+E(f479(x10771,x10773),f479(x10772,x10773)) % 154.70/154.57 [1078]~E(x10781,x10782)+E(f479(x10783,x10781),f479(x10783,x10782)) % 154.70/154.57 [1079]~E(x10791,x10792)+E(f381(x10791,x10793,x10794,x10795),f381(x10792,x10793,x10794,x10795)) % 154.70/154.57 [1080]~E(x10801,x10802)+E(f381(x10803,x10801,x10804,x10805),f381(x10803,x10802,x10804,x10805)) % 154.70/154.57 [1081]~E(x10811,x10812)+E(f381(x10813,x10814,x10811,x10815),f381(x10813,x10814,x10812,x10815)) % 154.70/154.57 [1082]~E(x10821,x10822)+E(f381(x10823,x10824,x10825,x10821),f381(x10823,x10824,x10825,x10822)) % 154.70/154.57 [1083]~E(x10831,x10832)+E(f406(x10831,x10833,x10834),f406(x10832,x10833,x10834)) % 154.70/154.57 [1084]~E(x10841,x10842)+E(f406(x10843,x10841,x10844),f406(x10843,x10842,x10844)) % 154.70/154.57 [1085]~E(x10851,x10852)+E(f406(x10853,x10854,x10851),f406(x10853,x10854,x10852)) % 154.70/154.57 [1086]~E(x10861,x10862)+E(f701(x10861,x10863,x10864,x10865),f701(x10862,x10863,x10864,x10865)) % 154.70/154.57 [1087]~E(x10871,x10872)+E(f701(x10873,x10871,x10874,x10875),f701(x10873,x10872,x10874,x10875)) % 154.70/154.57 [1088]~E(x10881,x10882)+E(f701(x10883,x10884,x10881,x10885),f701(x10883,x10884,x10882,x10885)) % 154.70/154.57 [1089]~E(x10891,x10892)+E(f701(x10893,x10894,x10895,x10891),f701(x10893,x10894,x10895,x10892)) % 154.70/154.57 [1090]~E(x10901,x10902)+E(f869(x10901,x10903,x10904,x10905),f869(x10902,x10903,x10904,x10905)) % 154.70/154.57 [1091]~E(x10911,x10912)+E(f869(x10913,x10911,x10914,x10915),f869(x10913,x10912,x10914,x10915)) % 154.70/154.57 [1092]~E(x10921,x10922)+E(f869(x10923,x10924,x10921,x10925),f869(x10923,x10924,x10922,x10925)) % 154.70/154.57 [1093]~E(x10931,x10932)+E(f869(x10933,x10934,x10935,x10931),f869(x10933,x10934,x10935,x10932)) % 154.70/154.57 [1094]~E(x10941,x10942)+E(f854(x10941,x10943,x10944),f854(x10942,x10943,x10944)) % 154.70/154.57 [1095]~E(x10951,x10952)+E(f854(x10953,x10951,x10954),f854(x10953,x10952,x10954)) % 154.70/154.57 [1096]~E(x10961,x10962)+E(f854(x10963,x10964,x10961),f854(x10963,x10964,x10962)) % 154.70/154.57 [1097]~E(x10971,x10972)+E(f339(x10971),f339(x10972)) % 154.70/154.57 [1098]~E(x10981,x10982)+E(f550(x10981),f550(x10982)) % 154.70/154.57 [1099]~E(x10991,x10992)+E(f595(x10991,x10993,x10994,x10995),f595(x10992,x10993,x10994,x10995)) % 154.70/154.57 [1100]~E(x11001,x11002)+E(f595(x11003,x11001,x11004,x11005),f595(x11003,x11002,x11004,x11005)) % 154.70/154.57 [1101]~E(x11011,x11012)+E(f595(x11013,x11014,x11011,x11015),f595(x11013,x11014,x11012,x11015)) % 154.70/154.57 [1102]~E(x11021,x11022)+E(f595(x11023,x11024,x11025,x11021),f595(x11023,x11024,x11025,x11022)) % 154.70/154.57 [1103]~E(x11031,x11032)+E(f130(x11031,x11033,x11034,x11035,x11036),f130(x11032,x11033,x11034,x11035,x11036)) % 154.70/154.57 [1104]~E(x11041,x11042)+E(f130(x11043,x11041,x11044,x11045,x11046),f130(x11043,x11042,x11044,x11045,x11046)) % 154.70/154.57 [1105]~E(x11051,x11052)+E(f130(x11053,x11054,x11051,x11055,x11056),f130(x11053,x11054,x11052,x11055,x11056)) % 154.70/154.57 [1106]~E(x11061,x11062)+E(f130(x11063,x11064,x11065,x11061,x11066),f130(x11063,x11064,x11065,x11062,x11066)) % 154.70/154.57 [1107]~E(x11071,x11072)+E(f130(x11073,x11074,x11075,x11076,x11071),f130(x11073,x11074,x11075,x11076,x11072)) % 154.70/154.57 [1108]~E(x11081,x11082)+E(f257(x11081,x11083,x11084),f257(x11082,x11083,x11084)) % 154.70/154.57 [1109]~E(x11091,x11092)+E(f257(x11093,x11091,x11094),f257(x11093,x11092,x11094)) % 154.70/154.57 [1110]~E(x11101,x11102)+E(f257(x11103,x11104,x11101),f257(x11103,x11104,x11102)) % 154.70/154.57 [1111]~E(x11111,x11112)+E(f600(x11111,x11113,x11114),f600(x11112,x11113,x11114)) % 154.70/154.57 [1112]~E(x11121,x11122)+E(f600(x11123,x11121,x11124),f600(x11123,x11122,x11124)) % 154.70/154.57 [1113]~E(x11131,x11132)+E(f600(x11133,x11134,x11131),f600(x11133,x11134,x11132)) % 154.70/154.57 [1114]~E(x11141,x11142)+E(f834(x11141,x11143,x11144,x11145,x11146,x11147,x11148),f834(x11142,x11143,x11144,x11145,x11146,x11147,x11148)) % 154.70/154.57 [1115]~E(x11151,x11152)+E(f834(x11153,x11151,x11154,x11155,x11156,x11157,x11158),f834(x11153,x11152,x11154,x11155,x11156,x11157,x11158)) % 154.70/154.57 [1116]~E(x11161,x11162)+E(f834(x11163,x11164,x11161,x11165,x11166,x11167,x11168),f834(x11163,x11164,x11162,x11165,x11166,x11167,x11168)) % 154.70/154.57 [1117]~E(x11171,x11172)+E(f834(x11173,x11174,x11175,x11171,x11176,x11177,x11178),f834(x11173,x11174,x11175,x11172,x11176,x11177,x11178)) % 154.70/154.57 [1118]~E(x11181,x11182)+E(f834(x11183,x11184,x11185,x11186,x11181,x11187,x11188),f834(x11183,x11184,x11185,x11186,x11182,x11187,x11188)) % 154.70/154.57 [1119]~E(x11191,x11192)+E(f834(x11193,x11194,x11195,x11196,x11197,x11191,x11198),f834(x11193,x11194,x11195,x11196,x11197,x11192,x11198)) % 154.70/154.57 [1120]~E(x11201,x11202)+E(f834(x11203,x11204,x11205,x11206,x11207,x11208,x11201),f834(x11203,x11204,x11205,x11206,x11207,x11208,x11202)) % 154.70/154.57 [1121]~E(x11211,x11212)+E(f601(x11211,x11213,x11214),f601(x11212,x11213,x11214)) % 154.70/154.57 [1122]~E(x11221,x11222)+E(f601(x11223,x11221,x11224),f601(x11223,x11222,x11224)) % 154.70/154.57 [1123]~E(x11231,x11232)+E(f601(x11233,x11234,x11231),f601(x11233,x11234,x11232)) % 154.70/154.57 [1124]~E(x11241,x11242)+E(f551(x11241,x11243,x11244,x11245,x11246),f551(x11242,x11243,x11244,x11245,x11246)) % 154.70/154.57 [1125]~E(x11251,x11252)+E(f551(x11253,x11251,x11254,x11255,x11256),f551(x11253,x11252,x11254,x11255,x11256)) % 154.70/154.57 [1126]~E(x11261,x11262)+E(f551(x11263,x11264,x11261,x11265,x11266),f551(x11263,x11264,x11262,x11265,x11266)) % 154.70/154.57 [1127]~E(x11271,x11272)+E(f551(x11273,x11274,x11275,x11271,x11276),f551(x11273,x11274,x11275,x11272,x11276)) % 154.70/154.57 [1128]~E(x11281,x11282)+E(f551(x11283,x11284,x11285,x11286,x11281),f551(x11283,x11284,x11285,x11286,x11282)) % 154.70/154.57 [1129]~E(x11291,x11292)+E(f586(x11291,x11293,x11294),f586(x11292,x11293,x11294)) % 154.70/154.57 [1130]~E(x11301,x11302)+E(f586(x11303,x11301,x11304),f586(x11303,x11302,x11304)) % 154.70/154.57 [1131]~E(x11311,x11312)+E(f586(x11313,x11314,x11311),f586(x11313,x11314,x11312)) % 154.70/154.57 [1132]~E(x11321,x11322)+E(f764(x11321,x11323,x11324,x11325),f764(x11322,x11323,x11324,x11325)) % 154.70/154.57 [1133]~E(x11331,x11332)+E(f764(x11333,x11331,x11334,x11335),f764(x11333,x11332,x11334,x11335)) % 154.70/154.57 [1134]~E(x11341,x11342)+E(f764(x11343,x11344,x11341,x11345),f764(x11343,x11344,x11342,x11345)) % 154.70/154.57 [1135]~E(x11351,x11352)+E(f764(x11353,x11354,x11355,x11351),f764(x11353,x11354,x11355,x11352)) % 154.70/154.57 [1136]~E(x11361,x11362)+E(f291(x11361,x11363,x11364),f291(x11362,x11363,x11364)) % 154.70/154.57 [1137]~E(x11371,x11372)+E(f291(x11373,x11371,x11374),f291(x11373,x11372,x11374)) % 154.70/154.57 [1138]~E(x11381,x11382)+E(f291(x11383,x11384,x11381),f291(x11383,x11384,x11382)) % 154.70/154.57 [1139]~E(x11391,x11392)+E(f45(x11391,x11393),f45(x11392,x11393)) % 154.70/154.57 [1140]~E(x11401,x11402)+E(f45(x11403,x11401),f45(x11403,x11402)) % 154.70/154.57 [1141]~E(x11411,x11412)+E(f413(x11411,x11413),f413(x11412,x11413)) % 154.70/154.57 [1142]~E(x11421,x11422)+E(f413(x11423,x11421),f413(x11423,x11422)) % 154.70/154.57 [1143]~E(x11431,x11432)+E(f481(x11431,x11433),f481(x11432,x11433)) % 154.70/154.57 [1144]~E(x11441,x11442)+E(f481(x11443,x11441),f481(x11443,x11442)) % 154.70/154.57 [1145]~E(x11451,x11452)+E(f828(x11451,x11453,x11454),f828(x11452,x11453,x11454)) % 154.70/154.57 [1146]~E(x11461,x11462)+E(f828(x11463,x11461,x11464),f828(x11463,x11462,x11464)) % 154.70/154.57 [1147]~E(x11471,x11472)+E(f828(x11473,x11474,x11471),f828(x11473,x11474,x11472)) % 154.70/154.57 [1148]~E(x11481,x11482)+E(f689(x11481,x11483,x11484,x11485),f689(x11482,x11483,x11484,x11485)) % 154.70/154.57 [1149]~E(x11491,x11492)+E(f689(x11493,x11491,x11494,x11495),f689(x11493,x11492,x11494,x11495)) % 154.70/154.57 [1150]~E(x11501,x11502)+E(f689(x11503,x11504,x11501,x11505),f689(x11503,x11504,x11502,x11505)) % 154.70/154.57 [1151]~E(x11511,x11512)+E(f689(x11513,x11514,x11515,x11511),f689(x11513,x11514,x11515,x11512)) % 154.70/154.57 [1152]~E(x11521,x11522)+E(f350(x11521,x11523,x11524,x11525,x11526),f350(x11522,x11523,x11524,x11525,x11526)) % 154.70/154.57 [1153]~E(x11531,x11532)+E(f350(x11533,x11531,x11534,x11535,x11536),f350(x11533,x11532,x11534,x11535,x11536)) % 154.70/154.57 [1154]~E(x11541,x11542)+E(f350(x11543,x11544,x11541,x11545,x11546),f350(x11543,x11544,x11542,x11545,x11546)) % 154.70/154.57 [1155]~E(x11551,x11552)+E(f350(x11553,x11554,x11555,x11551,x11556),f350(x11553,x11554,x11555,x11552,x11556)) % 154.70/154.57 [1156]~E(x11561,x11562)+E(f350(x11563,x11564,x11565,x11566,x11561),f350(x11563,x11564,x11565,x11566,x11562)) % 154.70/154.57 [1157]~E(x11571,x11572)+E(f720(x11571,x11573),f720(x11572,x11573)) % 154.70/154.57 [1158]~E(x11581,x11582)+E(f720(x11583,x11581),f720(x11583,x11582)) % 154.70/154.57 [1159]~E(x11591,x11592)+E(f594(x11591,x11593,x11594),f594(x11592,x11593,x11594)) % 154.70/154.57 [1160]~E(x11601,x11602)+E(f594(x11603,x11601,x11604),f594(x11603,x11602,x11604)) % 154.70/154.57 [1161]~E(x11611,x11612)+E(f594(x11613,x11614,x11611),f594(x11613,x11614,x11612)) % 154.70/154.57 [1162]~E(x11621,x11622)+E(f67(x11621,x11623,x11624),f67(x11622,x11623,x11624)) % 154.70/154.57 [1163]~E(x11631,x11632)+E(f67(x11633,x11631,x11634),f67(x11633,x11632,x11634)) % 154.70/154.57 [1164]~E(x11641,x11642)+E(f67(x11643,x11644,x11641),f67(x11643,x11644,x11642)) % 154.70/154.57 [1165]~E(x11651,x11652)+E(f504(x11651,x11653,x11654),f504(x11652,x11653,x11654)) % 154.70/154.57 [1166]~E(x11661,x11662)+E(f504(x11663,x11661,x11664),f504(x11663,x11662,x11664)) % 154.70/154.57 [1167]~E(x11671,x11672)+E(f504(x11673,x11674,x11671),f504(x11673,x11674,x11672)) % 154.70/154.57 [1168]~E(x11681,x11682)+E(f833(x11681,x11683,x11684,x11685,x11686),f833(x11682,x11683,x11684,x11685,x11686)) % 154.70/154.57 [1169]~E(x11691,x11692)+E(f833(x11693,x11691,x11694,x11695,x11696),f833(x11693,x11692,x11694,x11695,x11696)) % 154.70/154.57 [1170]~E(x11701,x11702)+E(f833(x11703,x11704,x11701,x11705,x11706),f833(x11703,x11704,x11702,x11705,x11706)) % 154.70/154.57 [1171]~E(x11711,x11712)+E(f833(x11713,x11714,x11715,x11711,x11716),f833(x11713,x11714,x11715,x11712,x11716)) % 154.70/154.57 [1172]~E(x11721,x11722)+E(f833(x11723,x11724,x11725,x11726,x11721),f833(x11723,x11724,x11725,x11726,x11722)) % 154.70/154.57 [1173]~E(x11731,x11732)+E(f503(x11731,x11733,x11734),f503(x11732,x11733,x11734)) % 154.70/154.57 [1174]~E(x11741,x11742)+E(f503(x11743,x11741,x11744),f503(x11743,x11742,x11744)) % 154.70/154.57 [1175]~E(x11751,x11752)+E(f503(x11753,x11754,x11751),f503(x11753,x11754,x11752)) % 154.70/154.57 [1176]~E(x11761,x11762)+E(f447(x11761,x11763),f447(x11762,x11763)) % 154.70/154.57 [1177]~E(x11771,x11772)+E(f447(x11773,x11771),f447(x11773,x11772)) % 154.70/154.57 [1178]~E(x11781,x11782)+E(f292(x11781,x11783,x11784,x11785),f292(x11782,x11783,x11784,x11785)) % 154.70/154.57 [1179]~E(x11791,x11792)+E(f292(x11793,x11791,x11794,x11795),f292(x11793,x11792,x11794,x11795)) % 154.70/154.57 [1180]~E(x11801,x11802)+E(f292(x11803,x11804,x11801,x11805),f292(x11803,x11804,x11802,x11805)) % 154.70/154.57 [1181]~E(x11811,x11812)+E(f292(x11813,x11814,x11815,x11811),f292(x11813,x11814,x11815,x11812)) % 154.70/154.57 [1182]~E(x11821,x11822)+E(f769(x11821,x11823),f769(x11822,x11823)) % 154.70/154.57 [1183]~E(x11831,x11832)+E(f769(x11833,x11831),f769(x11833,x11832)) % 154.70/154.57 [1184]~E(x11841,x11842)+E(f489(x11841,x11843,x11844,x11845,x11846),f489(x11842,x11843,x11844,x11845,x11846)) % 154.70/154.57 [1185]~E(x11851,x11852)+E(f489(x11853,x11851,x11854,x11855,x11856),f489(x11853,x11852,x11854,x11855,x11856)) % 154.70/154.57 [1186]~E(x11861,x11862)+E(f489(x11863,x11864,x11861,x11865,x11866),f489(x11863,x11864,x11862,x11865,x11866)) % 154.70/154.57 [1187]~E(x11871,x11872)+E(f489(x11873,x11874,x11875,x11871,x11876),f489(x11873,x11874,x11875,x11872,x11876)) % 154.70/154.57 [1188]~E(x11881,x11882)+E(f489(x11883,x11884,x11885,x11886,x11881),f489(x11883,x11884,x11885,x11886,x11882)) % 154.70/154.57 [1189]~E(x11891,x11892)+E(f694(x11891,x11893,x11894),f694(x11892,x11893,x11894)) % 154.70/154.57 [1190]~E(x11901,x11902)+E(f694(x11903,x11901,x11904),f694(x11903,x11902,x11904)) % 154.70/154.57 [1191]~E(x11911,x11912)+E(f694(x11913,x11914,x11911),f694(x11913,x11914,x11912)) % 154.70/154.57 [1192]~E(x11921,x11922)+E(f788(x11921,x11923,x11924,x11925,x11926),f788(x11922,x11923,x11924,x11925,x11926)) % 154.70/154.57 [1193]~E(x11931,x11932)+E(f788(x11933,x11931,x11934,x11935,x11936),f788(x11933,x11932,x11934,x11935,x11936)) % 154.70/154.57 [1194]~E(x11941,x11942)+E(f788(x11943,x11944,x11941,x11945,x11946),f788(x11943,x11944,x11942,x11945,x11946)) % 154.70/154.57 [1195]~E(x11951,x11952)+E(f788(x11953,x11954,x11955,x11951,x11956),f788(x11953,x11954,x11955,x11952,x11956)) % 154.70/154.57 [1196]~E(x11961,x11962)+E(f788(x11963,x11964,x11965,x11966,x11961),f788(x11963,x11964,x11965,x11966,x11962)) % 154.70/154.57 [1197]~E(x11971,x11972)+E(f700(x11971,x11973,x11974,x11975),f700(x11972,x11973,x11974,x11975)) % 154.70/154.57 [1198]~E(x11981,x11982)+E(f700(x11983,x11981,x11984,x11985),f700(x11983,x11982,x11984,x11985)) % 154.70/154.57 [1199]~E(x11991,x11992)+E(f700(x11993,x11994,x11991,x11995),f700(x11993,x11994,x11992,x11995)) % 154.70/154.57 [1200]~E(x12001,x12002)+E(f700(x12003,x12004,x12005,x12001),f700(x12003,x12004,x12005,x12002)) % 154.70/154.57 [1201]~E(x12011,x12012)+E(f400(x12011,x12013,x12014,x12015),f400(x12012,x12013,x12014,x12015)) % 154.70/154.57 [1202]~E(x12021,x12022)+E(f400(x12023,x12021,x12024,x12025),f400(x12023,x12022,x12024,x12025)) % 154.70/154.57 [1203]~E(x12031,x12032)+E(f400(x12033,x12034,x12031,x12035),f400(x12033,x12034,x12032,x12035)) % 154.70/154.57 [1204]~E(x12041,x12042)+E(f400(x12043,x12044,x12045,x12041),f400(x12043,x12044,x12045,x12042)) % 154.70/154.57 [1205]~E(x12051,x12052)+E(f784(x12051,x12053,x12054,x12055),f784(x12052,x12053,x12054,x12055)) % 154.70/154.57 [1206]~E(x12061,x12062)+E(f784(x12063,x12061,x12064,x12065),f784(x12063,x12062,x12064,x12065)) % 154.70/154.57 [1207]~E(x12071,x12072)+E(f784(x12073,x12074,x12071,x12075),f784(x12073,x12074,x12072,x12075)) % 154.70/154.57 [1208]~E(x12081,x12082)+E(f784(x12083,x12084,x12085,x12081),f784(x12083,x12084,x12085,x12082)) % 154.70/154.57 [1209]~E(x12091,x12092)+E(f126(x12091),f126(x12092)) % 154.70/154.57 [1210]~E(x12101,x12102)+E(f456(x12101,x12103,x12104,x12105),f456(x12102,x12103,x12104,x12105)) % 154.70/154.57 [1211]~E(x12111,x12112)+E(f456(x12113,x12111,x12114,x12115),f456(x12113,x12112,x12114,x12115)) % 154.70/154.57 [1212]~E(x12121,x12122)+E(f456(x12123,x12124,x12121,x12125),f456(x12123,x12124,x12122,x12125)) % 154.70/154.57 [1213]~E(x12131,x12132)+E(f456(x12133,x12134,x12135,x12131),f456(x12133,x12134,x12135,x12132)) % 154.70/154.57 [1214]~E(x12141,x12142)+E(f648(x12141,x12143,x12144,x12145),f648(x12142,x12143,x12144,x12145)) % 154.70/154.57 [1215]~E(x12151,x12152)+E(f648(x12153,x12151,x12154,x12155),f648(x12153,x12152,x12154,x12155)) % 154.70/154.57 [1216]~E(x12161,x12162)+E(f648(x12163,x12164,x12161,x12165),f648(x12163,x12164,x12162,x12165)) % 154.70/154.57 [1217]~E(x12171,x12172)+E(f648(x12173,x12174,x12175,x12171),f648(x12173,x12174,x12175,x12172)) % 154.70/154.57 [1218]~E(x12181,x12182)+E(f589(x12181,x12183,x12184),f589(x12182,x12183,x12184)) % 154.70/154.57 [1219]~E(x12191,x12192)+E(f589(x12193,x12191,x12194),f589(x12193,x12192,x12194)) % 154.70/154.57 [1220]~E(x12201,x12202)+E(f589(x12203,x12204,x12201),f589(x12203,x12204,x12202)) % 154.70/154.57 [1221]~E(x12211,x12212)+E(f841(x12211,x12213,x12214,x12215,x12216,x12217),f841(x12212,x12213,x12214,x12215,x12216,x12217)) % 154.70/154.57 [1222]~E(x12221,x12222)+E(f841(x12223,x12221,x12224,x12225,x12226,x12227),f841(x12223,x12222,x12224,x12225,x12226,x12227)) % 154.70/154.57 [1223]~E(x12231,x12232)+E(f841(x12233,x12234,x12231,x12235,x12236,x12237),f841(x12233,x12234,x12232,x12235,x12236,x12237)) % 154.70/154.57 [1224]~E(x12241,x12242)+E(f841(x12243,x12244,x12245,x12241,x12246,x12247),f841(x12243,x12244,x12245,x12242,x12246,x12247)) % 154.70/154.57 [1225]~E(x12251,x12252)+E(f841(x12253,x12254,x12255,x12256,x12251,x12257),f841(x12253,x12254,x12255,x12256,x12252,x12257)) % 154.70/154.57 [1226]~E(x12261,x12262)+E(f841(x12263,x12264,x12265,x12266,x12267,x12261),f841(x12263,x12264,x12265,x12266,x12267,x12262)) % 154.70/154.57 [1227]~E(x12271,x12272)+E(f696(x12271,x12273,x12274,x12275,x12276),f696(x12272,x12273,x12274,x12275,x12276)) % 154.70/154.57 [1228]~E(x12281,x12282)+E(f696(x12283,x12281,x12284,x12285,x12286),f696(x12283,x12282,x12284,x12285,x12286)) % 154.70/154.57 [1229]~E(x12291,x12292)+E(f696(x12293,x12294,x12291,x12295,x12296),f696(x12293,x12294,x12292,x12295,x12296)) % 154.70/154.57 [1230]~E(x12301,x12302)+E(f696(x12303,x12304,x12305,x12301,x12306),f696(x12303,x12304,x12305,x12302,x12306)) % 154.70/154.57 [1231]~E(x12311,x12312)+E(f696(x12313,x12314,x12315,x12316,x12311),f696(x12313,x12314,x12315,x12316,x12312)) % 154.70/154.57 [1232]~E(x12321,x12322)+E(f709(x12321,x12323,x12324),f709(x12322,x12323,x12324)) % 154.70/154.57 [1233]~E(x12331,x12332)+E(f709(x12333,x12331,x12334),f709(x12333,x12332,x12334)) % 154.70/154.57 [1234]~E(x12341,x12342)+E(f709(x12343,x12344,x12341),f709(x12343,x12344,x12342)) % 154.70/154.57 [1235]~E(x12351,x12352)+E(f630(x12351,x12353),f630(x12352,x12353)) % 154.70/154.57 [1236]~E(x12361,x12362)+E(f630(x12363,x12361),f630(x12363,x12362)) % 154.70/154.57 [1237]~E(x12371,x12372)+E(f638(x12371,x12373,x12374),f638(x12372,x12373,x12374)) % 154.70/154.57 [1238]~E(x12381,x12382)+E(f638(x12383,x12381,x12384),f638(x12383,x12382,x12384)) % 154.70/154.57 [1239]~E(x12391,x12392)+E(f638(x12393,x12394,x12391),f638(x12393,x12394,x12392)) % 154.70/154.57 [1240]~E(x12401,x12402)+E(f492(x12401,x12403,x12404),f492(x12402,x12403,x12404)) % 154.70/154.57 [1241]~E(x12411,x12412)+E(f492(x12413,x12411,x12414),f492(x12413,x12412,x12414)) % 154.70/154.57 [1242]~E(x12421,x12422)+E(f492(x12423,x12424,x12421),f492(x12423,x12424,x12422)) % 154.70/154.57 [1243]~E(x12431,x12432)+E(f501(x12431,x12433,x12434,x12435,x12436),f501(x12432,x12433,x12434,x12435,x12436)) % 154.70/154.57 [1244]~E(x12441,x12442)+E(f501(x12443,x12441,x12444,x12445,x12446),f501(x12443,x12442,x12444,x12445,x12446)) % 154.70/154.57 [1245]~E(x12451,x12452)+E(f501(x12453,x12454,x12451,x12455,x12456),f501(x12453,x12454,x12452,x12455,x12456)) % 154.70/154.57 [1246]~E(x12461,x12462)+E(f501(x12463,x12464,x12465,x12461,x12466),f501(x12463,x12464,x12465,x12462,x12466)) % 154.70/154.57 [1247]~E(x12471,x12472)+E(f501(x12473,x12474,x12475,x12476,x12471),f501(x12473,x12474,x12475,x12476,x12472)) % 154.70/154.57 [1248]~E(x12481,x12482)+E(f560(x12481,x12483,x12484,x12485,x12486),f560(x12482,x12483,x12484,x12485,x12486)) % 154.70/154.57 [1249]~E(x12491,x12492)+E(f560(x12493,x12491,x12494,x12495,x12496),f560(x12493,x12492,x12494,x12495,x12496)) % 154.70/154.57 [1250]~E(x12501,x12502)+E(f560(x12503,x12504,x12501,x12505,x12506),f560(x12503,x12504,x12502,x12505,x12506)) % 154.70/154.57 [1251]~E(x12511,x12512)+E(f560(x12513,x12514,x12515,x12511,x12516),f560(x12513,x12514,x12515,x12512,x12516)) % 154.70/154.57 [1252]~E(x12521,x12522)+E(f560(x12523,x12524,x12525,x12526,x12521),f560(x12523,x12524,x12525,x12526,x12522)) % 154.70/154.57 [1253]~E(x12531,x12532)+E(f523(x12531,x12533,x12534),f523(x12532,x12533,x12534)) % 154.70/154.57 [1254]~E(x12541,x12542)+E(f523(x12543,x12541,x12544),f523(x12543,x12542,x12544)) % 154.70/154.57 [1255]~E(x12551,x12552)+E(f523(x12553,x12554,x12551),f523(x12553,x12554,x12552)) % 154.70/154.57 [1256]~E(x12561,x12562)+E(f610(x12561,x12563,x12564,x12565,x12566,x12567),f610(x12562,x12563,x12564,x12565,x12566,x12567)) % 154.70/154.57 [1257]~E(x12571,x12572)+E(f610(x12573,x12571,x12574,x12575,x12576,x12577),f610(x12573,x12572,x12574,x12575,x12576,x12577)) % 154.70/154.57 [1258]~E(x12581,x12582)+E(f610(x12583,x12584,x12581,x12585,x12586,x12587),f610(x12583,x12584,x12582,x12585,x12586,x12587)) % 154.70/154.57 [1259]~E(x12591,x12592)+E(f610(x12593,x12594,x12595,x12591,x12596,x12597),f610(x12593,x12594,x12595,x12592,x12596,x12597)) % 154.70/154.57 [1260]~E(x12601,x12602)+E(f610(x12603,x12604,x12605,x12606,x12601,x12607),f610(x12603,x12604,x12605,x12606,x12602,x12607)) % 154.70/154.57 [1261]~E(x12611,x12612)+E(f610(x12613,x12614,x12615,x12616,x12617,x12611),f610(x12613,x12614,x12615,x12616,x12617,x12612)) % 154.70/154.57 [1262]~E(x12621,x12622)+E(f171(x12621,x12623,x12624),f171(x12622,x12623,x12624)) % 154.70/154.57 [1263]~E(x12631,x12632)+E(f171(x12633,x12631,x12634),f171(x12633,x12632,x12634)) % 154.70/154.57 [1264]~E(x12641,x12642)+E(f171(x12643,x12644,x12641),f171(x12643,x12644,x12642)) % 154.70/154.57 [1265]~E(x12651,x12652)+E(f275(x12651,x12653),f275(x12652,x12653)) % 154.70/154.57 [1266]~E(x12661,x12662)+E(f275(x12663,x12661),f275(x12663,x12662)) % 154.70/154.57 [1267]~E(x12671,x12672)+E(f662(x12671,x12673,x12674,x12675),f662(x12672,x12673,x12674,x12675)) % 154.70/154.57 [1268]~E(x12681,x12682)+E(f662(x12683,x12681,x12684,x12685),f662(x12683,x12682,x12684,x12685)) % 154.70/154.57 [1269]~E(x12691,x12692)+E(f662(x12693,x12694,x12691,x12695),f662(x12693,x12694,x12692,x12695)) % 154.70/154.57 [1270]~E(x12701,x12702)+E(f662(x12703,x12704,x12705,x12701),f662(x12703,x12704,x12705,x12702)) % 154.70/154.57 [1271]~E(x12711,x12712)+E(f592(x12711,x12713,x12714),f592(x12712,x12713,x12714)) % 154.70/154.57 [1272]~E(x12721,x12722)+E(f592(x12723,x12721,x12724),f592(x12723,x12722,x12724)) % 154.70/154.57 [1273]~E(x12731,x12732)+E(f592(x12733,x12734,x12731),f592(x12733,x12734,x12732)) % 154.70/154.57 [1274]~E(x12741,x12742)+E(f199(x12741,x12743),f199(x12742,x12743)) % 154.70/154.57 [1275]~E(x12751,x12752)+E(f199(x12753,x12751),f199(x12753,x12752)) % 154.70/154.57 [1276]~E(x12761,x12762)+E(f444(x12761,x12763,x12764,x12765,x12766),f444(x12762,x12763,x12764,x12765,x12766)) % 154.70/154.57 [1277]~E(x12771,x12772)+E(f444(x12773,x12771,x12774,x12775,x12776),f444(x12773,x12772,x12774,x12775,x12776)) % 154.70/154.57 [1278]~E(x12781,x12782)+E(f444(x12783,x12784,x12781,x12785,x12786),f444(x12783,x12784,x12782,x12785,x12786)) % 154.70/154.57 [1279]~E(x12791,x12792)+E(f444(x12793,x12794,x12795,x12791,x12796),f444(x12793,x12794,x12795,x12792,x12796)) % 154.70/154.57 [1280]~E(x12801,x12802)+E(f444(x12803,x12804,x12805,x12806,x12801),f444(x12803,x12804,x12805,x12806,x12802)) % 154.70/154.57 [1281]~E(x12811,x12812)+E(f62(x12811,x12813,x12814),f62(x12812,x12813,x12814)) % 154.70/154.57 [1282]~E(x12821,x12822)+E(f62(x12823,x12821,x12824),f62(x12823,x12822,x12824)) % 154.70/154.57 [1283]~E(x12831,x12832)+E(f62(x12833,x12834,x12831),f62(x12833,x12834,x12832)) % 154.70/154.57 [1284]~E(x12841,x12842)+E(f394(x12841,x12843,x12844),f394(x12842,x12843,x12844)) % 154.70/154.57 [1285]~E(x12851,x12852)+E(f394(x12853,x12851,x12854),f394(x12853,x12852,x12854)) % 154.70/154.57 [1286]~E(x12861,x12862)+E(f394(x12863,x12864,x12861),f394(x12863,x12864,x12862)) % 154.70/154.57 [1287]~E(x12871,x12872)+E(f293(x12871,x12873,x12874,x12875,x12876),f293(x12872,x12873,x12874,x12875,x12876)) % 154.70/154.57 [1288]~E(x12881,x12882)+E(f293(x12883,x12881,x12884,x12885,x12886),f293(x12883,x12882,x12884,x12885,x12886)) % 154.70/154.57 [1289]~E(x12891,x12892)+E(f293(x12893,x12894,x12891,x12895,x12896),f293(x12893,x12894,x12892,x12895,x12896)) % 154.70/154.57 [1290]~E(x12901,x12902)+E(f293(x12903,x12904,x12905,x12901,x12906),f293(x12903,x12904,x12905,x12902,x12906)) % 154.70/154.57 [1291]~E(x12911,x12912)+E(f293(x12913,x12914,x12915,x12916,x12911),f293(x12913,x12914,x12915,x12916,x12912)) % 154.70/154.57 [1292]~E(x12921,x12922)+E(f295(x12921,x12923,x12924,x12925),f295(x12922,x12923,x12924,x12925)) % 154.70/154.57 [1293]~E(x12931,x12932)+E(f295(x12933,x12931,x12934,x12935),f295(x12933,x12932,x12934,x12935)) % 154.70/154.57 [1294]~E(x12941,x12942)+E(f295(x12943,x12944,x12941,x12945),f295(x12943,x12944,x12942,x12945)) % 154.70/154.57 [1295]~E(x12951,x12952)+E(f295(x12953,x12954,x12955,x12951),f295(x12953,x12954,x12955,x12952)) % 154.70/154.57 [1296]~E(x12961,x12962)+E(f627(x12961,x12963,x12964,x12965,x12966),f627(x12962,x12963,x12964,x12965,x12966)) % 154.70/154.57 [1297]~E(x12971,x12972)+E(f627(x12973,x12971,x12974,x12975,x12976),f627(x12973,x12972,x12974,x12975,x12976)) % 154.70/154.57 [1298]~E(x12981,x12982)+E(f627(x12983,x12984,x12981,x12985,x12986),f627(x12983,x12984,x12982,x12985,x12986)) % 154.70/154.57 [1299]~E(x12991,x12992)+E(f627(x12993,x12994,x12995,x12991,x12996),f627(x12993,x12994,x12995,x12992,x12996)) % 154.70/154.57 [1300]~E(x13001,x13002)+E(f627(x13003,x13004,x13005,x13006,x13001),f627(x13003,x13004,x13005,x13006,x13002)) % 154.70/154.57 [1301]~E(x13011,x13012)+E(f521(x13011,x13013,x13014),f521(x13012,x13013,x13014)) % 154.70/154.57 [1302]~E(x13021,x13022)+E(f521(x13023,x13021,x13024),f521(x13023,x13022,x13024)) % 154.70/154.57 [1303]~E(x13031,x13032)+E(f521(x13033,x13034,x13031),f521(x13033,x13034,x13032)) % 154.70/154.57 [1304]~E(x13041,x13042)+E(f556(x13041,x13043),f556(x13042,x13043)) % 154.70/154.57 [1305]~E(x13051,x13052)+E(f556(x13053,x13051),f556(x13053,x13052)) % 154.70/154.57 [1306]~E(x13061,x13062)+E(f574(x13061,x13063,x13064,x13065),f574(x13062,x13063,x13064,x13065)) % 154.70/154.57 [1307]~E(x13071,x13072)+E(f574(x13073,x13071,x13074,x13075),f574(x13073,x13072,x13074,x13075)) % 154.70/154.57 [1308]~E(x13081,x13082)+E(f574(x13083,x13084,x13081,x13085),f574(x13083,x13084,x13082,x13085)) % 154.70/154.57 [1309]~E(x13091,x13092)+E(f574(x13093,x13094,x13095,x13091),f574(x13093,x13094,x13095,x13092)) % 154.70/154.57 [1310]~E(x13101,x13102)+E(f840(x13101,x13103,x13104,x13105,x13106,x13107),f840(x13102,x13103,x13104,x13105,x13106,x13107)) % 154.70/154.57 [1311]~E(x13111,x13112)+E(f840(x13113,x13111,x13114,x13115,x13116,x13117),f840(x13113,x13112,x13114,x13115,x13116,x13117)) % 154.70/154.57 [1312]~E(x13121,x13122)+E(f840(x13123,x13124,x13121,x13125,x13126,x13127),f840(x13123,x13124,x13122,x13125,x13126,x13127)) % 154.70/154.57 [1313]~E(x13131,x13132)+E(f840(x13133,x13134,x13135,x13131,x13136,x13137),f840(x13133,x13134,x13135,x13132,x13136,x13137)) % 154.70/154.57 [1314]~E(x13141,x13142)+E(f840(x13143,x13144,x13145,x13146,x13141,x13147),f840(x13143,x13144,x13145,x13146,x13142,x13147)) % 154.70/154.57 [1315]~E(x13151,x13152)+E(f840(x13153,x13154,x13155,x13156,x13157,x13151),f840(x13153,x13154,x13155,x13156,x13157,x13152)) % 154.70/154.57 [1316]~E(x13161,x13162)+E(f211(x13161),f211(x13162)) % 154.70/154.57 [1317]~E(x13171,x13172)+E(f810(x13171,x13173,x13174),f810(x13172,x13173,x13174)) % 154.70/154.57 [1318]~E(x13181,x13182)+E(f810(x13183,x13181,x13184),f810(x13183,x13182,x13184)) % 154.70/154.57 [1319]~E(x13191,x13192)+E(f810(x13193,x13194,x13191),f810(x13193,x13194,x13192)) % 154.70/154.57 [1320]~E(x13201,x13202)+E(f704(x13201,x13203,x13204,x13205,x13206),f704(x13202,x13203,x13204,x13205,x13206)) % 154.70/154.57 [1321]~E(x13211,x13212)+E(f704(x13213,x13211,x13214,x13215,x13216),f704(x13213,x13212,x13214,x13215,x13216)) % 154.70/154.57 [1322]~E(x13221,x13222)+E(f704(x13223,x13224,x13221,x13225,x13226),f704(x13223,x13224,x13222,x13225,x13226)) % 154.70/154.57 [1323]~E(x13231,x13232)+E(f704(x13233,x13234,x13235,x13231,x13236),f704(x13233,x13234,x13235,x13232,x13236)) % 154.70/154.57 [1324]~E(x13241,x13242)+E(f704(x13243,x13244,x13245,x13246,x13241),f704(x13243,x13244,x13245,x13246,x13242)) % 154.70/154.57 [1325]~E(x13251,x13252)+E(f425(x13251,x13253,x13254,x13255),f425(x13252,x13253,x13254,x13255)) % 154.70/154.57 [1326]~E(x13261,x13262)+E(f425(x13263,x13261,x13264,x13265),f425(x13263,x13262,x13264,x13265)) % 154.70/154.57 [1327]~E(x13271,x13272)+E(f425(x13273,x13274,x13271,x13275),f425(x13273,x13274,x13272,x13275)) % 154.70/154.57 [1328]~E(x13281,x13282)+E(f425(x13283,x13284,x13285,x13281),f425(x13283,x13284,x13285,x13282)) % 154.70/154.57 [1329]~E(x13291,x13292)+E(f650(x13291,x13293,x13294,x13295,x13296),f650(x13292,x13293,x13294,x13295,x13296)) % 154.70/154.57 [1330]~E(x13301,x13302)+E(f650(x13303,x13301,x13304,x13305,x13306),f650(x13303,x13302,x13304,x13305,x13306)) % 154.70/154.57 [1331]~E(x13311,x13312)+E(f650(x13313,x13314,x13311,x13315,x13316),f650(x13313,x13314,x13312,x13315,x13316)) % 154.70/154.57 [1332]~E(x13321,x13322)+E(f650(x13323,x13324,x13325,x13321,x13326),f650(x13323,x13324,x13325,x13322,x13326)) % 154.70/154.57 [1333]~E(x13331,x13332)+E(f650(x13333,x13334,x13335,x13336,x13331),f650(x13333,x13334,x13335,x13336,x13332)) % 154.70/154.57 [1334]~E(x13341,x13342)+E(f573(x13341,x13343,x13344,x13345),f573(x13342,x13343,x13344,x13345)) % 154.70/154.57 [1335]~E(x13351,x13352)+E(f573(x13353,x13351,x13354,x13355),f573(x13353,x13352,x13354,x13355)) % 154.70/154.57 [1336]~E(x13361,x13362)+E(f573(x13363,x13364,x13361,x13365),f573(x13363,x13364,x13362,x13365)) % 154.70/154.57 [1337]~E(x13371,x13372)+E(f573(x13373,x13374,x13375,x13371),f573(x13373,x13374,x13375,x13372)) % 154.70/154.57 [1338]~E(x13381,x13382)+E(f432(x13381,x13383,x13384,x13385),f432(x13382,x13383,x13384,x13385)) % 154.70/154.57 [1339]~E(x13391,x13392)+E(f432(x13393,x13391,x13394,x13395),f432(x13393,x13392,x13394,x13395)) % 154.70/154.57 [1340]~E(x13401,x13402)+E(f432(x13403,x13404,x13401,x13405),f432(x13403,x13404,x13402,x13405)) % 154.70/154.57 [1341]~E(x13411,x13412)+E(f432(x13413,x13414,x13415,x13411),f432(x13413,x13414,x13415,x13412)) % 154.70/154.57 [1342]~E(x13421,x13422)+E(f859(x13421,x13423,x13424,x13425),f859(x13422,x13423,x13424,x13425)) % 154.70/154.57 [1343]~E(x13431,x13432)+E(f859(x13433,x13431,x13434,x13435),f859(x13433,x13432,x13434,x13435)) % 154.70/154.57 [1344]~E(x13441,x13442)+E(f859(x13443,x13444,x13441,x13445),f859(x13443,x13444,x13442,x13445)) % 154.70/154.57 [1345]~E(x13451,x13452)+E(f859(x13453,x13454,x13455,x13451),f859(x13453,x13454,x13455,x13452)) % 154.70/154.57 [1346]~E(x13461,x13462)+E(f637(x13461,x13463,x13464,x13465,x13466,x13467,x13468),f637(x13462,x13463,x13464,x13465,x13466,x13467,x13468)) % 154.70/154.57 [1347]~E(x13471,x13472)+E(f637(x13473,x13471,x13474,x13475,x13476,x13477,x13478),f637(x13473,x13472,x13474,x13475,x13476,x13477,x13478)) % 154.70/154.57 [1348]~E(x13481,x13482)+E(f637(x13483,x13484,x13481,x13485,x13486,x13487,x13488),f637(x13483,x13484,x13482,x13485,x13486,x13487,x13488)) % 154.70/154.57 [1349]~E(x13491,x13492)+E(f637(x13493,x13494,x13495,x13491,x13496,x13497,x13498),f637(x13493,x13494,x13495,x13492,x13496,x13497,x13498)) % 154.70/154.57 [1350]~E(x13501,x13502)+E(f637(x13503,x13504,x13505,x13506,x13501,x13507,x13508),f637(x13503,x13504,x13505,x13506,x13502,x13507,x13508)) % 154.70/154.57 [1351]~E(x13511,x13512)+E(f637(x13513,x13514,x13515,x13516,x13517,x13511,x13518),f637(x13513,x13514,x13515,x13516,x13517,x13512,x13518)) % 154.70/154.57 [1352]~E(x13521,x13522)+E(f637(x13523,x13524,x13525,x13526,x13527,x13528,x13521),f637(x13523,x13524,x13525,x13526,x13527,x13528,x13522)) % 154.70/154.57 [1353]~E(x13531,x13532)+E(f544(x13531,x13533,x13534,x13535),f544(x13532,x13533,x13534,x13535)) % 154.70/154.57 [1354]~E(x13541,x13542)+E(f544(x13543,x13541,x13544,x13545),f544(x13543,x13542,x13544,x13545)) % 154.70/154.57 [1355]~E(x13551,x13552)+E(f544(x13553,x13554,x13551,x13555),f544(x13553,x13554,x13552,x13555)) % 154.70/154.57 [1356]~E(x13561,x13562)+E(f544(x13563,x13564,x13565,x13561),f544(x13563,x13564,x13565,x13562)) % 154.70/154.57 [1357]~E(x13571,x13572)+E(f718(x13571,x13573),f718(x13572,x13573)) % 154.70/154.57 [1358]~E(x13581,x13582)+E(f718(x13583,x13581),f718(x13583,x13582)) % 154.70/154.57 [1359]~E(x13591,x13592)+E(f868(x13591,x13593,x13594,x13595),f868(x13592,x13593,x13594,x13595)) % 154.70/154.57 [1360]~E(x13601,x13602)+E(f868(x13603,x13601,x13604,x13605),f868(x13603,x13602,x13604,x13605)) % 154.70/154.57 [1361]~E(x13611,x13612)+E(f868(x13613,x13614,x13611,x13615),f868(x13613,x13614,x13612,x13615)) % 154.70/154.57 [1362]~E(x13621,x13622)+E(f868(x13623,x13624,x13625,x13621),f868(x13623,x13624,x13625,x13622)) % 154.70/154.57 [1363]~E(x13631,x13632)+E(f424(x13631,x13633,x13634,x13635),f424(x13632,x13633,x13634,x13635)) % 154.70/154.57 [1364]~E(x13641,x13642)+E(f424(x13643,x13641,x13644,x13645),f424(x13643,x13642,x13644,x13645)) % 154.70/154.57 [1365]~E(x13651,x13652)+E(f424(x13653,x13654,x13651,x13655),f424(x13653,x13654,x13652,x13655)) % 154.70/154.57 [1366]~E(x13661,x13662)+E(f424(x13663,x13664,x13665,x13661),f424(x13663,x13664,x13665,x13662)) % 154.70/154.57 [1367]~E(x13671,x13672)+E(f817(x13671,x13673,x13674,x13675),f817(x13672,x13673,x13674,x13675)) % 154.70/154.57 [1368]~E(x13681,x13682)+E(f817(x13683,x13681,x13684,x13685),f817(x13683,x13682,x13684,x13685)) % 154.70/154.57 [1369]~E(x13691,x13692)+E(f817(x13693,x13694,x13691,x13695),f817(x13693,x13694,x13692,x13695)) % 154.70/154.57 [1370]~E(x13701,x13702)+E(f817(x13703,x13704,x13705,x13701),f817(x13703,x13704,x13705,x13702)) % 154.70/154.57 [1371]~E(x13711,x13712)+E(f276(x13711,x13713),f276(x13712,x13713)) % 154.70/154.57 [1372]~E(x13721,x13722)+E(f276(x13723,x13721),f276(x13723,x13722)) % 154.70/154.57 [1373]~E(x13731,x13732)+E(f490(x13731,x13733,x13734,x13735,x13736),f490(x13732,x13733,x13734,x13735,x13736)) % 154.70/154.57 [1374]~E(x13741,x13742)+E(f490(x13743,x13741,x13744,x13745,x13746),f490(x13743,x13742,x13744,x13745,x13746)) % 154.70/154.57 [1375]~E(x13751,x13752)+E(f490(x13753,x13754,x13751,x13755,x13756),f490(x13753,x13754,x13752,x13755,x13756)) % 154.70/154.57 [1376]~E(x13761,x13762)+E(f490(x13763,x13764,x13765,x13761,x13766),f490(x13763,x13764,x13765,x13762,x13766)) % 154.70/154.57 [1377]~E(x13771,x13772)+E(f490(x13773,x13774,x13775,x13776,x13771),f490(x13773,x13774,x13775,x13776,x13772)) % 154.70/154.57 [1378]~E(x13781,x13782)+E(f641(x13781,x13783,x13784,x13785,x13786),f641(x13782,x13783,x13784,x13785,x13786)) % 154.70/154.57 [1379]~E(x13791,x13792)+E(f641(x13793,x13791,x13794,x13795,x13796),f641(x13793,x13792,x13794,x13795,x13796)) % 154.70/154.57 [1380]~E(x13801,x13802)+E(f641(x13803,x13804,x13801,x13805,x13806),f641(x13803,x13804,x13802,x13805,x13806)) % 154.70/154.57 [1381]~E(x13811,x13812)+E(f641(x13813,x13814,x13815,x13811,x13816),f641(x13813,x13814,x13815,x13812,x13816)) % 154.70/154.57 [1382]~E(x13821,x13822)+E(f641(x13823,x13824,x13825,x13826,x13821),f641(x13823,x13824,x13825,x13826,x13822)) % 154.70/154.57 [1383]~E(x13831,x13832)+E(f629(x13831,x13833,x13834),f629(x13832,x13833,x13834)) % 154.70/154.57 [1384]~E(x13841,x13842)+E(f629(x13843,x13841,x13844),f629(x13843,x13842,x13844)) % 154.70/154.57 [1385]~E(x13851,x13852)+E(f629(x13853,x13854,x13851),f629(x13853,x13854,x13852)) % 154.70/154.57 [1386]~E(x13861,x13862)+E(f519(x13861,x13863,x13864,x13865),f519(x13862,x13863,x13864,x13865)) % 154.70/154.57 [1387]~E(x13871,x13872)+E(f519(x13873,x13871,x13874,x13875),f519(x13873,x13872,x13874,x13875)) % 154.70/154.57 [1388]~E(x13881,x13882)+E(f519(x13883,x13884,x13881,x13885),f519(x13883,x13884,x13882,x13885)) % 154.70/154.57 [1389]~E(x13891,x13892)+E(f519(x13893,x13894,x13895,x13891),f519(x13893,x13894,x13895,x13892)) % 154.70/154.57 [1390]~E(x13901,x13902)+E(f590(x13901,x13903,x13904,x13905,x13906),f590(x13902,x13903,x13904,x13905,x13906)) % 154.70/154.57 [1391]~E(x13911,x13912)+E(f590(x13913,x13911,x13914,x13915,x13916),f590(x13913,x13912,x13914,x13915,x13916)) % 154.70/154.57 [1392]~E(x13921,x13922)+E(f590(x13923,x13924,x13921,x13925,x13926),f590(x13923,x13924,x13922,x13925,x13926)) % 154.70/154.57 [1393]~E(x13931,x13932)+E(f590(x13933,x13934,x13935,x13931,x13936),f590(x13933,x13934,x13935,x13932,x13936)) % 154.70/154.57 [1394]~E(x13941,x13942)+E(f590(x13943,x13944,x13945,x13946,x13941),f590(x13943,x13944,x13945,x13946,x13942)) % 154.70/154.57 [1395]~E(x13951,x13952)+E(f188(x13951,x13953,x13954),f188(x13952,x13953,x13954)) % 154.70/154.57 [1396]~E(x13961,x13962)+E(f188(x13963,x13961,x13964),f188(x13963,x13962,x13964)) % 154.70/154.57 [1397]~E(x13971,x13972)+E(f188(x13973,x13974,x13971),f188(x13973,x13974,x13972)) % 154.70/154.57 [1398]~E(x13981,x13982)+E(f661(x13981,x13983,x13984,x13985,x13986,x13987),f661(x13982,x13983,x13984,x13985,x13986,x13987)) % 154.70/154.57 [1399]~E(x13991,x13992)+E(f661(x13993,x13991,x13994,x13995,x13996,x13997),f661(x13993,x13992,x13994,x13995,x13996,x13997)) % 154.70/154.57 [1400]~E(x14001,x14002)+E(f661(x14003,x14004,x14001,x14005,x14006,x14007),f661(x14003,x14004,x14002,x14005,x14006,x14007)) % 154.70/154.57 [1401]~E(x14011,x14012)+E(f661(x14013,x14014,x14015,x14011,x14016,x14017),f661(x14013,x14014,x14015,x14012,x14016,x14017)) % 154.70/154.57 [1402]~E(x14021,x14022)+E(f661(x14023,x14024,x14025,x14026,x14021,x14027),f661(x14023,x14024,x14025,x14026,x14022,x14027)) % 154.70/154.57 [1403]~E(x14031,x14032)+E(f661(x14033,x14034,x14035,x14036,x14037,x14031),f661(x14033,x14034,x14035,x14036,x14037,x14032)) % 154.70/154.57 [1404]~E(x14041,x14042)+E(f559(x14041,x14043,x14044,x14045),f559(x14042,x14043,x14044,x14045)) % 154.70/154.57 [1405]~E(x14051,x14052)+E(f559(x14053,x14051,x14054,x14055),f559(x14053,x14052,x14054,x14055)) % 154.70/154.57 [1406]~E(x14061,x14062)+E(f559(x14063,x14064,x14061,x14065),f559(x14063,x14064,x14062,x14065)) % 154.70/154.57 [1407]~E(x14071,x14072)+E(f559(x14073,x14074,x14075,x14071),f559(x14073,x14074,x14075,x14072)) % 154.70/154.57 [1408]~E(x14081,x14082)+E(f161(x14081,x14083,x14084,x14085),f161(x14082,x14083,x14084,x14085)) % 154.70/154.57 [1409]~E(x14091,x14092)+E(f161(x14093,x14091,x14094,x14095),f161(x14093,x14092,x14094,x14095)) % 154.70/154.57 [1410]~E(x14101,x14102)+E(f161(x14103,x14104,x14101,x14105),f161(x14103,x14104,x14102,x14105)) % 154.70/154.57 [1411]~E(x14111,x14112)+E(f161(x14113,x14114,x14115,x14111),f161(x14113,x14114,x14115,x14112)) % 154.70/154.57 [1412]~E(x14121,x14122)+E(f312(x14121,x14123,x14124),f312(x14122,x14123,x14124)) % 154.70/154.57 [1413]~E(x14131,x14132)+E(f312(x14133,x14131,x14134),f312(x14133,x14132,x14134)) % 154.70/154.57 [1414]~E(x14141,x14142)+E(f312(x14143,x14144,x14141),f312(x14143,x14144,x14142)) % 154.70/154.57 [1415]~E(x14151,x14152)+E(f759(x14151,x14153,x14154,x14155),f759(x14152,x14153,x14154,x14155)) % 154.70/154.57 [1416]~E(x14161,x14162)+E(f759(x14163,x14161,x14164,x14165),f759(x14163,x14162,x14164,x14165)) % 154.70/154.57 [1417]~E(x14171,x14172)+E(f759(x14173,x14174,x14171,x14175),f759(x14173,x14174,x14172,x14175)) % 154.70/154.57 [1418]~E(x14181,x14182)+E(f759(x14183,x14184,x14185,x14181),f759(x14183,x14184,x14185,x14182)) % 154.70/154.57 [1419]~E(x14191,x14192)+E(f534(x14191,x14193,x14194),f534(x14192,x14193,x14194)) % 154.70/154.57 [1420]~E(x14201,x14202)+E(f534(x14203,x14201,x14204),f534(x14203,x14202,x14204)) % 154.70/154.57 [1421]~E(x14211,x14212)+E(f534(x14213,x14214,x14211),f534(x14213,x14214,x14212)) % 154.70/154.57 [1422]~E(x14221,x14222)+E(f510(x14221),f510(x14222)) % 154.70/154.57 [1423]~E(x14231,x14232)+E(f639(x14231,x14233),f639(x14232,x14233)) % 154.70/154.57 [1424]~E(x14241,x14242)+E(f639(x14243,x14241),f639(x14243,x14242)) % 154.70/154.57 [1425]~E(x14251,x14252)+E(f514(x14251,x14253),f514(x14252,x14253)) % 154.70/154.57 [1426]~E(x14261,x14262)+E(f514(x14263,x14261),f514(x14263,x14262)) % 154.70/154.57 [1427]~E(x14271,x14272)+E(f714(x14271,x14273,x14274,x14275,x14276),f714(x14272,x14273,x14274,x14275,x14276)) % 154.70/154.57 [1428]~E(x14281,x14282)+E(f714(x14283,x14281,x14284,x14285,x14286),f714(x14283,x14282,x14284,x14285,x14286)) % 154.70/154.57 [1429]~E(x14291,x14292)+E(f714(x14293,x14294,x14291,x14295,x14296),f714(x14293,x14294,x14292,x14295,x14296)) % 154.70/154.57 [1430]~E(x14301,x14302)+E(f714(x14303,x14304,x14305,x14301,x14306),f714(x14303,x14304,x14305,x14302,x14306)) % 154.70/154.57 [1431]~E(x14311,x14312)+E(f714(x14313,x14314,x14315,x14316,x14311),f714(x14313,x14314,x14315,x14316,x14312)) % 154.70/154.57 [1432]~E(x14321,x14322)+E(f804(x14321,x14323,x14324),f804(x14322,x14323,x14324)) % 154.70/154.57 [1433]~E(x14331,x14332)+E(f804(x14333,x14331,x14334),f804(x14333,x14332,x14334)) % 154.70/154.57 [1434]~E(x14341,x14342)+E(f804(x14343,x14344,x14341),f804(x14343,x14344,x14342)) % 154.70/154.57 [1435]~E(x14351,x14352)+E(f236(x14351,x14353,x14354),f236(x14352,x14353,x14354)) % 154.70/154.57 [1436]~E(x14361,x14362)+E(f236(x14363,x14361,x14364),f236(x14363,x14362,x14364)) % 154.70/154.57 [1437]~E(x14371,x14372)+E(f236(x14373,x14374,x14371),f236(x14373,x14374,x14372)) % 154.70/154.57 [1438]~E(x14381,x14382)+E(f391(x14381),f391(x14382)) % 154.70/154.57 [1439]~E(x14391,x14392)+E(f623(x14391,x14393,x14394,x14395),f623(x14392,x14393,x14394,x14395)) % 154.70/154.57 [1440]~E(x14401,x14402)+E(f623(x14403,x14401,x14404,x14405),f623(x14403,x14402,x14404,x14405)) % 154.70/154.57 [1441]~E(x14411,x14412)+E(f623(x14413,x14414,x14411,x14415),f623(x14413,x14414,x14412,x14415)) % 154.70/154.57 [1442]~E(x14421,x14422)+E(f623(x14423,x14424,x14425,x14421),f623(x14423,x14424,x14425,x14422)) % 154.70/154.57 [1443]~E(x14431,x14432)+E(f486(x14431,x14433,x14434,x14435,x14436,x14437,x14438,x14439,x144310),f486(x14432,x14433,x14434,x14435,x14436,x14437,x14438,x14439,x144310)) % 154.70/154.57 [1444]~E(x14441,x14442)+E(f486(x14443,x14441,x14444,x14445,x14446,x14447,x14448,x14449,x144410),f486(x14443,x14442,x14444,x14445,x14446,x14447,x14448,x14449,x144410)) % 154.70/154.57 [1445]~E(x14451,x14452)+E(f486(x14453,x14454,x14451,x14455,x14456,x14457,x14458,x14459,x144510),f486(x14453,x14454,x14452,x14455,x14456,x14457,x14458,x14459,x144510)) % 154.70/154.57 [1446]~E(x14461,x14462)+E(f486(x14463,x14464,x14465,x14461,x14466,x14467,x14468,x14469,x144610),f486(x14463,x14464,x14465,x14462,x14466,x14467,x14468,x14469,x144610)) % 154.70/154.57 [1447]~E(x14471,x14472)+E(f486(x14473,x14474,x14475,x14476,x14471,x14477,x14478,x14479,x144710),f486(x14473,x14474,x14475,x14476,x14472,x14477,x14478,x14479,x144710)) % 154.70/154.57 [1448]~E(x14481,x14482)+E(f486(x14483,x14484,x14485,x14486,x14487,x14481,x14488,x14489,x144810),f486(x14483,x14484,x14485,x14486,x14487,x14482,x14488,x14489,x144810)) % 154.70/154.57 [1449]~E(x14491,x14492)+E(f486(x14493,x14494,x14495,x14496,x14497,x14498,x14491,x14499,x144910),f486(x14493,x14494,x14495,x14496,x14497,x14498,x14492,x14499,x144910)) % 154.70/154.57 [1450]~E(x14501,x14502)+E(f486(x14503,x14504,x14505,x14506,x14507,x14508,x14509,x14501,x145010),f486(x14503,x14504,x14505,x14506,x14507,x14508,x14509,x14502,x145010)) % 154.70/154.57 [1451]~E(x14511,x14512)+E(f486(x14513,x14514,x14515,x14516,x14517,x14518,x14519,x145110,x14511),f486(x14513,x14514,x14515,x14516,x14517,x14518,x14519,x145110,x14512)) % 154.70/154.57 [1452]~E(x14521,x14522)+E(f518(x14521,x14523,x14524,x14525),f518(x14522,x14523,x14524,x14525)) % 154.70/154.57 [1453]~E(x14531,x14532)+E(f518(x14533,x14531,x14534,x14535),f518(x14533,x14532,x14534,x14535)) % 154.70/154.57 [1454]~E(x14541,x14542)+E(f518(x14543,x14544,x14541,x14545),f518(x14543,x14544,x14542,x14545)) % 154.70/154.57 [1455]~E(x14551,x14552)+E(f518(x14553,x14554,x14555,x14551),f518(x14553,x14554,x14555,x14552)) % 154.70/154.57 [1456]~E(x14561,x14562)+E(f731(x14561,x14563,x14564,x14565,x14566),f731(x14562,x14563,x14564,x14565,x14566)) % 154.70/154.57 [1457]~E(x14571,x14572)+E(f731(x14573,x14571,x14574,x14575,x14576),f731(x14573,x14572,x14574,x14575,x14576)) % 154.70/154.57 [1458]~E(x14581,x14582)+E(f731(x14583,x14584,x14581,x14585,x14586),f731(x14583,x14584,x14582,x14585,x14586)) % 154.70/154.57 [1459]~E(x14591,x14592)+E(f731(x14593,x14594,x14595,x14591,x14596),f731(x14593,x14594,x14595,x14592,x14596)) % 154.70/154.57 [1460]~E(x14601,x14602)+E(f731(x14603,x14604,x14605,x14606,x14601),f731(x14603,x14604,x14605,x14606,x14602)) % 154.70/154.57 [1461]~E(x14611,x14612)+E(f430(x14611,x14613,x14614,x14615),f430(x14612,x14613,x14614,x14615)) % 154.70/154.57 [1462]~E(x14621,x14622)+E(f430(x14623,x14621,x14624,x14625),f430(x14623,x14622,x14624,x14625)) % 154.70/154.57 [1463]~E(x14631,x14632)+E(f430(x14633,x14634,x14631,x14635),f430(x14633,x14634,x14632,x14635)) % 154.70/154.57 [1464]~E(x14641,x14642)+E(f430(x14643,x14644,x14645,x14641),f430(x14643,x14644,x14645,x14642)) % 154.70/154.57 [1465]~E(x14651,x14652)+E(f442(x14651,x14653,x14654,x14655),f442(x14652,x14653,x14654,x14655)) % 154.70/154.57 [1466]~E(x14661,x14662)+E(f442(x14663,x14661,x14664,x14665),f442(x14663,x14662,x14664,x14665)) % 154.70/154.57 [1467]~E(x14671,x14672)+E(f442(x14673,x14674,x14671,x14675),f442(x14673,x14674,x14672,x14675)) % 154.70/154.57 [1468]~E(x14681,x14682)+E(f442(x14683,x14684,x14685,x14681),f442(x14683,x14684,x14685,x14682)) % 154.70/154.57 [1469]~E(x14691,x14692)+E(f356(x14691,x14693),f356(x14692,x14693)) % 154.70/154.57 [1470]~E(x14701,x14702)+E(f356(x14703,x14701),f356(x14703,x14702)) % 154.70/154.57 [1471]~E(x14711,x14712)+E(f446(x14711,x14713,x14714,x14715),f446(x14712,x14713,x14714,x14715)) % 154.70/154.57 [1472]~E(x14721,x14722)+E(f446(x14723,x14721,x14724,x14725),f446(x14723,x14722,x14724,x14725)) % 154.70/154.57 [1473]~E(x14731,x14732)+E(f446(x14733,x14734,x14731,x14735),f446(x14733,x14734,x14732,x14735)) % 154.70/154.57 [1474]~E(x14741,x14742)+E(f446(x14743,x14744,x14745,x14741),f446(x14743,x14744,x14745,x14742)) % 154.70/154.57 [1475]~E(x14751,x14752)+E(f561(x14751,x14753,x14754,x14755),f561(x14752,x14753,x14754,x14755)) % 154.70/154.57 [1476]~E(x14761,x14762)+E(f561(x14763,x14761,x14764,x14765),f561(x14763,x14762,x14764,x14765)) % 154.70/154.57 [1477]~E(x14771,x14772)+E(f561(x14773,x14774,x14771,x14775),f561(x14773,x14774,x14772,x14775)) % 154.70/154.57 [1478]~E(x14781,x14782)+E(f561(x14783,x14784,x14785,x14781),f561(x14783,x14784,x14785,x14782)) % 154.70/154.57 [1479]~E(x14791,x14792)+E(f131(x14791,x14793,x14794,x14795),f131(x14792,x14793,x14794,x14795)) % 154.70/154.57 [1480]~E(x14801,x14802)+E(f131(x14803,x14801,x14804,x14805),f131(x14803,x14802,x14804,x14805)) % 154.70/154.57 [1481]~E(x14811,x14812)+E(f131(x14813,x14814,x14811,x14815),f131(x14813,x14814,x14812,x14815)) % 154.70/154.57 [1482]~E(x14821,x14822)+E(f131(x14823,x14824,x14825,x14821),f131(x14823,x14824,x14825,x14822)) % 154.70/154.57 [1483]~E(x14831,x14832)+E(f502(x14831,x14833),f502(x14832,x14833)) % 154.70/154.57 [1484]~E(x14841,x14842)+E(f502(x14843,x14841),f502(x14843,x14842)) % 154.70/154.57 [1485]~E(x14851,x14852)+E(f597(x14851,x14853),f597(x14852,x14853)) % 154.70/154.57 [1486]~E(x14861,x14862)+E(f597(x14863,x14861),f597(x14863,x14862)) % 154.70/154.57 [1487]~E(x14871,x14872)+E(f457(x14871,x14873,x14874),f457(x14872,x14873,x14874)) % 154.70/154.57 [1488]~E(x14881,x14882)+E(f457(x14883,x14881,x14884),f457(x14883,x14882,x14884)) % 154.70/154.57 [1489]~E(x14891,x14892)+E(f457(x14893,x14894,x14891),f457(x14893,x14894,x14892)) % 154.70/154.57 [1490]~E(x14901,x14902)+E(f766(x14901,x14903,x14904,x14905),f766(x14902,x14903,x14904,x14905)) % 154.70/154.57 [1491]~E(x14911,x14912)+E(f766(x14913,x14911,x14914,x14915),f766(x14913,x14912,x14914,x14915)) % 154.70/154.57 [1492]~E(x14921,x14922)+E(f766(x14923,x14924,x14921,x14925),f766(x14923,x14924,x14922,x14925)) % 154.70/154.57 [1493]~E(x14931,x14932)+E(f766(x14933,x14934,x14935,x14931),f766(x14933,x14934,x14935,x14932)) % 154.70/154.57 [1494]~E(x14941,x14942)+E(f93(x14941,x14943,x14944),f93(x14942,x14943,x14944)) % 154.70/154.57 [1495]~E(x14951,x14952)+E(f93(x14953,x14951,x14954),f93(x14953,x14952,x14954)) % 154.70/154.57 [1496]~E(x14961,x14962)+E(f93(x14963,x14964,x14961),f93(x14963,x14964,x14962)) % 154.70/154.57 [1497]~E(x14971,x14972)+E(f159(x14971,x14973),f159(x14972,x14973)) % 154.70/154.57 [1498]~E(x14981,x14982)+E(f159(x14983,x14981),f159(x14983,x14982)) % 154.70/154.57 [1499]~E(x14991,x14992)+E(f659(x14991,x14993,x14994,x14995,x14996,x14997),f659(x14992,x14993,x14994,x14995,x14996,x14997)) % 154.70/154.57 [1500]~E(x15001,x15002)+E(f659(x15003,x15001,x15004,x15005,x15006,x15007),f659(x15003,x15002,x15004,x15005,x15006,x15007)) % 154.70/154.57 [1501]~E(x15011,x15012)+E(f659(x15013,x15014,x15011,x15015,x15016,x15017),f659(x15013,x15014,x15012,x15015,x15016,x15017)) % 154.70/154.57 [1502]~E(x15021,x15022)+E(f659(x15023,x15024,x15025,x15021,x15026,x15027),f659(x15023,x15024,x15025,x15022,x15026,x15027)) % 154.70/154.57 [1503]~E(x15031,x15032)+E(f659(x15033,x15034,x15035,x15036,x15031,x15037),f659(x15033,x15034,x15035,x15036,x15032,x15037)) % 154.70/154.57 [1504]~E(x15041,x15042)+E(f659(x15043,x15044,x15045,x15046,x15047,x15041),f659(x15043,x15044,x15045,x15046,x15047,x15042)) % 154.70/154.57 [1505]~E(x15051,x15052)+E(f675(x15051,x15053,x15054,x15055),f675(x15052,x15053,x15054,x15055)) % 154.70/154.57 [1506]~E(x15061,x15062)+E(f675(x15063,x15061,x15064,x15065),f675(x15063,x15062,x15064,x15065)) % 154.70/154.57 [1507]~E(x15071,x15072)+E(f675(x15073,x15074,x15071,x15075),f675(x15073,x15074,x15072,x15075)) % 154.70/154.57 [1508]~E(x15081,x15082)+E(f675(x15083,x15084,x15085,x15081),f675(x15083,x15084,x15085,x15082)) % 154.70/154.57 [1509]~E(x15091,x15092)+E(f272(x15091,x15093),f272(x15092,x15093)) % 154.70/154.57 [1510]~E(x15101,x15102)+E(f272(x15103,x15101),f272(x15103,x15102)) % 154.70/154.57 [1511]~E(x15111,x15112)+E(f663(x15111,x15113,x15114,x15115),f663(x15112,x15113,x15114,x15115)) % 154.70/154.57 [1512]~E(x15121,x15122)+E(f663(x15123,x15121,x15124,x15125),f663(x15123,x15122,x15124,x15125)) % 154.70/154.57 [1513]~E(x15131,x15132)+E(f663(x15133,x15134,x15131,x15135),f663(x15133,x15134,x15132,x15135)) % 154.70/154.57 [1514]~E(x15141,x15142)+E(f663(x15143,x15144,x15145,x15141),f663(x15143,x15144,x15145,x15142)) % 154.70/154.57 [1515]~E(x15151,x15152)+E(f366(x15151,x15153,x15154,x15155,x15156),f366(x15152,x15153,x15154,x15155,x15156)) % 154.70/154.57 [1516]~E(x15161,x15162)+E(f366(x15163,x15161,x15164,x15165,x15166),f366(x15163,x15162,x15164,x15165,x15166)) % 154.70/154.57 [1517]~E(x15171,x15172)+E(f366(x15173,x15174,x15171,x15175,x15176),f366(x15173,x15174,x15172,x15175,x15176)) % 154.70/154.57 [1518]~E(x15181,x15182)+E(f366(x15183,x15184,x15185,x15181,x15186),f366(x15183,x15184,x15185,x15182,x15186)) % 154.70/154.57 [1519]~E(x15191,x15192)+E(f366(x15193,x15194,x15195,x15196,x15191),f366(x15193,x15194,x15195,x15196,x15192)) % 154.70/154.57 [1520]~E(x15201,x15202)+E(f683(x15201,x15203,x15204,x15205),f683(x15202,x15203,x15204,x15205)) % 154.70/154.57 [1521]~E(x15211,x15212)+E(f683(x15213,x15211,x15214,x15215),f683(x15213,x15212,x15214,x15215)) % 154.70/154.57 [1522]~E(x15221,x15222)+E(f683(x15223,x15224,x15221,x15225),f683(x15223,x15224,x15222,x15225)) % 154.70/154.57 [1523]~E(x15231,x15232)+E(f683(x15233,x15234,x15235,x15231),f683(x15233,x15234,x15235,x15232)) % 154.70/154.57 [1524]~E(x15241,x15242)+E(f666(x15241,x15243,x15244),f666(x15242,x15243,x15244)) % 154.70/154.57 [1525]~E(x15251,x15252)+E(f666(x15253,x15251,x15254),f666(x15253,x15252,x15254)) % 154.70/154.57 [1526]~E(x15261,x15262)+E(f666(x15263,x15264,x15261),f666(x15263,x15264,x15262)) % 154.70/154.57 [1527]~E(x15271,x15272)+E(f132(x15271),f132(x15272)) % 154.70/154.57 [1528]~E(x15281,x15282)+E(f649(x15281,x15283,x15284,x15285,x15286),f649(x15282,x15283,x15284,x15285,x15286)) % 154.70/154.57 [1529]~E(x15291,x15292)+E(f649(x15293,x15291,x15294,x15295,x15296),f649(x15293,x15292,x15294,x15295,x15296)) % 154.70/154.57 [1530]~E(x15301,x15302)+E(f649(x15303,x15304,x15301,x15305,x15306),f649(x15303,x15304,x15302,x15305,x15306)) % 154.70/154.57 [1531]~E(x15311,x15312)+E(f649(x15313,x15314,x15315,x15311,x15316),f649(x15313,x15314,x15315,x15312,x15316)) % 154.70/154.57 [1532]~E(x15321,x15322)+E(f649(x15323,x15324,x15325,x15326,x15321),f649(x15323,x15324,x15325,x15326,x15322)) % 154.70/154.57 [1533]~E(x15331,x15332)+E(f843(x15331,x15333,x15334),f843(x15332,x15333,x15334)) % 154.70/154.57 [1534]~E(x15341,x15342)+E(f843(x15343,x15341,x15344),f843(x15343,x15342,x15344)) % 154.70/154.57 [1535]~E(x15351,x15352)+E(f843(x15353,x15354,x15351),f843(x15353,x15354,x15352)) % 154.70/154.57 [1536]~E(x15361,x15362)+E(f564(x15361,x15363,x15364,x15365),f564(x15362,x15363,x15364,x15365)) % 154.70/154.57 [1537]~E(x15371,x15372)+E(f564(x15373,x15371,x15374,x15375),f564(x15373,x15372,x15374,x15375)) % 154.70/154.57 [1538]~E(x15381,x15382)+E(f564(x15383,x15384,x15381,x15385),f564(x15383,x15384,x15382,x15385)) % 154.70/154.57 [1539]~E(x15391,x15392)+E(f564(x15393,x15394,x15395,x15391),f564(x15393,x15394,x15395,x15392)) % 154.70/154.57 [1540]~E(x15401,x15402)+E(f653(x15401,x15403,x15404),f653(x15402,x15403,x15404)) % 154.70/154.57 [1541]~E(x15411,x15412)+E(f653(x15413,x15411,x15414),f653(x15413,x15412,x15414)) % 154.70/154.57 [1542]~E(x15421,x15422)+E(f653(x15423,x15424,x15421),f653(x15423,x15424,x15422)) % 154.70/154.57 [1543]~E(x15431,x15432)+E(f273(x15431),f273(x15432)) % 154.70/154.57 [1544]~E(x15441,x15442)+E(f772(x15441,x15443,x15444,x15445),f772(x15442,x15443,x15444,x15445)) % 154.70/154.57 [1545]~E(x15451,x15452)+E(f772(x15453,x15451,x15454,x15455),f772(x15453,x15452,x15454,x15455)) % 154.70/154.57 [1546]~E(x15461,x15462)+E(f772(x15463,x15464,x15461,x15465),f772(x15463,x15464,x15462,x15465)) % 154.70/154.57 [1547]~E(x15471,x15472)+E(f772(x15473,x15474,x15475,x15471),f772(x15473,x15474,x15475,x15472)) % 154.70/154.57 [1548]~E(x15481,x15482)+E(f493(x15481,x15483,x15484),f493(x15482,x15483,x15484)) % 154.70/154.57 [1549]~E(x15491,x15492)+E(f493(x15493,x15491,x15494),f493(x15493,x15492,x15494)) % 154.70/154.57 [1550]~E(x15501,x15502)+E(f493(x15503,x15504,x15501),f493(x15503,x15504,x15502)) % 154.70/154.57 [1551]~E(x15511,x15512)+E(f374(x15511,x15513),f374(x15512,x15513)) % 154.70/154.57 [1552]~E(x15521,x15522)+E(f374(x15523,x15521),f374(x15523,x15522)) % 154.70/154.57 [1553]~E(x15531,x15532)+E(f631(x15531,x15533),f631(x15532,x15533)) % 154.70/154.57 [1554]~E(x15541,x15542)+E(f631(x15543,x15541),f631(x15543,x15542)) % 154.70/154.57 [1555]~E(x15551,x15552)+E(f775(x15551,x15553,x15554,x15555),f775(x15552,x15553,x15554,x15555)) % 154.70/154.57 [1556]~E(x15561,x15562)+E(f775(x15563,x15561,x15564,x15565),f775(x15563,x15562,x15564,x15565)) % 154.70/154.57 [1557]~E(x15571,x15572)+E(f775(x15573,x15574,x15571,x15575),f775(x15573,x15574,x15572,x15575)) % 154.70/154.57 [1558]~E(x15581,x15582)+E(f775(x15583,x15584,x15585,x15581),f775(x15583,x15584,x15585,x15582)) % 154.70/154.57 [1559]~E(x15591,x15592)+E(f677(x15591,x15593,x15594),f677(x15592,x15593,x15594)) % 154.70/154.57 [1560]~E(x15601,x15602)+E(f677(x15603,x15601,x15604),f677(x15603,x15602,x15604)) % 154.70/154.57 [1561]~E(x15611,x15612)+E(f677(x15613,x15614,x15611),f677(x15613,x15614,x15612)) % 154.70/154.57 [1562]~E(x15621,x15622)+E(f842(x15621,x15623,x15624,x15625),f842(x15622,x15623,x15624,x15625)) % 154.70/154.57 [1563]~E(x15631,x15632)+E(f842(x15633,x15631,x15634,x15635),f842(x15633,x15632,x15634,x15635)) % 154.70/154.57 [1564]~E(x15641,x15642)+E(f842(x15643,x15644,x15641,x15645),f842(x15643,x15644,x15642,x15645)) % 154.70/154.57 [1565]~E(x15651,x15652)+E(f842(x15653,x15654,x15655,x15651),f842(x15653,x15654,x15655,x15652)) % 154.70/154.57 [1566]~E(x15661,x15662)+E(f423(x15661,x15663),f423(x15662,x15663)) % 154.70/154.57 [1567]~E(x15671,x15672)+E(f423(x15673,x15671),f423(x15673,x15672)) % 154.70/154.57 [1568]~E(x15681,x15682)+E(f538(x15681,x15683,x15684),f538(x15682,x15683,x15684)) % 154.70/154.57 [1569]~E(x15691,x15692)+E(f538(x15693,x15691,x15694),f538(x15693,x15692,x15694)) % 154.70/154.57 [1570]~E(x15701,x15702)+E(f538(x15703,x15704,x15701),f538(x15703,x15704,x15702)) % 154.70/154.57 [1571]~E(x15711,x15712)+E(f431(x15711,x15713,x15714,x15715),f431(x15712,x15713,x15714,x15715)) % 154.70/154.57 [1572]~E(x15721,x15722)+E(f431(x15723,x15721,x15724,x15725),f431(x15723,x15722,x15724,x15725)) % 154.70/154.57 [1573]~E(x15731,x15732)+E(f431(x15733,x15734,x15731,x15735),f431(x15733,x15734,x15732,x15735)) % 154.70/154.57 [1574]~E(x15741,x15742)+E(f431(x15743,x15744,x15745,x15741),f431(x15743,x15744,x15745,x15742)) % 154.70/154.57 [1575]~E(x15751,x15752)+E(f429(x15751,x15753,x15754,x15755),f429(x15752,x15753,x15754,x15755)) % 154.70/154.57 [1576]~E(x15761,x15762)+E(f429(x15763,x15761,x15764,x15765),f429(x15763,x15762,x15764,x15765)) % 154.70/154.57 [1577]~E(x15771,x15772)+E(f429(x15773,x15774,x15771,x15775),f429(x15773,x15774,x15772,x15775)) % 154.70/154.57 [1578]~E(x15781,x15782)+E(f429(x15783,x15784,x15785,x15781),f429(x15783,x15784,x15785,x15782)) % 154.70/154.57 [1579]~E(x15791,x15792)+E(f825(x15791,x15793,x15794),f825(x15792,x15793,x15794)) % 154.70/154.57 [1580]~E(x15801,x15802)+E(f825(x15803,x15801,x15804),f825(x15803,x15802,x15804)) % 154.70/154.57 [1581]~E(x15811,x15812)+E(f825(x15813,x15814,x15811),f825(x15813,x15814,x15812)) % 154.70/154.57 [1582]~E(x15821,x15822)+E(f478(x15821,x15823,x15824),f478(x15822,x15823,x15824)) % 154.70/154.57 [1583]~E(x15831,x15832)+E(f478(x15833,x15831,x15834),f478(x15833,x15832,x15834)) % 154.70/154.57 [1584]~E(x15841,x15842)+E(f478(x15843,x15844,x15841),f478(x15843,x15844,x15842)) % 154.70/154.57 [1585]~E(x15851,x15852)+E(f642(x15851,x15853,x15854,x15855,x15856),f642(x15852,x15853,x15854,x15855,x15856)) % 154.70/154.57 [1586]~E(x15861,x15862)+E(f642(x15863,x15861,x15864,x15865,x15866),f642(x15863,x15862,x15864,x15865,x15866)) % 154.70/154.57 [1587]~E(x15871,x15872)+E(f642(x15873,x15874,x15871,x15875,x15876),f642(x15873,x15874,x15872,x15875,x15876)) % 154.70/154.57 [1588]~E(x15881,x15882)+E(f642(x15883,x15884,x15885,x15881,x15886),f642(x15883,x15884,x15885,x15882,x15886)) % 154.70/154.57 [1589]~E(x15891,x15892)+E(f642(x15893,x15894,x15895,x15896,x15891),f642(x15893,x15894,x15895,x15896,x15892)) % 154.70/154.57 [1590]~E(x15901,x15902)+E(f258(x15901,x15903,x15904),f258(x15902,x15903,x15904)) % 154.70/154.57 [1591]~E(x15911,x15912)+E(f258(x15913,x15911,x15914),f258(x15913,x15912,x15914)) % 154.70/154.57 [1592]~E(x15921,x15922)+E(f258(x15923,x15924,x15921),f258(x15923,x15924,x15922)) % 154.70/154.57 [1593]~E(x15931,x15932)+E(f278(x15931,x15933,x15934),f278(x15932,x15933,x15934)) % 154.70/154.57 [1594]~E(x15941,x15942)+E(f278(x15943,x15941,x15944),f278(x15943,x15942,x15944)) % 154.70/154.57 [1595]~E(x15951,x15952)+E(f278(x15953,x15954,x15951),f278(x15953,x15954,x15952)) % 154.70/154.57 [1596]~E(x15961,x15962)+E(f368(x15961,x15963),f368(x15962,x15963)) % 154.70/154.57 [1597]~E(x15971,x15972)+E(f368(x15973,x15971),f368(x15973,x15972)) % 154.70/154.57 [1598]~E(x15981,x15982)+E(f467(x15981,x15983,x15984),f467(x15982,x15983,x15984)) % 154.70/154.57 [1599]~E(x15991,x15992)+E(f467(x15993,x15991,x15994),f467(x15993,x15992,x15994)) % 154.70/154.57 [1600]~E(x16001,x16002)+E(f467(x16003,x16004,x16001),f467(x16003,x16004,x16002)) % 154.70/154.57 [1601]~E(x16011,x16012)+E(f699(x16011,x16013,x16014,x16015,x16016),f699(x16012,x16013,x16014,x16015,x16016)) % 154.70/154.57 [1602]~E(x16021,x16022)+E(f699(x16023,x16021,x16024,x16025,x16026),f699(x16023,x16022,x16024,x16025,x16026)) % 154.70/154.57 [1603]~E(x16031,x16032)+E(f699(x16033,x16034,x16031,x16035,x16036),f699(x16033,x16034,x16032,x16035,x16036)) % 154.70/154.57 [1604]~E(x16041,x16042)+E(f699(x16043,x16044,x16045,x16041,x16046),f699(x16043,x16044,x16045,x16042,x16046)) % 154.70/154.57 [1605]~E(x16051,x16052)+E(f699(x16053,x16054,x16055,x16056,x16051),f699(x16053,x16054,x16055,x16056,x16052)) % 154.70/154.57 [1606]~E(x16061,x16062)+E(f808(x16061,x16063),f808(x16062,x16063)) % 154.70/154.57 [1607]~E(x16071,x16072)+E(f808(x16073,x16071),f808(x16073,x16072)) % 154.70/154.57 [1608]~E(x16081,x16082)+E(f427(x16081,x16083,x16084,x16085),f427(x16082,x16083,x16084,x16085)) % 154.70/154.57 [1609]~E(x16091,x16092)+E(f427(x16093,x16091,x16094,x16095),f427(x16093,x16092,x16094,x16095)) % 154.70/154.57 [1610]~E(x16101,x16102)+E(f427(x16103,x16104,x16101,x16105),f427(x16103,x16104,x16102,x16105)) % 154.70/154.57 [1611]~E(x16111,x16112)+E(f427(x16113,x16114,x16115,x16111),f427(x16113,x16114,x16115,x16112)) % 154.70/154.57 [1612]~E(x16121,x16122)+E(f530(x16121,x16123,x16124),f530(x16122,x16123,x16124)) % 154.70/154.57 [1613]~E(x16131,x16132)+E(f530(x16133,x16131,x16134),f530(x16133,x16132,x16134)) % 154.70/154.57 [1614]~E(x16141,x16142)+E(f530(x16143,x16144,x16141),f530(x16143,x16144,x16142)) % 154.70/154.57 [1615]~E(x16151,x16152)+E(f746(x16151,x16153),f746(x16152,x16153)) % 154.70/154.57 [1616]~E(x16161,x16162)+E(f746(x16163,x16161),f746(x16163,x16162)) % 154.70/154.57 [1617]~E(x16171,x16172)+E(f546(x16171,x16173,x16174,x16175,x16176,x16177,x16178),f546(x16172,x16173,x16174,x16175,x16176,x16177,x16178)) % 154.70/154.57 [1618]~E(x16181,x16182)+E(f546(x16183,x16181,x16184,x16185,x16186,x16187,x16188),f546(x16183,x16182,x16184,x16185,x16186,x16187,x16188)) % 154.70/154.57 [1619]~E(x16191,x16192)+E(f546(x16193,x16194,x16191,x16195,x16196,x16197,x16198),f546(x16193,x16194,x16192,x16195,x16196,x16197,x16198)) % 154.70/154.57 [1620]~E(x16201,x16202)+E(f546(x16203,x16204,x16205,x16201,x16206,x16207,x16208),f546(x16203,x16204,x16205,x16202,x16206,x16207,x16208)) % 154.70/154.57 [1621]~E(x16211,x16212)+E(f546(x16213,x16214,x16215,x16216,x16211,x16217,x16218),f546(x16213,x16214,x16215,x16216,x16212,x16217,x16218)) % 154.70/154.57 [1622]~E(x16221,x16222)+E(f546(x16223,x16224,x16225,x16226,x16227,x16221,x16228),f546(x16223,x16224,x16225,x16226,x16227,x16222,x16228)) % 154.70/154.57 [1623]~E(x16231,x16232)+E(f546(x16233,x16234,x16235,x16236,x16237,x16238,x16231),f546(x16233,x16234,x16235,x16236,x16237,x16238,x16232)) % 154.70/154.57 [1624]~E(x16241,x16242)+E(f581(x16241,x16243,x16244,x16245),f581(x16242,x16243,x16244,x16245)) % 154.70/154.57 [1625]~E(x16251,x16252)+E(f581(x16253,x16251,x16254,x16255),f581(x16253,x16252,x16254,x16255)) % 154.70/154.57 [1626]~E(x16261,x16262)+E(f581(x16263,x16264,x16261,x16265),f581(x16263,x16264,x16262,x16265)) % 154.70/154.57 [1627]~E(x16271,x16272)+E(f581(x16273,x16274,x16275,x16271),f581(x16273,x16274,x16275,x16272)) % 154.70/154.57 [1628]~E(x16281,x16282)+E(f522(x16281,x16283,x16284),f522(x16282,x16283,x16284)) % 154.70/154.57 [1629]~E(x16291,x16292)+E(f522(x16293,x16291,x16294),f522(x16293,x16292,x16294)) % 154.70/154.57 [1630]~E(x16301,x16302)+E(f522(x16303,x16304,x16301),f522(x16303,x16304,x16302)) % 154.70/154.57 [1631]~E(x16311,x16312)+E(f210(x16311,x16313),f210(x16312,x16313)) % 154.70/154.57 [1632]~E(x16321,x16322)+E(f210(x16323,x16321),f210(x16323,x16322)) % 154.70/154.57 [1633]~E(x16331,x16332)+E(f408(x16331,x16333,x16334,x16335),f408(x16332,x16333,x16334,x16335)) % 154.70/154.57 [1634]~E(x16341,x16342)+E(f408(x16343,x16341,x16344,x16345),f408(x16343,x16342,x16344,x16345)) % 154.70/154.57 [1635]~E(x16351,x16352)+E(f408(x16353,x16354,x16351,x16355),f408(x16353,x16354,x16352,x16355)) % 154.70/154.57 [1636]~E(x16361,x16362)+E(f408(x16363,x16364,x16365,x16361),f408(x16363,x16364,x16365,x16362)) % 154.70/154.57 [1637]~E(x16371,x16372)+E(f369(x16371,x16373),f369(x16372,x16373)) % 154.70/154.57 [1638]~E(x16381,x16382)+E(f369(x16383,x16381),f369(x16383,x16382)) % 154.70/154.57 [1639]~E(x16391,x16392)+E(f736(x16391,x16393,x16394,x16395),f736(x16392,x16393,x16394,x16395)) % 154.70/154.57 [1640]~E(x16401,x16402)+E(f736(x16403,x16401,x16404,x16405),f736(x16403,x16402,x16404,x16405)) % 154.70/154.57 [1641]~E(x16411,x16412)+E(f736(x16413,x16414,x16411,x16415),f736(x16413,x16414,x16412,x16415)) % 154.70/154.57 [1642]~E(x16421,x16422)+E(f736(x16423,x16424,x16425,x16421),f736(x16423,x16424,x16425,x16422)) % 154.70/154.57 [1643]~E(x16431,x16432)+E(f76(x16431,x16433,x16434,x16435,x16436),f76(x16432,x16433,x16434,x16435,x16436)) % 154.70/154.57 [1644]~E(x16441,x16442)+E(f76(x16443,x16441,x16444,x16445,x16446),f76(x16443,x16442,x16444,x16445,x16446)) % 154.70/154.57 [1645]~E(x16451,x16452)+E(f76(x16453,x16454,x16451,x16455,x16456),f76(x16453,x16454,x16452,x16455,x16456)) % 154.70/154.57 [1646]~E(x16461,x16462)+E(f76(x16463,x16464,x16465,x16461,x16466),f76(x16463,x16464,x16465,x16462,x16466)) % 154.70/154.57 [1647]~E(x16471,x16472)+E(f76(x16473,x16474,x16475,x16476,x16471),f76(x16473,x16474,x16475,x16476,x16472)) % 154.70/154.57 [1648]~E(x16481,x16482)+E(f393(x16481,x16483),f393(x16482,x16483)) % 154.70/154.57 [1649]~E(x16491,x16492)+E(f393(x16493,x16491),f393(x16493,x16492)) % 154.70/154.57 [1650]~E(x16501,x16502)+E(f599(x16501,x16503,x16504),f599(x16502,x16503,x16504)) % 154.70/154.57 [1651]~E(x16511,x16512)+E(f599(x16513,x16511,x16514),f599(x16513,x16512,x16514)) % 154.70/154.57 [1652]~E(x16521,x16522)+E(f599(x16523,x16524,x16521),f599(x16523,x16524,x16522)) % 154.70/154.57 [1653]~E(x16531,x16532)+E(f495(x16531,x16533,x16534),f495(x16532,x16533,x16534)) % 154.70/154.57 [1654]~E(x16541,x16542)+E(f495(x16543,x16541,x16544),f495(x16543,x16542,x16544)) % 154.70/154.57 [1655]~E(x16551,x16552)+E(f495(x16553,x16554,x16551),f495(x16553,x16554,x16552)) % 154.70/154.57 [1656]~E(x16561,x16562)+E(f607(x16561,x16563,x16564,x16565,x16566,x16567),f607(x16562,x16563,x16564,x16565,x16566,x16567)) % 154.70/154.57 [1657]~E(x16571,x16572)+E(f607(x16573,x16571,x16574,x16575,x16576,x16577),f607(x16573,x16572,x16574,x16575,x16576,x16577)) % 154.70/154.57 [1658]~E(x16581,x16582)+E(f607(x16583,x16584,x16581,x16585,x16586,x16587),f607(x16583,x16584,x16582,x16585,x16586,x16587)) % 154.70/154.57 [1659]~E(x16591,x16592)+E(f607(x16593,x16594,x16595,x16591,x16596,x16597),f607(x16593,x16594,x16595,x16592,x16596,x16597)) % 154.70/154.57 [1660]~E(x16601,x16602)+E(f607(x16603,x16604,x16605,x16606,x16601,x16607),f607(x16603,x16604,x16605,x16606,x16602,x16607)) % 154.70/154.57 [1661]~E(x16611,x16612)+E(f607(x16613,x16614,x16615,x16616,x16617,x16611),f607(x16613,x16614,x16615,x16616,x16617,x16612)) % 154.70/154.57 [1662]~E(x16621,x16622)+E(f644(x16621,x16623,x16624,x16625,x16626),f644(x16622,x16623,x16624,x16625,x16626)) % 154.70/154.57 [1663]~E(x16631,x16632)+E(f644(x16633,x16631,x16634,x16635,x16636),f644(x16633,x16632,x16634,x16635,x16636)) % 154.70/154.57 [1664]~E(x16641,x16642)+E(f644(x16643,x16644,x16641,x16645,x16646),f644(x16643,x16644,x16642,x16645,x16646)) % 154.70/154.57 [1665]~E(x16651,x16652)+E(f644(x16653,x16654,x16655,x16651,x16656),f644(x16653,x16654,x16655,x16652,x16656)) % 154.70/154.57 [1666]~E(x16661,x16662)+E(f644(x16663,x16664,x16665,x16666,x16661),f644(x16663,x16664,x16665,x16666,x16662)) % 154.70/154.57 [1667]~E(x16671,x16672)+E(f336(x16671),f336(x16672)) % 154.70/154.57 [1668]~E(x16681,x16682)+E(f707(x16681,x16683,x16684),f707(x16682,x16683,x16684)) % 154.70/154.57 [1669]~E(x16691,x16692)+E(f707(x16693,x16691,x16694),f707(x16693,x16692,x16694)) % 154.70/154.57 [1670]~E(x16701,x16702)+E(f707(x16703,x16704,x16701),f707(x16703,x16704,x16702)) % 154.70/154.57 [1671]~E(x16711,x16712)+E(f795(x16711,x16713,x16714),f795(x16712,x16713,x16714)) % 154.70/154.57 [1672]~E(x16721,x16722)+E(f795(x16723,x16721,x16724),f795(x16723,x16722,x16724)) % 154.70/154.57 [1673]~E(x16731,x16732)+E(f795(x16733,x16734,x16731),f795(x16733,x16734,x16732)) % 154.70/154.57 [1674]~E(x16741,x16742)+E(f529(x16741,x16743,x16744,x16745,x16746),f529(x16742,x16743,x16744,x16745,x16746)) % 154.70/154.57 [1675]~E(x16751,x16752)+E(f529(x16753,x16751,x16754,x16755,x16756),f529(x16753,x16752,x16754,x16755,x16756)) % 154.70/154.57 [1676]~E(x16761,x16762)+E(f529(x16763,x16764,x16761,x16765,x16766),f529(x16763,x16764,x16762,x16765,x16766)) % 154.70/154.57 [1677]~E(x16771,x16772)+E(f529(x16773,x16774,x16775,x16771,x16776),f529(x16773,x16774,x16775,x16772,x16776)) % 154.70/154.57 [1678]~E(x16781,x16782)+E(f529(x16783,x16784,x16785,x16786,x16781),f529(x16783,x16784,x16785,x16786,x16782)) % 154.70/154.57 [1679]~E(x16791,x16792)+E(f755(x16791,x16793,x16794),f755(x16792,x16793,x16794)) % 154.70/154.57 [1680]~E(x16801,x16802)+E(f755(x16803,x16801,x16804),f755(x16803,x16802,x16804)) % 154.70/154.57 [1681]~E(x16811,x16812)+E(f755(x16813,x16814,x16811),f755(x16813,x16814,x16812)) % 154.70/154.57 [1682]~E(x16821,x16822)+E(f673(x16821,x16823,x16824,x16825,x16826),f673(x16822,x16823,x16824,x16825,x16826)) % 154.70/154.57 [1683]~E(x16831,x16832)+E(f673(x16833,x16831,x16834,x16835,x16836),f673(x16833,x16832,x16834,x16835,x16836)) % 154.70/154.57 [1684]~E(x16841,x16842)+E(f673(x16843,x16844,x16841,x16845,x16846),f673(x16843,x16844,x16842,x16845,x16846)) % 154.70/154.57 [1685]~E(x16851,x16852)+E(f673(x16853,x16854,x16855,x16851,x16856),f673(x16853,x16854,x16855,x16852,x16856)) % 154.70/154.57 [1686]~E(x16861,x16862)+E(f673(x16863,x16864,x16865,x16866,x16861),f673(x16863,x16864,x16865,x16866,x16862)) % 154.70/154.57 [1687]~E(x16871,x16872)+E(f577(x16871,x16873,x16874,x16875,x16876,x16877),f577(x16872,x16873,x16874,x16875,x16876,x16877)) % 154.70/154.57 [1688]~E(x16881,x16882)+E(f577(x16883,x16881,x16884,x16885,x16886,x16887),f577(x16883,x16882,x16884,x16885,x16886,x16887)) % 154.70/154.57 [1689]~E(x16891,x16892)+E(f577(x16893,x16894,x16891,x16895,x16896,x16897),f577(x16893,x16894,x16892,x16895,x16896,x16897)) % 154.70/154.57 [1690]~E(x16901,x16902)+E(f577(x16903,x16904,x16905,x16901,x16906,x16907),f577(x16903,x16904,x16905,x16902,x16906,x16907)) % 154.70/154.57 [1691]~E(x16911,x16912)+E(f577(x16913,x16914,x16915,x16916,x16911,x16917),f577(x16913,x16914,x16915,x16916,x16912,x16917)) % 154.70/154.57 [1692]~E(x16921,x16922)+E(f577(x16923,x16924,x16925,x16926,x16927,x16921),f577(x16923,x16924,x16925,x16926,x16927,x16922)) % 154.70/154.57 [1693]~E(x16931,x16932)+E(f463(x16931,x16933,x16934,x16935),f463(x16932,x16933,x16934,x16935)) % 154.70/154.57 [1694]~E(x16941,x16942)+E(f463(x16943,x16941,x16944,x16945),f463(x16943,x16942,x16944,x16945)) % 154.70/154.57 [1695]~E(x16951,x16952)+E(f463(x16953,x16954,x16951,x16955),f463(x16953,x16954,x16952,x16955)) % 154.70/154.57 [1696]~E(x16961,x16962)+E(f463(x16963,x16964,x16965,x16961),f463(x16963,x16964,x16965,x16962)) % 154.70/154.57 [1697]~E(x16971,x16972)+E(f562(x16971,x16973,x16974,x16975),f562(x16972,x16973,x16974,x16975)) % 154.70/154.57 [1698]~E(x16981,x16982)+E(f562(x16983,x16981,x16984,x16985),f562(x16983,x16982,x16984,x16985)) % 154.70/154.57 [1699]~E(x16991,x16992)+E(f562(x16993,x16994,x16991,x16995),f562(x16993,x16994,x16992,x16995)) % 154.70/154.57 [1700]~E(x17001,x17002)+E(f562(x17003,x17004,x17005,x17001),f562(x17003,x17004,x17005,x17002)) % 154.70/154.57 [1701]~E(x17011,x17012)+E(f462(x17011,x17013,x17014,x17015),f462(x17012,x17013,x17014,x17015)) % 154.70/154.57 [1702]~E(x17021,x17022)+E(f462(x17023,x17021,x17024,x17025),f462(x17023,x17022,x17024,x17025)) % 154.70/154.57 [1703]~E(x17031,x17032)+E(f462(x17033,x17034,x17031,x17035),f462(x17033,x17034,x17032,x17035)) % 154.70/154.57 [1704]~E(x17041,x17042)+E(f462(x17043,x17044,x17045,x17041),f462(x17043,x17044,x17045,x17042)) % 154.70/154.57 [1705]~E(x17051,x17052)+E(f866(x17051,x17053,x17054,x17055,x17056,x17057,x17058),f866(x17052,x17053,x17054,x17055,x17056,x17057,x17058)) % 154.70/154.57 [1706]~E(x17061,x17062)+E(f866(x17063,x17061,x17064,x17065,x17066,x17067,x17068),f866(x17063,x17062,x17064,x17065,x17066,x17067,x17068)) % 154.70/154.57 [1707]~E(x17071,x17072)+E(f866(x17073,x17074,x17071,x17075,x17076,x17077,x17078),f866(x17073,x17074,x17072,x17075,x17076,x17077,x17078)) % 154.70/154.57 [1708]~E(x17081,x17082)+E(f866(x17083,x17084,x17085,x17081,x17086,x17087,x17088),f866(x17083,x17084,x17085,x17082,x17086,x17087,x17088)) % 154.70/154.57 [1709]~E(x17091,x17092)+E(f866(x17093,x17094,x17095,x17096,x17091,x17097,x17098),f866(x17093,x17094,x17095,x17096,x17092,x17097,x17098)) % 154.70/154.57 [1710]~E(x17101,x17102)+E(f866(x17103,x17104,x17105,x17106,x17107,x17101,x17108),f866(x17103,x17104,x17105,x17106,x17107,x17102,x17108)) % 154.70/154.57 [1711]~E(x17111,x17112)+E(f866(x17113,x17114,x17115,x17116,x17117,x17118,x17111),f866(x17113,x17114,x17115,x17116,x17117,x17118,x17112)) % 154.70/154.57 [1712]~E(x17121,x17122)+E(f497(x17121,x17123,x17124),f497(x17122,x17123,x17124)) % 154.70/154.57 [1713]~E(x17131,x17132)+E(f497(x17133,x17131,x17134),f497(x17133,x17132,x17134)) % 154.70/154.57 [1714]~E(x17141,x17142)+E(f497(x17143,x17144,x17141),f497(x17143,x17144,x17142)) % 154.70/154.57 [1715]~E(x17151,x17152)+E(f94(x17151),f94(x17152)) % 154.70/154.57 [1716]~E(x17161,x17162)+E(f615(x17161,x17163,x17164),f615(x17162,x17163,x17164)) % 154.70/154.57 [1717]~E(x17171,x17172)+E(f615(x17173,x17171,x17174),f615(x17173,x17172,x17174)) % 154.70/154.57 [1718]~E(x17181,x17182)+E(f615(x17183,x17184,x17181),f615(x17183,x17184,x17182)) % 154.70/154.57 [1719]~E(x17191,x17192)+E(f786(x17191,x17193,x17194,x17195,x17196),f786(x17192,x17193,x17194,x17195,x17196)) % 154.70/154.57 [1720]~E(x17201,x17202)+E(f786(x17203,x17201,x17204,x17205,x17206),f786(x17203,x17202,x17204,x17205,x17206)) % 154.70/154.57 [1721]~E(x17211,x17212)+E(f786(x17213,x17214,x17211,x17215,x17216),f786(x17213,x17214,x17212,x17215,x17216)) % 154.70/154.57 [1722]~E(x17221,x17222)+E(f786(x17223,x17224,x17225,x17221,x17226),f786(x17223,x17224,x17225,x17222,x17226)) % 154.70/154.57 [1723]~E(x17231,x17232)+E(f786(x17233,x17234,x17235,x17236,x17231),f786(x17233,x17234,x17235,x17236,x17232)) % 154.70/154.57 [1724]~E(x17241,x17242)+E(f208(x17241),f208(x17242)) % 154.70/154.57 [1725]~E(x17251,x17252)+E(f233(x17251,x17253,x17254,x17255),f233(x17252,x17253,x17254,x17255)) % 154.70/154.57 [1726]~E(x17261,x17262)+E(f233(x17263,x17261,x17264,x17265),f233(x17263,x17262,x17264,x17265)) % 154.70/154.57 [1727]~E(x17271,x17272)+E(f233(x17273,x17274,x17271,x17275),f233(x17273,x17274,x17272,x17275)) % 154.70/154.57 [1728]~E(x17281,x17282)+E(f233(x17283,x17284,x17285,x17281),f233(x17283,x17284,x17285,x17282)) % 154.70/154.57 [1729]~E(x17291,x17292)+E(f509(x17291,x17293,x17294,x17295),f509(x17292,x17293,x17294,x17295)) % 154.70/154.57 [1730]~E(x17301,x17302)+E(f509(x17303,x17301,x17304,x17305),f509(x17303,x17302,x17304,x17305)) % 154.70/154.57 [1731]~E(x17311,x17312)+E(f509(x17313,x17314,x17311,x17315),f509(x17313,x17314,x17312,x17315)) % 154.70/154.57 [1732]~E(x17321,x17322)+E(f509(x17323,x17324,x17325,x17321),f509(x17323,x17324,x17325,x17322)) % 154.70/154.57 [1733]~E(x17331,x17332)+E(f284(x17331,x17333),f284(x17332,x17333)) % 154.70/154.57 [1734]~E(x17341,x17342)+E(f284(x17343,x17341),f284(x17343,x17342)) % 154.70/154.57 [1735]~E(x17351,x17352)+E(f294(x17351,x17353,x17354),f294(x17352,x17353,x17354)) % 154.70/154.57 [1736]~E(x17361,x17362)+E(f294(x17363,x17361,x17364),f294(x17363,x17362,x17364)) % 154.70/154.57 [1737]~E(x17371,x17372)+E(f294(x17373,x17374,x17371),f294(x17373,x17374,x17372)) % 154.70/154.57 [1738]~E(x17381,x17382)+E(f711(x17381,x17383,x17384),f711(x17382,x17383,x17384)) % 154.70/154.57 [1739]~E(x17391,x17392)+E(f711(x17393,x17391,x17394),f711(x17393,x17392,x17394)) % 154.70/154.57 [1740]~E(x17401,x17402)+E(f711(x17403,x17404,x17401),f711(x17403,x17404,x17402)) % 154.70/154.57 [1741]~E(x17411,x17412)+E(f500(x17411,x17413,x17414,x17415,x17416,x17417,x17418,x17419),f500(x17412,x17413,x17414,x17415,x17416,x17417,x17418,x17419)) % 154.70/154.57 [1742]~E(x17421,x17422)+E(f500(x17423,x17421,x17424,x17425,x17426,x17427,x17428,x17429),f500(x17423,x17422,x17424,x17425,x17426,x17427,x17428,x17429)) % 154.70/154.57 [1743]~E(x17431,x17432)+E(f500(x17433,x17434,x17431,x17435,x17436,x17437,x17438,x17439),f500(x17433,x17434,x17432,x17435,x17436,x17437,x17438,x17439)) % 154.70/154.57 [1744]~E(x17441,x17442)+E(f500(x17443,x17444,x17445,x17441,x17446,x17447,x17448,x17449),f500(x17443,x17444,x17445,x17442,x17446,x17447,x17448,x17449)) % 154.70/154.57 [1745]~E(x17451,x17452)+E(f500(x17453,x17454,x17455,x17456,x17451,x17457,x17458,x17459),f500(x17453,x17454,x17455,x17456,x17452,x17457,x17458,x17459)) % 154.70/154.57 [1746]~E(x17461,x17462)+E(f500(x17463,x17464,x17465,x17466,x17467,x17461,x17468,x17469),f500(x17463,x17464,x17465,x17466,x17467,x17462,x17468,x17469)) % 154.70/154.57 [1747]~E(x17471,x17472)+E(f500(x17473,x17474,x17475,x17476,x17477,x17478,x17471,x17479),f500(x17473,x17474,x17475,x17476,x17477,x17478,x17472,x17479)) % 154.70/154.57 [1748]~E(x17481,x17482)+E(f500(x17483,x17484,x17485,x17486,x17487,x17488,x17489,x17481),f500(x17483,x17484,x17485,x17486,x17487,x17488,x17489,x17482)) % 154.70/154.57 [1749]~E(x17491,x17492)+E(f643(x17491,x17493,x17494,x17495,x17496),f643(x17492,x17493,x17494,x17495,x17496)) % 154.70/154.57 [1750]~E(x17501,x17502)+E(f643(x17503,x17501,x17504,x17505,x17506),f643(x17503,x17502,x17504,x17505,x17506)) % 154.70/154.57 [1751]~E(x17511,x17512)+E(f643(x17513,x17514,x17511,x17515,x17516),f643(x17513,x17514,x17512,x17515,x17516)) % 154.70/154.57 [1752]~E(x17521,x17522)+E(f643(x17523,x17524,x17525,x17521,x17526),f643(x17523,x17524,x17525,x17522,x17526)) % 154.70/154.57 [1753]~E(x17531,x17532)+E(f643(x17533,x17534,x17535,x17536,x17531),f643(x17533,x17534,x17535,x17536,x17532)) % 154.70/154.57 [1754]~E(x17541,x17542)+E(f440(x17541,x17543,x17544),f440(x17542,x17543,x17544)) % 154.70/154.57 [1755]~E(x17551,x17552)+E(f440(x17553,x17551,x17554),f440(x17553,x17552,x17554)) % 154.70/154.57 [1756]~E(x17561,x17562)+E(f440(x17563,x17564,x17561),f440(x17563,x17564,x17562)) % 154.70/154.57 [1757]~E(x17571,x17572)+E(f437(x17571,x17573,x17574,x17575),f437(x17572,x17573,x17574,x17575)) % 154.70/154.57 [1758]~E(x17581,x17582)+E(f437(x17583,x17581,x17584,x17585),f437(x17583,x17582,x17584,x17585)) % 154.70/154.57 [1759]~E(x17591,x17592)+E(f437(x17593,x17594,x17591,x17595),f437(x17593,x17594,x17592,x17595)) % 154.70/154.57 [1760]~E(x17601,x17602)+E(f437(x17603,x17604,x17605,x17601),f437(x17603,x17604,x17605,x17602)) % 154.70/154.57 [1761]~E(x17611,x17612)+E(f485(x17611,x17613),f485(x17612,x17613)) % 154.70/154.57 [1762]~E(x17621,x17622)+E(f485(x17623,x17621),f485(x17623,x17622)) % 154.70/154.57 [1763]~E(x17631,x17632)+E(f669(x17631,x17633),f669(x17632,x17633)) % 154.70/154.57 [1764]~E(x17641,x17642)+E(f669(x17643,x17641),f669(x17643,x17642)) % 154.70/154.57 [1765]~E(x17651,x17652)+E(f435(x17651,x17653,x17654,x17655),f435(x17652,x17653,x17654,x17655)) % 154.70/154.57 [1766]~E(x17661,x17662)+E(f435(x17663,x17661,x17664,x17665),f435(x17663,x17662,x17664,x17665)) % 154.70/154.57 [1767]~E(x17671,x17672)+E(f435(x17673,x17674,x17671,x17675),f435(x17673,x17674,x17672,x17675)) % 154.70/154.57 [1768]~E(x17681,x17682)+E(f435(x17683,x17684,x17685,x17681),f435(x17683,x17684,x17685,x17682)) % 154.70/154.57 [1769]~E(x17691,x17692)+E(f617(x17691,x17693,x17694),f617(x17692,x17693,x17694)) % 154.70/154.57 [1770]~E(x17701,x17702)+E(f617(x17703,x17701,x17704),f617(x17703,x17702,x17704)) % 154.70/154.57 [1771]~E(x17711,x17712)+E(f617(x17713,x17714,x17711),f617(x17713,x17714,x17712)) % 154.70/154.57 [1772]~E(x17721,x17722)+E(f851(x17721,x17723,x17724),f851(x17722,x17723,x17724)) % 154.70/154.57 [1773]~E(x17731,x17732)+E(f851(x17733,x17731,x17734),f851(x17733,x17732,x17734)) % 154.70/154.57 [1774]~E(x17741,x17742)+E(f851(x17743,x17744,x17741),f851(x17743,x17744,x17742)) % 154.70/154.57 [1775]~E(x17751,x17752)+E(f333(x17751),f333(x17752)) % 154.70/154.57 [1776]~E(x17761,x17762)+E(f733(x17761,x17763,x17764),f733(x17762,x17763,x17764)) % 154.70/154.57 [1777]~E(x17771,x17772)+E(f733(x17773,x17771,x17774),f733(x17773,x17772,x17774)) % 154.70/154.57 [1778]~E(x17781,x17782)+E(f733(x17783,x17784,x17781),f733(x17783,x17784,x17782)) % 154.70/154.57 [1779]~E(x17791,x17792)+E(f780(x17791,x17793,x17794),f780(x17792,x17793,x17794)) % 154.70/154.57 [1780]~E(x17801,x17802)+E(f780(x17803,x17801,x17804),f780(x17803,x17802,x17804)) % 154.70/154.57 [1781]~E(x17811,x17812)+E(f780(x17813,x17814,x17811),f780(x17813,x17814,x17812)) % 154.70/154.57 [1782]~E(x17821,x17822)+E(f359(x17821,x17823),f359(x17822,x17823)) % 154.70/154.57 [1783]~E(x17831,x17832)+E(f359(x17833,x17831),f359(x17833,x17832)) % 154.70/154.57 [1784]~E(x17841,x17842)+E(f712(x17841,x17843,x17844,x17845,x17846),f712(x17842,x17843,x17844,x17845,x17846)) % 154.70/154.57 [1785]~E(x17851,x17852)+E(f712(x17853,x17851,x17854,x17855,x17856),f712(x17853,x17852,x17854,x17855,x17856)) % 154.70/154.57 [1786]~E(x17861,x17862)+E(f712(x17863,x17864,x17861,x17865,x17866),f712(x17863,x17864,x17862,x17865,x17866)) % 154.70/154.57 [1787]~E(x17871,x17872)+E(f712(x17873,x17874,x17875,x17871,x17876),f712(x17873,x17874,x17875,x17872,x17876)) % 154.70/154.57 [1788]~E(x17881,x17882)+E(f712(x17883,x17884,x17885,x17886,x17881),f712(x17883,x17884,x17885,x17886,x17882)) % 154.70/154.57 [1789]~E(x17891,x17892)+E(f857(x17891,x17893,x17894),f857(x17892,x17893,x17894)) % 154.70/154.57 [1790]~E(x17901,x17902)+E(f857(x17903,x17901,x17904),f857(x17903,x17902,x17904)) % 154.70/154.57 [1791]~E(x17911,x17912)+E(f857(x17913,x17914,x17911),f857(x17913,x17914,x17912)) % 154.70/154.57 [1792]~E(x17921,x17922)+E(f777(x17921,x17923,x17924,x17925,x17926),f777(x17922,x17923,x17924,x17925,x17926)) % 154.70/154.57 [1793]~E(x17931,x17932)+E(f777(x17933,x17931,x17934,x17935,x17936),f777(x17933,x17932,x17934,x17935,x17936)) % 154.70/154.57 [1794]~E(x17941,x17942)+E(f777(x17943,x17944,x17941,x17945,x17946),f777(x17943,x17944,x17942,x17945,x17946)) % 154.70/154.57 [1795]~E(x17951,x17952)+E(f777(x17953,x17954,x17955,x17951,x17956),f777(x17953,x17954,x17955,x17952,x17956)) % 154.70/154.57 [1796]~E(x17961,x17962)+E(f777(x17963,x17964,x17965,x17966,x17961),f777(x17963,x17964,x17965,x17966,x17962)) % 154.70/154.57 [1797]~E(x17971,x17972)+E(f793(x17971,x17973,x17974),f793(x17972,x17973,x17974)) % 154.70/154.57 [1798]~E(x17981,x17982)+E(f793(x17983,x17981,x17984),f793(x17983,x17982,x17984)) % 154.70/154.57 [1799]~E(x17991,x17992)+E(f793(x17993,x17994,x17991),f793(x17993,x17994,x17992)) % 154.70/154.57 [1800]~E(x18001,x18002)+E(f771(x18001,x18003,x18004,x18005,x18006,x18007,x18008),f771(x18002,x18003,x18004,x18005,x18006,x18007,x18008)) % 154.70/154.57 [1801]~E(x18011,x18012)+E(f771(x18013,x18011,x18014,x18015,x18016,x18017,x18018),f771(x18013,x18012,x18014,x18015,x18016,x18017,x18018)) % 154.70/154.57 [1802]~E(x18021,x18022)+E(f771(x18023,x18024,x18021,x18025,x18026,x18027,x18028),f771(x18023,x18024,x18022,x18025,x18026,x18027,x18028)) % 154.70/154.57 [1803]~E(x18031,x18032)+E(f771(x18033,x18034,x18035,x18031,x18036,x18037,x18038),f771(x18033,x18034,x18035,x18032,x18036,x18037,x18038)) % 154.70/154.57 [1804]~E(x18041,x18042)+E(f771(x18043,x18044,x18045,x18046,x18041,x18047,x18048),f771(x18043,x18044,x18045,x18046,x18042,x18047,x18048)) % 154.70/154.57 [1805]~E(x18051,x18052)+E(f771(x18053,x18054,x18055,x18056,x18057,x18051,x18058),f771(x18053,x18054,x18055,x18056,x18057,x18052,x18058)) % 154.70/154.57 [1806]~E(x18061,x18062)+E(f771(x18063,x18064,x18065,x18066,x18067,x18068,x18061),f771(x18063,x18064,x18065,x18066,x18067,x18068,x18062)) % 154.70/154.57 [1807]~E(x18071,x18072)+E(f770(x18071,x18073,x18074,x18075,x18076,x18077),f770(x18072,x18073,x18074,x18075,x18076,x18077)) % 154.70/154.57 [1808]~E(x18081,x18082)+E(f770(x18083,x18081,x18084,x18085,x18086,x18087),f770(x18083,x18082,x18084,x18085,x18086,x18087)) % 154.70/154.57 [1809]~E(x18091,x18092)+E(f770(x18093,x18094,x18091,x18095,x18096,x18097),f770(x18093,x18094,x18092,x18095,x18096,x18097)) % 154.70/154.57 [1810]~E(x18101,x18102)+E(f770(x18103,x18104,x18105,x18101,x18106,x18107),f770(x18103,x18104,x18105,x18102,x18106,x18107)) % 154.70/154.57 [1811]~E(x18111,x18112)+E(f770(x18113,x18114,x18115,x18116,x18111,x18117),f770(x18113,x18114,x18115,x18116,x18112,x18117)) % 154.70/154.57 [1812]~E(x18121,x18122)+E(f770(x18123,x18124,x18125,x18126,x18127,x18121),f770(x18123,x18124,x18125,x18126,x18127,x18122)) % 154.70/154.57 [1813]~E(x18131,x18132)+E(f508(x18131,x18133,x18134),f508(x18132,x18133,x18134)) % 154.70/154.57 [1814]~E(x18141,x18142)+E(f508(x18143,x18141,x18144),f508(x18143,x18142,x18144)) % 154.70/154.57 [1815]~E(x18151,x18152)+E(f508(x18153,x18154,x18151),f508(x18153,x18154,x18152)) % 154.70/154.57 [1816]~E(x18161,x18162)+E(f287(x18161,x18163),f287(x18162,x18163)) % 154.70/154.57 [1817]~E(x18171,x18172)+E(f287(x18173,x18171),f287(x18173,x18172)) % 154.70/154.57 [1818]~E(x18181,x18182)+E(f742(x18181,x18183,x18184),f742(x18182,x18183,x18184)) % 154.70/154.57 [1819]~E(x18191,x18192)+E(f742(x18193,x18191,x18194),f742(x18193,x18192,x18194)) % 154.70/154.57 [1820]~E(x18201,x18202)+E(f742(x18203,x18204,x18201),f742(x18203,x18204,x18202)) % 154.70/154.57 [1821]~E(x18211,x18212)+E(f428(x18211,x18213,x18214,x18215),f428(x18212,x18213,x18214,x18215)) % 154.70/154.57 [1822]~E(x18221,x18222)+E(f428(x18223,x18221,x18224,x18225),f428(x18223,x18222,x18224,x18225)) % 154.70/154.57 [1823]~E(x18231,x18232)+E(f428(x18233,x18234,x18231,x18235),f428(x18233,x18234,x18232,x18235)) % 154.70/154.57 [1824]~E(x18241,x18242)+E(f428(x18243,x18244,x18245,x18241),f428(x18243,x18244,x18245,x18242)) % 154.70/154.57 [1825]~E(x18251,x18252)+E(f541(x18251,x18253,x18254),f541(x18252,x18253,x18254)) % 154.70/154.57 [1826]~E(x18261,x18262)+E(f541(x18263,x18261,x18264),f541(x18263,x18262,x18264)) % 154.70/154.57 [1827]~E(x18271,x18272)+E(f541(x18273,x18274,x18271),f541(x18273,x18274,x18272)) % 154.70/154.57 [1828]~E(x18281,x18282)+E(f655(x18281,x18283,x18284,x18285),f655(x18282,x18283,x18284,x18285)) % 154.70/154.57 [1829]~E(x18291,x18292)+E(f655(x18293,x18291,x18294,x18295),f655(x18293,x18292,x18294,x18295)) % 154.70/154.57 [1830]~E(x18301,x18302)+E(f655(x18303,x18304,x18301,x18305),f655(x18303,x18304,x18302,x18305)) % 154.70/154.57 [1831]~E(x18311,x18312)+E(f655(x18313,x18314,x18315,x18311),f655(x18313,x18314,x18315,x18312)) % 154.70/154.57 [1832]~E(x18321,x18322)+E(f505(x18321,x18323,x18324),f505(x18322,x18323,x18324)) % 154.70/154.57 [1833]~E(x18331,x18332)+E(f505(x18333,x18331,x18334),f505(x18333,x18332,x18334)) % 154.70/154.57 [1834]~E(x18341,x18342)+E(f505(x18343,x18344,x18341),f505(x18343,x18344,x18342)) % 154.70/154.57 [1835]~E(x18351,x18352)+E(f809(x18351,x18353,x18354),f809(x18352,x18353,x18354)) % 154.70/154.57 [1836]~E(x18361,x18362)+E(f809(x18363,x18361,x18364),f809(x18363,x18362,x18364)) % 154.70/154.57 [1837]~E(x18371,x18372)+E(f809(x18373,x18374,x18371),f809(x18373,x18374,x18372)) % 154.70/154.57 [1838]~E(x18381,x18382)+E(f436(x18381,x18383,x18384,x18385),f436(x18382,x18383,x18384,x18385)) % 154.70/154.57 [1839]~E(x18391,x18392)+E(f436(x18393,x18391,x18394,x18395),f436(x18393,x18392,x18394,x18395)) % 154.70/154.57 [1840]~E(x18401,x18402)+E(f436(x18403,x18404,x18401,x18405),f436(x18403,x18404,x18402,x18405)) % 154.70/154.57 [1841]~E(x18411,x18412)+E(f436(x18413,x18414,x18415,x18411),f436(x18413,x18414,x18415,x18412)) % 154.70/154.57 [1842]~E(x18421,x18422)+E(f684(x18421,x18423),f684(x18422,x18423)) % 154.70/154.57 [1843]~E(x18431,x18432)+E(f684(x18433,x18431),f684(x18433,x18432)) % 154.70/154.57 [1844]~E(x18441,x18442)+E(f439(x18441,x18443,x18444,x18445),f439(x18442,x18443,x18444,x18445)) % 154.70/154.57 [1845]~E(x18451,x18452)+E(f439(x18453,x18451,x18454,x18455),f439(x18453,x18452,x18454,x18455)) % 154.70/154.57 [1846]~E(x18461,x18462)+E(f439(x18463,x18464,x18461,x18465),f439(x18463,x18464,x18462,x18465)) % 154.70/154.57 [1847]~E(x18471,x18472)+E(f439(x18473,x18474,x18475,x18471),f439(x18473,x18474,x18475,x18472)) % 154.70/154.57 [1848]~E(x18481,x18482)+E(f506(x18481,x18483,x18484,x18485,x18486),f506(x18482,x18483,x18484,x18485,x18486)) % 154.70/154.57 [1849]~E(x18491,x18492)+E(f506(x18493,x18491,x18494,x18495,x18496),f506(x18493,x18492,x18494,x18495,x18496)) % 154.70/154.57 [1850]~E(x18501,x18502)+E(f506(x18503,x18504,x18501,x18505,x18506),f506(x18503,x18504,x18502,x18505,x18506)) % 154.70/154.57 [1851]~E(x18511,x18512)+E(f506(x18513,x18514,x18515,x18511,x18516),f506(x18513,x18514,x18515,x18512,x18516)) % 154.70/154.57 [1852]~E(x18521,x18522)+E(f506(x18523,x18524,x18525,x18526,x18521),f506(x18523,x18524,x18525,x18526,x18522)) % 154.70/154.57 [1853]~E(x18531,x18532)+E(f349(x18531,x18533,x18534,x18535),f349(x18532,x18533,x18534,x18535)) % 154.70/154.57 [1854]~E(x18541,x18542)+E(f349(x18543,x18541,x18544,x18545),f349(x18543,x18542,x18544,x18545)) % 154.70/154.57 [1855]~E(x18551,x18552)+E(f349(x18553,x18554,x18551,x18555),f349(x18553,x18554,x18552,x18555)) % 154.70/154.57 [1856]~E(x18561,x18562)+E(f349(x18563,x18564,x18565,x18561),f349(x18563,x18564,x18565,x18562)) % 154.70/154.57 [1857]~E(x18571,x18572)+E(f672(x18571,x18573,x18574,x18575,x18576),f672(x18572,x18573,x18574,x18575,x18576)) % 154.70/154.57 [1858]~E(x18581,x18582)+E(f672(x18583,x18581,x18584,x18585,x18586),f672(x18583,x18582,x18584,x18585,x18586)) % 154.70/154.57 [1859]~E(x18591,x18592)+E(f672(x18593,x18594,x18591,x18595,x18596),f672(x18593,x18594,x18592,x18595,x18596)) % 154.70/154.57 [1860]~E(x18601,x18602)+E(f672(x18603,x18604,x18605,x18601,x18606),f672(x18603,x18604,x18605,x18602,x18606)) % 154.70/154.57 [1861]~E(x18611,x18612)+E(f672(x18613,x18614,x18615,x18616,x18611),f672(x18613,x18614,x18615,x18616,x18612)) % 154.70/154.57 [1862]~E(x18621,x18622)+E(f785(x18621,x18623,x18624,x18625,x18626),f785(x18622,x18623,x18624,x18625,x18626)) % 154.70/154.57 [1863]~E(x18631,x18632)+E(f785(x18633,x18631,x18634,x18635,x18636),f785(x18633,x18632,x18634,x18635,x18636)) % 154.70/154.57 [1864]~E(x18641,x18642)+E(f785(x18643,x18644,x18641,x18645,x18646),f785(x18643,x18644,x18642,x18645,x18646)) % 154.70/154.57 [1865]~E(x18651,x18652)+E(f785(x18653,x18654,x18655,x18651,x18656),f785(x18653,x18654,x18655,x18652,x18656)) % 154.70/154.57 [1866]~E(x18661,x18662)+E(f785(x18663,x18664,x18665,x18666,x18661),f785(x18663,x18664,x18665,x18666,x18662)) % 154.70/154.57 [1867]~E(x18671,x18672)+E(f609(x18671,x18673,x18674,x18675,x18676,x18677),f609(x18672,x18673,x18674,x18675,x18676,x18677)) % 154.70/154.57 [1868]~E(x18681,x18682)+E(f609(x18683,x18681,x18684,x18685,x18686,x18687),f609(x18683,x18682,x18684,x18685,x18686,x18687)) % 154.70/154.57 [1869]~E(x18691,x18692)+E(f609(x18693,x18694,x18691,x18695,x18696,x18697),f609(x18693,x18694,x18692,x18695,x18696,x18697)) % 154.70/154.57 [1870]~E(x18701,x18702)+E(f609(x18703,x18704,x18705,x18701,x18706,x18707),f609(x18703,x18704,x18705,x18702,x18706,x18707)) % 154.70/154.57 [1871]~E(x18711,x18712)+E(f609(x18713,x18714,x18715,x18716,x18711,x18717),f609(x18713,x18714,x18715,x18716,x18712,x18717)) % 154.70/154.57 [1872]~E(x18721,x18722)+E(f609(x18723,x18724,x18725,x18726,x18727,x18721),f609(x18723,x18724,x18725,x18726,x18727,x18722)) % 154.70/154.57 [1873]~E(x18731,x18732)+E(f716(x18731,x18733,x18734,x18735,x18736),f716(x18732,x18733,x18734,x18735,x18736)) % 154.70/154.57 [1874]~E(x18741,x18742)+E(f716(x18743,x18741,x18744,x18745,x18746),f716(x18743,x18742,x18744,x18745,x18746)) % 154.70/154.57 [1875]~E(x18751,x18752)+E(f716(x18753,x18754,x18751,x18755,x18756),f716(x18753,x18754,x18752,x18755,x18756)) % 154.70/154.57 [1876]~E(x18761,x18762)+E(f716(x18763,x18764,x18765,x18761,x18766),f716(x18763,x18764,x18765,x18762,x18766)) % 154.70/154.57 [1877]~E(x18771,x18772)+E(f716(x18773,x18774,x18775,x18776,x18771),f716(x18773,x18774,x18775,x18776,x18772)) % 154.70/154.57 [1878]~E(x18781,x18782)+E(f558(x18781,x18783,x18784),f558(x18782,x18783,x18784)) % 154.70/154.57 [1879]~E(x18791,x18792)+E(f558(x18793,x18791,x18794),f558(x18793,x18792,x18794)) % 154.70/154.57 [1880]~E(x18801,x18802)+E(f558(x18803,x18804,x18801),f558(x18803,x18804,x18802)) % 154.70/154.57 [1881]~E(x18811,x18812)+E(f466(x18811,x18813,x18814,x18815),f466(x18812,x18813,x18814,x18815)) % 154.70/154.57 [1882]~E(x18821,x18822)+E(f466(x18823,x18821,x18824,x18825),f466(x18823,x18822,x18824,x18825)) % 154.70/154.57 [1883]~E(x18831,x18832)+E(f466(x18833,x18834,x18831,x18835),f466(x18833,x18834,x18832,x18835)) % 154.70/154.57 [1884]~E(x18841,x18842)+E(f466(x18843,x18844,x18845,x18841),f466(x18843,x18844,x18845,x18842)) % 154.70/154.57 [1885]~E(x18851,x18852)+E(f498(x18851,x18853,x18854),f498(x18852,x18853,x18854)) % 154.70/154.57 [1886]~E(x18861,x18862)+E(f498(x18863,x18861,x18864),f498(x18863,x18862,x18864)) % 154.70/154.57 [1887]~E(x18871,x18872)+E(f498(x18873,x18874,x18871),f498(x18873,x18874,x18872)) % 154.70/154.57 [1888]~E(x18881,x18882)+E(f377(x18881,x18883,x18884),f377(x18882,x18883,x18884)) % 154.70/154.57 [1889]~E(x18891,x18892)+E(f377(x18893,x18891,x18894),f377(x18893,x18892,x18894)) % 154.70/154.57 [1890]~E(x18901,x18902)+E(f377(x18903,x18904,x18901),f377(x18903,x18904,x18902)) % 154.70/154.57 [1891]~E(x18911,x18912)+E(f619(x18911,x18913,x18914,x18915,x18916),f619(x18912,x18913,x18914,x18915,x18916)) % 154.70/154.57 [1892]~E(x18921,x18922)+E(f619(x18923,x18921,x18924,x18925,x18926),f619(x18923,x18922,x18924,x18925,x18926)) % 154.70/154.57 [1893]~E(x18931,x18932)+E(f619(x18933,x18934,x18931,x18935,x18936),f619(x18933,x18934,x18932,x18935,x18936)) % 154.70/154.57 [1894]~E(x18941,x18942)+E(f619(x18943,x18944,x18945,x18941,x18946),f619(x18943,x18944,x18945,x18942,x18946)) % 154.70/154.57 [1895]~E(x18951,x18952)+E(f619(x18953,x18954,x18955,x18956,x18951),f619(x18953,x18954,x18955,x18956,x18952)) % 154.70/154.57 [1896]~E(x18961,x18962)+E(f591(x18961,x18963,x18964),f591(x18962,x18963,x18964)) % 154.70/154.57 [1897]~E(x18971,x18972)+E(f591(x18973,x18971,x18974),f591(x18973,x18972,x18974)) % 154.70/154.57 [1898]~E(x18981,x18982)+E(f591(x18983,x18984,x18981),f591(x18983,x18984,x18982)) % 154.70/154.57 [1899]~E(x18991,x18992)+E(f363(x18991,x18993,x18994,x18995,x18996),f363(x18992,x18993,x18994,x18995,x18996)) % 154.70/154.57 [1900]~E(x19001,x19002)+E(f363(x19003,x19001,x19004,x19005,x19006),f363(x19003,x19002,x19004,x19005,x19006)) % 154.70/154.57 [1901]~E(x19011,x19012)+E(f363(x19013,x19014,x19011,x19015,x19016),f363(x19013,x19014,x19012,x19015,x19016)) % 154.70/154.57 [1902]~E(x19021,x19022)+E(f363(x19023,x19024,x19025,x19021,x19026),f363(x19023,x19024,x19025,x19022,x19026)) % 154.70/154.57 [1903]~E(x19031,x19032)+E(f363(x19033,x19034,x19035,x19036,x19031),f363(x19033,x19034,x19035,x19036,x19032)) % 154.70/154.57 [1904]~E(x19041,x19042)+E(f487(x19041,x19043),f487(x19042,x19043)) % 154.70/154.57 [1905]~E(x19051,x19052)+E(f487(x19053,x19051),f487(x19053,x19052)) % 154.70/154.57 [1906]~E(x19061,x19062)+E(f692(x19061,x19063,x19064),f692(x19062,x19063,x19064)) % 154.70/154.57 [1907]~E(x19071,x19072)+E(f692(x19073,x19071,x19074),f692(x19073,x19072,x19074)) % 154.70/154.57 [1908]~E(x19081,x19082)+E(f692(x19083,x19084,x19081),f692(x19083,x19084,x19082)) % 154.70/154.57 [1909]~E(x19091,x19092)+E(f565(x19091,x19093),f565(x19092,x19093)) % 154.70/154.57 [1910]~E(x19101,x19102)+E(f565(x19103,x19101),f565(x19103,x19102)) % 154.70/154.57 [1911]~E(x19111,x19112)+E(f227(x19111,x19113),f227(x19112,x19113)) % 154.70/154.57 [1912]~E(x19121,x19122)+E(f227(x19123,x19121),f227(x19123,x19122)) % 154.70/154.57 [1913]~E(x19131,x19132)+E(f608(x19131,x19133,x19134,x19135,x19136,x19137),f608(x19132,x19133,x19134,x19135,x19136,x19137)) % 154.70/154.57 [1914]~E(x19141,x19142)+E(f608(x19143,x19141,x19144,x19145,x19146,x19147),f608(x19143,x19142,x19144,x19145,x19146,x19147)) % 154.70/154.57 [1915]~E(x19151,x19152)+E(f608(x19153,x19154,x19151,x19155,x19156,x19157),f608(x19153,x19154,x19152,x19155,x19156,x19157)) % 154.70/154.57 [1916]~E(x19161,x19162)+E(f608(x19163,x19164,x19165,x19161,x19166,x19167),f608(x19163,x19164,x19165,x19162,x19166,x19167)) % 154.70/154.57 [1917]~E(x19171,x19172)+E(f608(x19173,x19174,x19175,x19176,x19171,x19177),f608(x19173,x19174,x19175,x19176,x19172,x19177)) % 154.70/154.57 [1918]~E(x19181,x19182)+E(f608(x19183,x19184,x19185,x19186,x19187,x19181),f608(x19183,x19184,x19185,x19186,x19187,x19182)) % 154.70/154.57 [1919]~E(x19191,x19192)+E(f676(x19191,x19193,x19194),f676(x19192,x19193,x19194)) % 154.70/154.57 [1920]~E(x19201,x19202)+E(f676(x19203,x19201,x19204),f676(x19203,x19202,x19204)) % 154.70/154.57 [1921]~E(x19211,x19212)+E(f676(x19213,x19214,x19211),f676(x19213,x19214,x19212)) % 154.70/154.57 [1922]~E(x19221,x19222)+E(f665(x19221,x19223,x19224),f665(x19222,x19223,x19224)) % 154.70/154.57 [1923]~E(x19231,x19232)+E(f665(x19233,x19231,x19234),f665(x19233,x19232,x19234)) % 154.70/154.57 [1924]~E(x19241,x19242)+E(f665(x19243,x19244,x19241),f665(x19243,x19244,x19242)) % 154.70/154.57 [1925]~E(x19251,x19252)+E(f622(x19251,x19253,x19254,x19255),f622(x19252,x19253,x19254,x19255)) % 154.70/154.57 [1926]~E(x19261,x19262)+E(f622(x19263,x19261,x19264,x19265),f622(x19263,x19262,x19264,x19265)) % 154.70/154.57 [1927]~E(x19271,x19272)+E(f622(x19273,x19274,x19271,x19275),f622(x19273,x19274,x19272,x19275)) % 154.70/154.57 [1928]~E(x19281,x19282)+E(f622(x19283,x19284,x19285,x19281),f622(x19283,x19284,x19285,x19282)) % 154.70/154.57 [1929]~E(x19291,x19292)+E(f728(x19291,x19293,x19294,x19295),f728(x19292,x19293,x19294,x19295)) % 154.70/154.57 [1930]~E(x19301,x19302)+E(f728(x19303,x19301,x19304,x19305),f728(x19303,x19302,x19304,x19305)) % 154.70/154.57 [1931]~E(x19311,x19312)+E(f728(x19313,x19314,x19311,x19315),f728(x19313,x19314,x19312,x19315)) % 154.70/154.57 [1932]~E(x19321,x19322)+E(f728(x19323,x19324,x19325,x19321),f728(x19323,x19324,x19325,x19322)) % 154.70/154.57 [1933]~E(x19331,x19332)+E(f778(x19331,x19333,x19334),f778(x19332,x19333,x19334)) % 154.70/154.57 [1934]~E(x19341,x19342)+E(f778(x19343,x19341,x19344),f778(x19343,x19342,x19344)) % 154.70/154.57 [1935]~E(x19351,x19352)+E(f778(x19353,x19354,x19351),f778(x19353,x19354,x19352)) % 154.70/154.57 [1936]~E(x19361,x19362)+E(f836(x19361,x19363,x19364,x19365),f836(x19362,x19363,x19364,x19365)) % 154.70/154.57 [1937]~E(x19371,x19372)+E(f836(x19373,x19371,x19374,x19375),f836(x19373,x19372,x19374,x19375)) % 154.70/154.57 [1938]~E(x19381,x19382)+E(f836(x19383,x19384,x19381,x19385),f836(x19383,x19384,x19382,x19385)) % 154.70/154.57 [1939]~E(x19391,x19392)+E(f836(x19393,x19394,x19395,x19391),f836(x19393,x19394,x19395,x19392)) % 154.70/154.57 [1940]~E(x19401,x19402)+E(f420(x19401,x19403,x19404,x19405),f420(x19402,x19403,x19404,x19405)) % 154.70/154.57 [1941]~E(x19411,x19412)+E(f420(x19413,x19411,x19414,x19415),f420(x19413,x19412,x19414,x19415)) % 154.70/154.57 [1942]~E(x19421,x19422)+E(f420(x19423,x19424,x19421,x19425),f420(x19423,x19424,x19422,x19425)) % 154.70/154.57 [1943]~E(x19431,x19432)+E(f420(x19433,x19434,x19435,x19431),f420(x19433,x19434,x19435,x19432)) % 154.70/154.57 [1944]~E(x19441,x19442)+E(f579(x19441,x19443,x19444,x19445),f579(x19442,x19443,x19444,x19445)) % 154.70/154.57 [1945]~E(x19451,x19452)+E(f579(x19453,x19451,x19454,x19455),f579(x19453,x19452,x19454,x19455)) % 154.70/154.57 [1946]~E(x19461,x19462)+E(f579(x19463,x19464,x19461,x19465),f579(x19463,x19464,x19462,x19465)) % 154.70/154.57 [1947]~E(x19471,x19472)+E(f579(x19473,x19474,x19475,x19471),f579(x19473,x19474,x19475,x19472)) % 154.70/154.57 [1948]~E(x19481,x19482)+E(f123(x19481,x19483,x19484,x19485),f123(x19482,x19483,x19484,x19485)) % 154.70/154.57 [1949]~E(x19491,x19492)+E(f123(x19493,x19491,x19494,x19495),f123(x19493,x19492,x19494,x19495)) % 154.70/154.57 [1950]~E(x19501,x19502)+E(f123(x19503,x19504,x19501,x19505),f123(x19503,x19504,x19502,x19505)) % 154.70/154.57 [1951]~E(x19511,x19512)+E(f123(x19513,x19514,x19515,x19511),f123(x19513,x19514,x19515,x19512)) % 154.70/154.57 [1952]~E(x19521,x19522)+E(f539(x19521,x19523),f539(x19522,x19523)) % 154.70/154.57 [1953]~E(x19531,x19532)+E(f539(x19533,x19531),f539(x19533,x19532)) % 154.70/154.57 [1954]~E(x19541,x19542)+E(f352(x19541,x19543,x19544,x19545,x19546),f352(x19542,x19543,x19544,x19545,x19546)) % 154.70/154.57 [1955]~E(x19551,x19552)+E(f352(x19553,x19551,x19554,x19555,x19556),f352(x19553,x19552,x19554,x19555,x19556)) % 154.70/154.57 [1956]~E(x19561,x19562)+E(f352(x19563,x19564,x19561,x19565,x19566),f352(x19563,x19564,x19562,x19565,x19566)) % 154.70/154.57 [1957]~E(x19571,x19572)+E(f352(x19573,x19574,x19575,x19571,x19576),f352(x19573,x19574,x19575,x19572,x19576)) % 154.70/154.57 [1958]~E(x19581,x19582)+E(f352(x19583,x19584,x19585,x19586,x19581),f352(x19583,x19584,x19585,x19586,x19582)) % 154.70/154.57 [1959]~E(x19591,x19592)+E(f705(x19591),f705(x19592)) % 154.70/154.57 [1960]~E(x19601,x19602)+E(f335(x19601),f335(x19602)) % 154.70/154.57 [1961]~E(x19611,x19612)+E(f288(x19611,x19613),f288(x19612,x19613)) % 154.70/154.57 [1962]~E(x19621,x19622)+E(f288(x19623,x19621),f288(x19623,x19622)) % 154.70/154.57 [1963]~E(x19631,x19632)+E(f513(x19631,x19633,x19634),f513(x19632,x19633,x19634)) % 154.70/154.57 [1964]~E(x19641,x19642)+E(f513(x19643,x19641,x19644),f513(x19643,x19642,x19644)) % 154.70/154.57 [1965]~E(x19651,x19652)+E(f513(x19653,x19654,x19651),f513(x19653,x19654,x19652)) % 154.70/154.57 [1966]~E(x19661,x19662)+E(f469(x19661,x19663,x19664),f469(x19662,x19663,x19664)) % 154.70/154.57 [1967]~E(x19671,x19672)+E(f469(x19673,x19671,x19674),f469(x19673,x19672,x19674)) % 154.70/154.57 [1968]~E(x19681,x19682)+E(f469(x19683,x19684,x19681),f469(x19683,x19684,x19682)) % 154.70/154.57 [1969]~E(x19691,x19692)+E(f343(x19691,x19693,x19694),f343(x19692,x19693,x19694)) % 154.70/154.57 [1970]~E(x19701,x19702)+E(f343(x19703,x19701,x19704),f343(x19703,x19702,x19704)) % 154.70/154.57 [1971]~E(x19711,x19712)+E(f343(x19713,x19714,x19711),f343(x19713,x19714,x19712)) % 154.70/154.57 [1972]~E(x19721,x19722)+E(f475(x19721,x19723),f475(x19722,x19723)) % 154.70/154.57 [1973]~E(x19731,x19732)+E(f475(x19733,x19731),f475(x19733,x19732)) % 154.70/154.57 [1974]~E(x19741,x19742)+E(f383(x19741,x19743,x19744,x19745,x19746,x19747),f383(x19742,x19743,x19744,x19745,x19746,x19747)) % 154.70/154.57 [1975]~E(x19751,x19752)+E(f383(x19753,x19751,x19754,x19755,x19756,x19757),f383(x19753,x19752,x19754,x19755,x19756,x19757)) % 154.70/154.57 [1976]~E(x19761,x19762)+E(f383(x19763,x19764,x19761,x19765,x19766,x19767),f383(x19763,x19764,x19762,x19765,x19766,x19767)) % 154.70/154.57 [1977]~E(x19771,x19772)+E(f383(x19773,x19774,x19775,x19771,x19776,x19777),f383(x19773,x19774,x19775,x19772,x19776,x19777)) % 154.70/154.57 [1978]~E(x19781,x19782)+E(f383(x19783,x19784,x19785,x19786,x19781,x19787),f383(x19783,x19784,x19785,x19786,x19782,x19787)) % 154.70/154.57 [1979]~E(x19791,x19792)+E(f383(x19793,x19794,x19795,x19796,x19797,x19791),f383(x19793,x19794,x19795,x19796,x19797,x19792)) % 154.70/154.57 [1980]~E(x19801,x19802)+E(f129(x19801,x19803),f129(x19802,x19803)) % 154.70/154.57 [1981]~E(x19811,x19812)+E(f129(x19813,x19811),f129(x19813,x19812)) % 154.70/154.57 [1982]~E(x19821,x19822)+E(f706(x19821,x19823),f706(x19822,x19823)) % 154.70/154.57 [1983]~E(x19831,x19832)+E(f706(x19833,x19831),f706(x19833,x19832)) % 154.70/154.57 [1984]~E(x19841,x19842)+E(f520(x19841,x19843,x19844),f520(x19842,x19843,x19844)) % 154.70/154.57 [1985]~E(x19851,x19852)+E(f520(x19853,x19851,x19854),f520(x19853,x19852,x19854)) % 154.70/154.57 [1986]~E(x19861,x19862)+E(f520(x19863,x19864,x19861),f520(x19863,x19864,x19862)) % 154.70/154.57 [1987]~E(x19871,x19872)+E(f418(x19871,x19873,x19874,x19875,x19876,x19877),f418(x19872,x19873,x19874,x19875,x19876,x19877)) % 154.70/154.57 [1988]~E(x19881,x19882)+E(f418(x19883,x19881,x19884,x19885,x19886,x19887),f418(x19883,x19882,x19884,x19885,x19886,x19887)) % 154.70/154.57 [1989]~E(x19891,x19892)+E(f418(x19893,x19894,x19891,x19895,x19896,x19897),f418(x19893,x19894,x19892,x19895,x19896,x19897)) % 154.70/154.57 [1990]~E(x19901,x19902)+E(f418(x19903,x19904,x19905,x19901,x19906,x19907),f418(x19903,x19904,x19905,x19902,x19906,x19907)) % 154.70/154.57 [1991]~E(x19911,x19912)+E(f418(x19913,x19914,x19915,x19916,x19911,x19917),f418(x19913,x19914,x19915,x19916,x19912,x19917)) % 154.70/154.57 [1992]~E(x19921,x19922)+E(f418(x19923,x19924,x19925,x19926,x19927,x19921),f418(x19923,x19924,x19925,x19926,x19927,x19922)) % 154.70/154.57 [1993]~E(x19931,x19932)+E(f789(x19931,x19933,x19934,x19935,x19936),f789(x19932,x19933,x19934,x19935,x19936)) % 154.70/154.57 [1994]~E(x19941,x19942)+E(f789(x19943,x19941,x19944,x19945,x19946),f789(x19943,x19942,x19944,x19945,x19946)) % 154.70/154.57 [1995]~E(x19951,x19952)+E(f789(x19953,x19954,x19951,x19955,x19956),f789(x19953,x19954,x19952,x19955,x19956)) % 154.70/154.57 [1996]~E(x19961,x19962)+E(f789(x19963,x19964,x19965,x19961,x19966),f789(x19963,x19964,x19965,x19962,x19966)) % 154.70/154.57 [1997]~E(x19971,x19972)+E(f789(x19973,x19974,x19975,x19976,x19971),f789(x19973,x19974,x19975,x19976,x19972)) % 154.70/154.57 [1998]~E(x19981,x19982)+E(f345(x19981,x19983,x19984,x19985,x19986),f345(x19982,x19983,x19984,x19985,x19986)) % 154.70/154.57 [1999]~E(x19991,x19992)+E(f345(x19993,x19991,x19994,x19995,x19996),f345(x19993,x19992,x19994,x19995,x19996)) % 154.70/154.57 [2000]~E(x20001,x20002)+E(f345(x20003,x20004,x20001,x20005,x20006),f345(x20003,x20004,x20002,x20005,x20006)) % 154.70/154.57 [2001]~E(x20011,x20012)+E(f345(x20013,x20014,x20015,x20011,x20016),f345(x20013,x20014,x20015,x20012,x20016)) % 154.70/154.57 [2002]~E(x20021,x20022)+E(f345(x20023,x20024,x20025,x20026,x20021),f345(x20023,x20024,x20025,x20026,x20022)) % 154.70/154.57 [2003]~E(x20031,x20032)+E(f204(x20031,x20033,x20034,x20035),f204(x20032,x20033,x20034,x20035)) % 154.70/154.57 [2004]~E(x20041,x20042)+E(f204(x20043,x20041,x20044,x20045),f204(x20043,x20042,x20044,x20045)) % 154.70/154.57 [2005]~E(x20051,x20052)+E(f204(x20053,x20054,x20051,x20055),f204(x20053,x20054,x20052,x20055)) % 154.70/154.57 [2006]~E(x20061,x20062)+E(f204(x20063,x20064,x20065,x20061),f204(x20063,x20064,x20065,x20062)) % 154.70/154.57 [2007]~E(x20071,x20072)+E(f382(x20071,x20073,x20074,x20075,x20076,x20077),f382(x20072,x20073,x20074,x20075,x20076,x20077)) % 154.70/154.57 [2008]~E(x20081,x20082)+E(f382(x20083,x20081,x20084,x20085,x20086,x20087),f382(x20083,x20082,x20084,x20085,x20086,x20087)) % 154.70/154.57 [2009]~E(x20091,x20092)+E(f382(x20093,x20094,x20091,x20095,x20096,x20097),f382(x20093,x20094,x20092,x20095,x20096,x20097)) % 154.70/154.57 [2010]~E(x20101,x20102)+E(f382(x20103,x20104,x20105,x20101,x20106,x20107),f382(x20103,x20104,x20105,x20102,x20106,x20107)) % 154.70/154.57 [2011]~E(x20111,x20112)+E(f382(x20113,x20114,x20115,x20116,x20111,x20117),f382(x20113,x20114,x20115,x20116,x20112,x20117)) % 154.70/154.57 [2012]~E(x20121,x20122)+E(f382(x20123,x20124,x20125,x20126,x20127,x20121),f382(x20123,x20124,x20125,x20126,x20127,x20122)) % 154.70/154.57 [2013]~E(x20131,x20132)+E(f726(x20131,x20133,x20134,x20135),f726(x20132,x20133,x20134,x20135)) % 154.70/154.57 [2014]~E(x20141,x20142)+E(f726(x20143,x20141,x20144,x20145),f726(x20143,x20142,x20144,x20145)) % 154.70/154.57 [2015]~E(x20151,x20152)+E(f726(x20153,x20154,x20151,x20155),f726(x20153,x20154,x20152,x20155)) % 154.70/154.57 [2016]~E(x20161,x20162)+E(f726(x20163,x20164,x20165,x20161),f726(x20163,x20164,x20165,x20162)) % 154.70/154.57 [2017]~E(x20171,x20172)+E(f743(x20171,x20173,x20174,x20175,x20176,x20177,x20178),f743(x20172,x20173,x20174,x20175,x20176,x20177,x20178)) % 154.70/154.57 [2018]~E(x20181,x20182)+E(f743(x20183,x20181,x20184,x20185,x20186,x20187,x20188),f743(x20183,x20182,x20184,x20185,x20186,x20187,x20188)) % 154.70/154.57 [2019]~E(x20191,x20192)+E(f743(x20193,x20194,x20191,x20195,x20196,x20197,x20198),f743(x20193,x20194,x20192,x20195,x20196,x20197,x20198)) % 154.70/154.57 [2020]~E(x20201,x20202)+E(f743(x20203,x20204,x20205,x20201,x20206,x20207,x20208),f743(x20203,x20204,x20205,x20202,x20206,x20207,x20208)) % 154.70/154.57 [2021]~E(x20211,x20212)+E(f743(x20213,x20214,x20215,x20216,x20211,x20217,x20218),f743(x20213,x20214,x20215,x20216,x20212,x20217,x20218)) % 154.70/154.57 [2022]~E(x20221,x20222)+E(f743(x20223,x20224,x20225,x20226,x20227,x20221,x20228),f743(x20223,x20224,x20225,x20226,x20227,x20222,x20228)) % 154.70/154.57 [2023]~E(x20231,x20232)+E(f743(x20233,x20234,x20235,x20236,x20237,x20238,x20231),f743(x20233,x20234,x20235,x20236,x20237,x20238,x20232)) % 154.70/154.57 [2024]~E(x20241,x20242)+E(f781(x20241,x20243,x20244),f781(x20242,x20243,x20244)) % 154.70/154.57 [2025]~E(x20251,x20252)+E(f781(x20253,x20251,x20254),f781(x20253,x20252,x20254)) % 154.70/154.57 [2026]~E(x20261,x20262)+E(f781(x20263,x20264,x20261),f781(x20263,x20264,x20262)) % 154.70/154.57 [2027]~E(x20271,x20272)+E(f364(x20271,x20273),f364(x20272,x20273)) % 154.70/154.57 [2028]~E(x20281,x20282)+E(f364(x20283,x20281),f364(x20283,x20282)) % 154.70/154.57 [2029]~E(x20291,x20292)+E(f373(x20291,x20293),f373(x20292,x20293)) % 154.70/154.57 [2030]~E(x20301,x20302)+E(f373(x20303,x20301),f373(x20303,x20302)) % 154.70/154.57 [2031]~E(x20311,x20312)+E(f353(x20311,x20313,x20314,x20315,x20316),f353(x20312,x20313,x20314,x20315,x20316)) % 154.70/154.57 [2032]~E(x20321,x20322)+E(f353(x20323,x20321,x20324,x20325,x20326),f353(x20323,x20322,x20324,x20325,x20326)) % 154.70/154.57 [2033]~E(x20331,x20332)+E(f353(x20333,x20334,x20331,x20335,x20336),f353(x20333,x20334,x20332,x20335,x20336)) % 154.70/154.57 [2034]~E(x20341,x20342)+E(f353(x20343,x20344,x20345,x20341,x20346),f353(x20343,x20344,x20345,x20342,x20346)) % 154.70/154.57 [2035]~E(x20351,x20352)+E(f353(x20353,x20354,x20355,x20356,x20351),f353(x20353,x20354,x20355,x20356,x20352)) % 154.70/154.57 [2036]~E(x20361,x20362)+E(f203(x20361,x20363,x20364,x20365),f203(x20362,x20363,x20364,x20365)) % 154.70/154.57 [2037]~E(x20371,x20372)+E(f203(x20373,x20371,x20374,x20375),f203(x20373,x20372,x20374,x20375)) % 154.70/154.57 [2038]~E(x20381,x20382)+E(f203(x20383,x20384,x20381,x20385),f203(x20383,x20384,x20382,x20385)) % 154.70/154.57 [2039]~E(x20391,x20392)+E(f203(x20393,x20394,x20395,x20391),f203(x20393,x20394,x20395,x20392)) % 154.70/154.57 [2040]~E(x20401,x20402)+E(f713(x20401,x20403,x20404,x20405,x20406),f713(x20402,x20403,x20404,x20405,x20406)) % 154.70/154.57 [2041]~E(x20411,x20412)+E(f713(x20413,x20411,x20414,x20415,x20416),f713(x20413,x20412,x20414,x20415,x20416)) % 154.70/154.57 [2042]~E(x20421,x20422)+E(f713(x20423,x20424,x20421,x20425,x20426),f713(x20423,x20424,x20422,x20425,x20426)) % 154.70/154.57 [2043]~E(x20431,x20432)+E(f713(x20433,x20434,x20435,x20431,x20436),f713(x20433,x20434,x20435,x20432,x20436)) % 154.70/154.57 [2044]~E(x20441,x20442)+E(f713(x20443,x20444,x20445,x20446,x20441),f713(x20443,x20444,x20445,x20446,x20442)) % 154.70/154.57 [2045]~E(x20451,x20452)+E(f471(x20451,x20453,x20454),f471(x20452,x20453,x20454)) % 154.70/154.57 [2046]~E(x20461,x20462)+E(f471(x20463,x20461,x20464),f471(x20463,x20462,x20464)) % 154.70/154.57 [2047]~E(x20471,x20472)+E(f471(x20473,x20474,x20471),f471(x20473,x20474,x20472)) % 154.70/154.57 [2048]~E(x20481,x20482)+E(f794(x20481,x20483,x20484),f794(x20482,x20483,x20484)) % 154.70/154.57 [2049]~E(x20491,x20492)+E(f794(x20493,x20491,x20494),f794(x20493,x20492,x20494)) % 154.70/154.57 [2050]~E(x20501,x20502)+E(f794(x20503,x20504,x20501),f794(x20503,x20504,x20502)) % 154.70/154.57 [2051]~E(x20511,x20512)+E(f850(x20511,x20513,x20514,x20515),f850(x20512,x20513,x20514,x20515)) % 154.70/154.57 [2052]~E(x20521,x20522)+E(f850(x20523,x20521,x20524,x20525),f850(x20523,x20522,x20524,x20525)) % 154.70/154.57 [2053]~E(x20531,x20532)+E(f850(x20533,x20534,x20531,x20535),f850(x20533,x20534,x20532,x20535)) % 154.70/154.57 [2054]~E(x20541,x20542)+E(f850(x20543,x20544,x20545,x20541),f850(x20543,x20544,x20545,x20542)) % 154.70/154.57 [2055]~E(x20551,x20552)+E(f727(x20551,x20553,x20554,x20555),f727(x20552,x20553,x20554,x20555)) % 154.70/154.57 [2056]~E(x20561,x20562)+E(f727(x20563,x20561,x20564,x20565),f727(x20563,x20562,x20564,x20565)) % 154.70/154.57 [2057]~E(x20571,x20572)+E(f727(x20573,x20574,x20571,x20575),f727(x20573,x20574,x20572,x20575)) % 154.70/154.57 [2058]~E(x20581,x20582)+E(f727(x20583,x20584,x20585,x20581),f727(x20583,x20584,x20585,x20582)) % 154.70/154.57 [2059]~E(x20591,x20592)+E(f688(x20591,x20593,x20594,x20595),f688(x20592,x20593,x20594,x20595)) % 154.70/154.57 [2060]~E(x20601,x20602)+E(f688(x20603,x20601,x20604,x20605),f688(x20603,x20602,x20604,x20605)) % 154.70/154.57 [2061]~E(x20611,x20612)+E(f688(x20613,x20614,x20611,x20615),f688(x20613,x20614,x20612,x20615)) % 154.70/154.57 [2062]~E(x20621,x20622)+E(f688(x20623,x20624,x20625,x20621),f688(x20623,x20624,x20625,x20622)) % 154.70/154.57 [2063]~E(x20631,x20632)+E(f790(x20631,x20633,x20634,x20635,x20636,x20637,x20638),f790(x20632,x20633,x20634,x20635,x20636,x20637,x20638)) % 154.70/154.57 [2064]~E(x20641,x20642)+E(f790(x20643,x20641,x20644,x20645,x20646,x20647,x20648),f790(x20643,x20642,x20644,x20645,x20646,x20647,x20648)) % 154.70/154.57 [2065]~E(x20651,x20652)+E(f790(x20653,x20654,x20651,x20655,x20656,x20657,x20658),f790(x20653,x20654,x20652,x20655,x20656,x20657,x20658)) % 154.70/154.57 [2066]~E(x20661,x20662)+E(f790(x20663,x20664,x20665,x20661,x20666,x20667,x20668),f790(x20663,x20664,x20665,x20662,x20666,x20667,x20668)) % 154.70/154.57 [2067]~E(x20671,x20672)+E(f790(x20673,x20674,x20675,x20676,x20671,x20677,x20678),f790(x20673,x20674,x20675,x20676,x20672,x20677,x20678)) % 154.70/154.57 [2068]~E(x20681,x20682)+E(f790(x20683,x20684,x20685,x20686,x20687,x20681,x20688),f790(x20683,x20684,x20685,x20686,x20687,x20682,x20688)) % 154.70/154.57 [2069]~E(x20691,x20692)+E(f790(x20693,x20694,x20695,x20696,x20697,x20698,x20691),f790(x20693,x20694,x20695,x20696,x20697,x20698,x20692)) % 154.70/154.57 [2070]~E(x20701,x20702)+E(f760(x20701,x20703,x20704,x20705),f760(x20702,x20703,x20704,x20705)) % 154.70/154.57 [2071]~E(x20711,x20712)+E(f760(x20713,x20711,x20714,x20715),f760(x20713,x20712,x20714,x20715)) % 154.70/154.57 [2072]~E(x20721,x20722)+E(f760(x20723,x20724,x20721,x20725),f760(x20723,x20724,x20722,x20725)) % 154.70/154.57 [2073]~E(x20731,x20732)+E(f760(x20733,x20734,x20735,x20731),f760(x20733,x20734,x20735,x20732)) % 154.70/154.57 [2074]~E(x20741,x20742)+E(f448(x20741,x20743,x20744),f448(x20742,x20743,x20744)) % 154.70/154.57 [2075]~E(x20751,x20752)+E(f448(x20753,x20751,x20754),f448(x20753,x20752,x20754)) % 154.70/154.57 [2076]~E(x20761,x20762)+E(f448(x20763,x20764,x20761),f448(x20763,x20764,x20762)) % 154.70/154.57 [2077]~E(x20771,x20772)+E(f21(x20771,x20773),f21(x20772,x20773)) % 154.70/154.57 [2078]~E(x20781,x20782)+E(f21(x20783,x20781),f21(x20783,x20782)) % 154.70/154.57 [2079]~E(x20791,x20792)+E(f749(x20791,x20793,x20794),f749(x20792,x20793,x20794)) % 154.70/154.57 [2080]~E(x20801,x20802)+E(f749(x20803,x20801,x20804),f749(x20803,x20802,x20804)) % 154.70/154.57 [2081]~E(x20811,x20812)+E(f749(x20813,x20814,x20811),f749(x20813,x20814,x20812)) % 154.70/154.57 [2082]~E(x20821,x20822)+E(f341(x20821,x20823),f341(x20822,x20823)) % 154.70/154.57 [2083]~E(x20831,x20832)+E(f341(x20833,x20831),f341(x20833,x20832)) % 154.70/154.57 [2084]~E(x20841,x20842)+E(f459(x20841,x20843,x20844),f459(x20842,x20843,x20844)) % 154.70/154.57 [2085]~E(x20851,x20852)+E(f459(x20853,x20851,x20854),f459(x20853,x20852,x20854)) % 154.70/154.57 [2086]~E(x20861,x20862)+E(f459(x20863,x20864,x20861),f459(x20863,x20864,x20862)) % 154.70/154.57 [2087]~E(x20871,x20872)+E(f525(x20871,x20873,x20874,x20875,x20876,x20877),f525(x20872,x20873,x20874,x20875,x20876,x20877)) % 154.70/154.57 [2088]~E(x20881,x20882)+E(f525(x20883,x20881,x20884,x20885,x20886,x20887),f525(x20883,x20882,x20884,x20885,x20886,x20887)) % 154.70/154.57 [2089]~E(x20891,x20892)+E(f525(x20893,x20894,x20891,x20895,x20896,x20897),f525(x20893,x20894,x20892,x20895,x20896,x20897)) % 154.70/154.57 [2090]~E(x20901,x20902)+E(f525(x20903,x20904,x20905,x20901,x20906,x20907),f525(x20903,x20904,x20905,x20902,x20906,x20907)) % 154.70/154.57 [2091]~E(x20911,x20912)+E(f525(x20913,x20914,x20915,x20916,x20911,x20917),f525(x20913,x20914,x20915,x20916,x20912,x20917)) % 154.70/154.57 [2092]~E(x20921,x20922)+E(f525(x20923,x20924,x20925,x20926,x20927,x20921),f525(x20923,x20924,x20925,x20926,x20927,x20922)) % 154.70/154.57 [2093]~E(x20931,x20932)+E(f461(x20931,x20933),f461(x20932,x20933)) % 154.70/154.57 [2094]~E(x20941,x20942)+E(f461(x20943,x20941),f461(x20943,x20942)) % 154.70/154.57 [2095]~E(x20951,x20952)+E(f451(x20951,x20953,x20954,x20955,x20956,x20957),f451(x20952,x20953,x20954,x20955,x20956,x20957)) % 154.70/154.57 [2096]~E(x20961,x20962)+E(f451(x20963,x20961,x20964,x20965,x20966,x20967),f451(x20963,x20962,x20964,x20965,x20966,x20967)) % 154.70/154.57 [2097]~E(x20971,x20972)+E(f451(x20973,x20974,x20971,x20975,x20976,x20977),f451(x20973,x20974,x20972,x20975,x20976,x20977)) % 154.70/154.57 [2098]~E(x20981,x20982)+E(f451(x20983,x20984,x20985,x20981,x20986,x20987),f451(x20983,x20984,x20985,x20982,x20986,x20987)) % 154.70/154.57 [2099]~E(x20991,x20992)+E(f451(x20993,x20994,x20995,x20996,x20991,x20997),f451(x20993,x20994,x20995,x20996,x20992,x20997)) % 154.70/154.57 [2100]~E(x21001,x21002)+E(f451(x21003,x21004,x21005,x21006,x21007,x21001),f451(x21003,x21004,x21005,x21006,x21007,x21002)) % 154.70/154.57 [2101]~E(x21011,x21012)+E(f528(x21011,x21013,x21014,x21015),f528(x21012,x21013,x21014,x21015)) % 154.70/154.57 [2102]~E(x21021,x21022)+E(f528(x21023,x21021,x21024,x21025),f528(x21023,x21022,x21024,x21025)) % 154.70/154.57 [2103]~E(x21031,x21032)+E(f528(x21033,x21034,x21031,x21035),f528(x21033,x21034,x21032,x21035)) % 154.70/154.57 [2104]~E(x21041,x21042)+E(f528(x21043,x21044,x21045,x21041),f528(x21043,x21044,x21045,x21042)) % 154.70/154.57 [2105]~E(x21051,x21052)+E(f332(x21051,x21053,x21054,x21055),f332(x21052,x21053,x21054,x21055)) % 154.70/154.57 [2106]~E(x21061,x21062)+E(f332(x21063,x21061,x21064,x21065),f332(x21063,x21062,x21064,x21065)) % 154.70/154.57 [2107]~E(x21071,x21072)+E(f332(x21073,x21074,x21071,x21075),f332(x21073,x21074,x21072,x21075)) % 154.70/154.57 [2108]~E(x21081,x21082)+E(f332(x21083,x21084,x21085,x21081),f332(x21083,x21084,x21085,x21082)) % 154.70/154.57 [2109]~E(x21091,x21092)+E(f372(x21091,x21093,x21094,x21095,x21096),f372(x21092,x21093,x21094,x21095,x21096)) % 154.70/154.57 [2110]~E(x21101,x21102)+E(f372(x21103,x21101,x21104,x21105,x21106),f372(x21103,x21102,x21104,x21105,x21106)) % 154.70/154.57 [2111]~E(x21111,x21112)+E(f372(x21113,x21114,x21111,x21115,x21116),f372(x21113,x21114,x21112,x21115,x21116)) % 154.70/154.57 [2112]~E(x21121,x21122)+E(f372(x21123,x21124,x21125,x21121,x21126),f372(x21123,x21124,x21125,x21122,x21126)) % 154.70/154.57 [2113]~E(x21131,x21132)+E(f372(x21133,x21134,x21135,x21136,x21131),f372(x21133,x21134,x21135,x21136,x21132)) % 154.70/154.57 [2114]~E(x21141,x21142)+E(f515(x21141,x21143,x21144),f515(x21142,x21143,x21144)) % 154.70/154.57 [2115]~E(x21151,x21152)+E(f515(x21153,x21151,x21154),f515(x21153,x21152,x21154)) % 154.70/154.57 [2116]~E(x21161,x21162)+E(f515(x21163,x21164,x21161),f515(x21163,x21164,x21162)) % 154.70/154.57 [2117]~E(x21171,x21172)+E(f361(x21171,x21173),f361(x21172,x21173)) % 154.70/154.57 [2118]~E(x21181,x21182)+E(f361(x21183,x21181),f361(x21183,x21182)) % 154.70/154.57 [2119]~E(x21191,x21192)+E(f839(x21191,x21193,x21194,x21195,x21196),f839(x21192,x21193,x21194,x21195,x21196)) % 154.70/154.57 [2120]~E(x21201,x21202)+E(f839(x21203,x21201,x21204,x21205,x21206),f839(x21203,x21202,x21204,x21205,x21206)) % 154.70/154.58 [2121]~E(x21211,x21212)+E(f839(x21213,x21214,x21211,x21215,x21216),f839(x21213,x21214,x21212,x21215,x21216)) % 154.70/154.58 [2122]~E(x21221,x21222)+E(f839(x21223,x21224,x21225,x21221,x21226),f839(x21223,x21224,x21225,x21222,x21226)) % 154.70/154.58 [2123]~E(x21231,x21232)+E(f839(x21233,x21234,x21235,x21236,x21231),f839(x21233,x21234,x21235,x21236,x21232)) % 154.70/154.58 [2124]~E(x21241,x21242)+E(f277(x21241,x21243,x21244,x21245),f277(x21242,x21243,x21244,x21245)) % 154.70/154.58 [2125]~E(x21251,x21252)+E(f277(x21253,x21251,x21254,x21255),f277(x21253,x21252,x21254,x21255)) % 154.70/154.58 [2126]~E(x21261,x21262)+E(f277(x21263,x21264,x21261,x21265),f277(x21263,x21264,x21262,x21265)) % 154.70/154.58 [2127]~E(x21271,x21272)+E(f277(x21273,x21274,x21275,x21271),f277(x21273,x21274,x21275,x21272)) % 154.70/154.58 [2128]~E(x21281,x21282)+E(f815(x21281,x21283,x21284,x21285),f815(x21282,x21283,x21284,x21285)) % 154.70/154.58 [2129]~E(x21291,x21292)+E(f815(x21293,x21291,x21294,x21295),f815(x21293,x21292,x21294,x21295)) % 154.70/154.58 [2130]~E(x21301,x21302)+E(f815(x21303,x21304,x21301,x21305),f815(x21303,x21304,x21302,x21305)) % 154.70/154.58 [2131]~E(x21311,x21312)+E(f815(x21313,x21314,x21315,x21311),f815(x21313,x21314,x21315,x21312)) % 154.70/154.58 [2132]~E(x21321,x21322)+E(f74(x21321,x21323),f74(x21322,x21323)) % 154.70/154.58 [2133]~E(x21331,x21332)+E(f74(x21333,x21331),f74(x21333,x21332)) % 154.70/154.58 [2134]~E(x21341,x21342)+E(f807(x21341,x21343),f807(x21342,x21343)) % 154.70/154.58 [2135]~E(x21351,x21352)+E(f807(x21353,x21351),f807(x21353,x21352)) % 154.70/154.58 [2136]~E(x21361,x21362)+E(f460(x21361,x21363),f460(x21362,x21363)) % 154.70/154.58 [2137]~E(x21371,x21372)+E(f460(x21373,x21371),f460(x21373,x21372)) % 154.70/154.58 [2138]~E(x21381,x21382)+E(f602(x21381,x21383,x21384),f602(x21382,x21383,x21384)) % 154.70/154.58 [2139]~E(x21391,x21392)+E(f602(x21393,x21391,x21394),f602(x21393,x21392,x21394)) % 154.70/154.58 [2140]~E(x21401,x21402)+E(f602(x21403,x21404,x21401),f602(x21403,x21404,x21402)) % 154.70/154.58 [2141]~E(x21411,x21412)+E(f782(x21411,x21413,x21414),f782(x21412,x21413,x21414)) % 154.70/154.58 [2142]~E(x21421,x21422)+E(f782(x21423,x21421,x21424),f782(x21423,x21422,x21424)) % 154.70/154.58 [2143]~E(x21431,x21432)+E(f782(x21433,x21434,x21431),f782(x21433,x21434,x21432)) % 154.70/154.58 [2144]~E(x21441,x21442)+E(f703(x21441,x21443,x21444,x21445),f703(x21442,x21443,x21444,x21445)) % 154.70/154.58 [2145]~E(x21451,x21452)+E(f703(x21453,x21451,x21454,x21455),f703(x21453,x21452,x21454,x21455)) % 154.70/154.58 [2146]~E(x21461,x21462)+E(f703(x21463,x21464,x21461,x21465),f703(x21463,x21464,x21462,x21465)) % 154.70/154.58 [2147]~E(x21471,x21472)+E(f703(x21473,x21474,x21475,x21471),f703(x21473,x21474,x21475,x21472)) % 154.70/154.58 [2148]~E(x21481,x21482)+E(f476(x21481,x21483,x21484),f476(x21482,x21483,x21484)) % 154.70/154.58 [2149]~E(x21491,x21492)+E(f476(x21493,x21491,x21494),f476(x21493,x21492,x21494)) % 154.70/154.58 [2150]~E(x21501,x21502)+E(f476(x21503,x21504,x21501),f476(x21503,x21504,x21502)) % 154.70/154.58 [2151]~E(x21511,x21512)+E(f614(x21511,x21513,x21514),f614(x21512,x21513,x21514)) % 154.70/154.58 [2152]~E(x21521,x21522)+E(f614(x21523,x21521,x21524),f614(x21523,x21522,x21524)) % 154.70/154.58 [2153]~E(x21531,x21532)+E(f614(x21533,x21534,x21531),f614(x21533,x21534,x21532)) % 154.70/154.58 [2154]~E(x21541,x21542)+E(f598(x21541,x21543,x21544),f598(x21542,x21543,x21544)) % 154.70/154.58 [2155]~E(x21551,x21552)+E(f598(x21553,x21551,x21554),f598(x21553,x21552,x21554)) % 154.70/154.58 [2156]~E(x21561,x21562)+E(f598(x21563,x21564,x21561),f598(x21563,x21564,x21562)) % 154.70/154.58 [2157]~E(x21571,x21572)+E(f647(x21571,x21573,x21574,x21575),f647(x21572,x21573,x21574,x21575)) % 154.70/154.58 [2158]~E(x21581,x21582)+E(f647(x21583,x21581,x21584,x21585),f647(x21583,x21582,x21584,x21585)) % 154.70/154.58 [2159]~E(x21591,x21592)+E(f647(x21593,x21594,x21591,x21595),f647(x21593,x21594,x21592,x21595)) % 154.70/154.58 [2160]~E(x21601,x21602)+E(f647(x21603,x21604,x21605,x21601),f647(x21603,x21604,x21605,x21602)) % 154.70/154.58 [2161]~E(x21611,x21612)+E(f552(x21611),f552(x21612)) % 154.96/154.58 [2162]~E(x21621,x21622)+E(f792(x21621,x21623,x21624,x21625,x21626,x21627,x21628),f792(x21622,x21623,x21624,x21625,x21626,x21627,x21628)) % 154.96/154.58 [2163]~E(x21631,x21632)+E(f792(x21633,x21631,x21634,x21635,x21636,x21637,x21638),f792(x21633,x21632,x21634,x21635,x21636,x21637,x21638)) % 154.96/154.58 [2164]~E(x21641,x21642)+E(f792(x21643,x21644,x21641,x21645,x21646,x21647,x21648),f792(x21643,x21644,x21642,x21645,x21646,x21647,x21648)) % 154.96/154.58 [2165]~E(x21651,x21652)+E(f792(x21653,x21654,x21655,x21651,x21656,x21657,x21658),f792(x21653,x21654,x21655,x21652,x21656,x21657,x21658)) % 154.96/154.58 [2166]~E(x21661,x21662)+E(f792(x21663,x21664,x21665,x21666,x21661,x21667,x21668),f792(x21663,x21664,x21665,x21666,x21662,x21667,x21668)) % 154.96/154.58 [2167]~E(x21671,x21672)+E(f792(x21673,x21674,x21675,x21676,x21677,x21671,x21678),f792(x21673,x21674,x21675,x21676,x21677,x21672,x21678)) % 154.96/154.58 [2168]~E(x21681,x21682)+E(f792(x21683,x21684,x21685,x21686,x21687,x21688,x21681),f792(x21683,x21684,x21685,x21686,x21687,x21688,x21682)) % 154.96/154.58 [2169]~E(x21691,x21692)+E(f845(x21691,x21693,x21694,x21695,x21696,x21697,x21698),f845(x21692,x21693,x21694,x21695,x21696,x21697,x21698)) % 154.96/154.58 [2170]~E(x21701,x21702)+E(f845(x21703,x21701,x21704,x21705,x21706,x21707,x21708),f845(x21703,x21702,x21704,x21705,x21706,x21707,x21708)) % 154.96/154.58 [2171]~E(x21711,x21712)+E(f845(x21713,x21714,x21711,x21715,x21716,x21717,x21718),f845(x21713,x21714,x21712,x21715,x21716,x21717,x21718)) % 154.96/154.58 [2172]~E(x21721,x21722)+E(f845(x21723,x21724,x21725,x21721,x21726,x21727,x21728),f845(x21723,x21724,x21725,x21722,x21726,x21727,x21728)) % 154.96/154.58 [2173]~E(x21731,x21732)+E(f845(x21733,x21734,x21735,x21736,x21731,x21737,x21738),f845(x21733,x21734,x21735,x21736,x21732,x21737,x21738)) % 154.96/154.58 [2174]~E(x21741,x21742)+E(f845(x21743,x21744,x21745,x21746,x21747,x21741,x21748),f845(x21743,x21744,x21745,x21746,x21747,x21742,x21748)) % 154.96/154.58 [2175]~E(x21751,x21752)+E(f845(x21753,x21754,x21755,x21756,x21757,x21758,x21751),f845(x21753,x21754,x21755,x21756,x21757,x21758,x21752)) % 154.96/154.58 [2176]~E(x21761,x21762)+E(f433(x21761,x21763,x21764,x21765,x21766),f433(x21762,x21763,x21764,x21765,x21766)) % 154.96/154.58 [2177]~E(x21771,x21772)+E(f433(x21773,x21771,x21774,x21775,x21776),f433(x21773,x21772,x21774,x21775,x21776)) % 154.96/154.58 [2178]~E(x21781,x21782)+E(f433(x21783,x21784,x21781,x21785,x21786),f433(x21783,x21784,x21782,x21785,x21786)) % 154.96/154.58 [2179]~E(x21791,x21792)+E(f433(x21793,x21794,x21795,x21791,x21796),f433(x21793,x21794,x21795,x21792,x21796)) % 154.96/154.58 [2180]~E(x21801,x21802)+E(f433(x21803,x21804,x21805,x21806,x21801),f433(x21803,x21804,x21805,x21806,x21802)) % 154.96/154.58 [2181]~E(x21811,x21812)+E(f255(x21811,x21813,x21814),f255(x21812,x21813,x21814)) % 154.96/154.58 [2182]~E(x21821,x21822)+E(f255(x21823,x21821,x21824),f255(x21823,x21822,x21824)) % 154.96/154.58 [2183]~E(x21831,x21832)+E(f255(x21833,x21834,x21831),f255(x21833,x21834,x21832)) % 154.96/154.58 [2184]~E(x21841,x21842)+E(f426(x21841,x21843,x21844),f426(x21842,x21843,x21844)) % 154.96/154.58 [2185]~E(x21851,x21852)+E(f426(x21853,x21851,x21854),f426(x21853,x21852,x21854)) % 154.96/154.58 [2186]~E(x21861,x21862)+E(f426(x21863,x21864,x21861),f426(x21863,x21864,x21862)) % 154.96/154.58 [2187]~E(x21871,x21872)+E(f774(x21871,x21873,x21874,x21875,x21876,x21877,x21878,x21879),f774(x21872,x21873,x21874,x21875,x21876,x21877,x21878,x21879)) % 154.96/154.58 [2188]~E(x21881,x21882)+E(f774(x21883,x21881,x21884,x21885,x21886,x21887,x21888,x21889),f774(x21883,x21882,x21884,x21885,x21886,x21887,x21888,x21889)) % 154.96/154.58 [2189]~E(x21891,x21892)+E(f774(x21893,x21894,x21891,x21895,x21896,x21897,x21898,x21899),f774(x21893,x21894,x21892,x21895,x21896,x21897,x21898,x21899)) % 154.96/154.58 [2190]~E(x21901,x21902)+E(f774(x21903,x21904,x21905,x21901,x21906,x21907,x21908,x21909),f774(x21903,x21904,x21905,x21902,x21906,x21907,x21908,x21909)) % 154.96/154.58 [2191]~E(x21911,x21912)+E(f774(x21913,x21914,x21915,x21916,x21911,x21917,x21918,x21919),f774(x21913,x21914,x21915,x21916,x21912,x21917,x21918,x21919)) % 154.96/154.58 [2192]~E(x21921,x21922)+E(f774(x21923,x21924,x21925,x21926,x21927,x21921,x21928,x21929),f774(x21923,x21924,x21925,x21926,x21927,x21922,x21928,x21929)) % 154.96/154.58 [2193]~E(x21931,x21932)+E(f774(x21933,x21934,x21935,x21936,x21937,x21938,x21931,x21939),f774(x21933,x21934,x21935,x21936,x21937,x21938,x21932,x21939)) % 154.96/154.58 [2194]~E(x21941,x21942)+E(f774(x21943,x21944,x21945,x21946,x21947,x21948,x21949,x21941),f774(x21943,x21944,x21945,x21946,x21947,x21948,x21949,x21942)) % 154.96/154.58 [2195]~E(x21951,x21952)+E(f776(x21951,x21953,x21954,x21955),f776(x21952,x21953,x21954,x21955)) % 154.96/154.58 [2196]~E(x21961,x21962)+E(f776(x21963,x21961,x21964,x21965),f776(x21963,x21962,x21964,x21965)) % 154.96/154.58 [2197]~E(x21971,x21972)+E(f776(x21973,x21974,x21971,x21975),f776(x21973,x21974,x21972,x21975)) % 154.96/154.58 [2198]~E(x21981,x21982)+E(f776(x21983,x21984,x21985,x21981),f776(x21983,x21984,x21985,x21982)) % 154.96/154.58 [2199]~E(x21991,x21992)+E(f401(x21991,x21993,x21994,x21995),f401(x21992,x21993,x21994,x21995)) % 154.96/154.58 [2200]~E(x22001,x22002)+E(f401(x22003,x22001,x22004,x22005),f401(x22003,x22002,x22004,x22005)) % 154.96/154.58 [2201]~E(x22011,x22012)+E(f401(x22013,x22014,x22011,x22015),f401(x22013,x22014,x22012,x22015)) % 154.96/154.58 [2202]~E(x22021,x22022)+E(f401(x22023,x22024,x22025,x22021),f401(x22023,x22024,x22025,x22022)) % 154.96/154.58 [2203]~E(x22031,x22032)+E(f414(x22031,x22033,x22034,x22035),f414(x22032,x22033,x22034,x22035)) % 154.96/154.58 [2204]~E(x22041,x22042)+E(f414(x22043,x22041,x22044,x22045),f414(x22043,x22042,x22044,x22045)) % 154.96/154.58 [2205]~E(x22051,x22052)+E(f414(x22053,x22054,x22051,x22055),f414(x22053,x22054,x22052,x22055)) % 154.96/154.58 [2206]~E(x22061,x22062)+E(f414(x22063,x22064,x22065,x22061),f414(x22063,x22064,x22065,x22062)) % 154.96/154.58 [2207]~E(x22071,x22072)+E(f311(x22071,x22073,x22074),f311(x22072,x22073,x22074)) % 154.96/154.58 [2208]~E(x22081,x22082)+E(f311(x22083,x22081,x22084),f311(x22083,x22082,x22084)) % 154.96/154.58 [2209]~E(x22091,x22092)+E(f311(x22093,x22094,x22091),f311(x22093,x22094,x22092)) % 154.96/154.58 [2210]~E(x22101,x22102)+E(f434(x22101,x22103,x22104,x22105,x22106),f434(x22102,x22103,x22104,x22105,x22106)) % 154.96/154.58 [2211]~E(x22111,x22112)+E(f434(x22113,x22111,x22114,x22115,x22116),f434(x22113,x22112,x22114,x22115,x22116)) % 154.96/154.58 [2212]~E(x22121,x22122)+E(f434(x22123,x22124,x22121,x22125,x22126),f434(x22123,x22124,x22122,x22125,x22126)) % 154.96/154.58 [2213]~E(x22131,x22132)+E(f434(x22133,x22134,x22135,x22131,x22136),f434(x22133,x22134,x22135,x22132,x22136)) % 154.96/154.58 [2214]~E(x22141,x22142)+E(f434(x22143,x22144,x22145,x22146,x22141),f434(x22143,x22144,x22145,x22146,x22142)) % 154.96/154.58 [2215]~E(x22151,x22152)+E(f488(x22151,x22153,x22154,x22155,x22156),f488(x22152,x22153,x22154,x22155,x22156)) % 154.96/154.58 [2216]~E(x22161,x22162)+E(f488(x22163,x22161,x22164,x22165,x22166),f488(x22163,x22162,x22164,x22165,x22166)) % 154.96/154.58 [2217]~E(x22171,x22172)+E(f488(x22173,x22174,x22171,x22175,x22176),f488(x22173,x22174,x22172,x22175,x22176)) % 154.96/154.58 [2218]~E(x22181,x22182)+E(f488(x22183,x22184,x22185,x22181,x22186),f488(x22183,x22184,x22185,x22182,x22186)) % 154.96/154.58 [2219]~E(x22191,x22192)+E(f488(x22193,x22194,x22195,x22196,x22191),f488(x22193,x22194,x22195,x22196,x22192)) % 154.96/154.58 [2220]~E(x22201,x22202)+E(f570(x22201,x22203),f570(x22202,x22203)) % 154.96/154.58 [2221]~E(x22211,x22212)+E(f570(x22213,x22211),f570(x22213,x22212)) % 154.96/154.58 [2222]~E(x22221,x22222)+E(f390(x22221),f390(x22222)) % 154.96/154.58 [2223]~E(x22231,x22232)+E(f491(x22231,x22233,x22234),f491(x22232,x22233,x22234)) % 154.96/154.58 [2224]~E(x22241,x22242)+E(f491(x22243,x22241,x22244),f491(x22243,x22242,x22244)) % 154.96/154.58 [2225]~E(x22251,x22252)+E(f491(x22253,x22254,x22251),f491(x22253,x22254,x22252)) % 154.96/154.58 [2226]~E(x22261,x22262)+E(f625(x22261,x22263),f625(x22262,x22263)) % 154.96/154.58 [2227]~E(x22271,x22272)+E(f625(x22273,x22271),f625(x22273,x22272)) % 154.96/154.58 [2228]~E(x22281,x22282)+E(f773(x22281,x22283,x22284,x22285,x22286),f773(x22282,x22283,x22284,x22285,x22286)) % 154.96/154.58 [2229]~E(x22291,x22292)+E(f773(x22293,x22291,x22294,x22295,x22296),f773(x22293,x22292,x22294,x22295,x22296)) % 154.96/154.58 [2230]~E(x22301,x22302)+E(f773(x22303,x22304,x22301,x22305,x22306),f773(x22303,x22304,x22302,x22305,x22306)) % 154.96/154.58 [2231]~E(x22311,x22312)+E(f773(x22313,x22314,x22315,x22311,x22316),f773(x22313,x22314,x22315,x22312,x22316)) % 154.96/154.58 [2232]~E(x22321,x22322)+E(f773(x22323,x22324,x22325,x22326,x22321),f773(x22323,x22324,x22325,x22326,x22322)) % 154.96/154.58 [2233]~E(x22331,x22332)+E(f863(x22331,x22333,x22334),f863(x22332,x22333,x22334)) % 154.96/154.58 [2234]~E(x22341,x22342)+E(f863(x22343,x22341,x22344),f863(x22343,x22342,x22344)) % 154.96/154.58 [2235]~E(x22351,x22352)+E(f863(x22353,x22354,x22351),f863(x22353,x22354,x22352)) % 154.96/154.58 [2236]~E(x22361,x22362)+E(f386(x22361,x22363,x22364),f386(x22362,x22363,x22364)) % 154.96/154.58 [2237]~E(x22371,x22372)+E(f386(x22373,x22371,x22374),f386(x22373,x22372,x22374)) % 154.96/154.58 [2238]~E(x22381,x22382)+E(f386(x22383,x22384,x22381),f386(x22383,x22384,x22382)) % 154.96/154.58 [2239]~E(x22391,x22392)+E(f848(x22391,x22393,x22394,x22395,x22396),f848(x22392,x22393,x22394,x22395,x22396)) % 154.96/154.58 [2240]~E(x22401,x22402)+E(f848(x22403,x22401,x22404,x22405,x22406),f848(x22403,x22402,x22404,x22405,x22406)) % 154.96/154.58 [2241]~E(x22411,x22412)+E(f848(x22413,x22414,x22411,x22415,x22416),f848(x22413,x22414,x22412,x22415,x22416)) % 154.96/154.58 [2242]~E(x22421,x22422)+E(f848(x22423,x22424,x22425,x22421,x22426),f848(x22423,x22424,x22425,x22422,x22426)) % 154.96/154.58 [2243]~E(x22431,x22432)+E(f848(x22433,x22434,x22435,x22436,x22431),f848(x22433,x22434,x22435,x22436,x22432)) % 154.96/154.58 [2244]~E(x22441,x22442)+E(f837(x22441,x22443,x22444,x22445,x22446),f837(x22442,x22443,x22444,x22445,x22446)) % 154.96/154.58 [2245]~E(x22451,x22452)+E(f837(x22453,x22451,x22454,x22455,x22456),f837(x22453,x22452,x22454,x22455,x22456)) % 154.96/154.58 [2246]~E(x22461,x22462)+E(f837(x22463,x22464,x22461,x22465,x22466),f837(x22463,x22464,x22462,x22465,x22466)) % 154.96/154.58 [2247]~E(x22471,x22472)+E(f837(x22473,x22474,x22475,x22471,x22476),f837(x22473,x22474,x22475,x22472,x22476)) % 154.96/154.58 [2248]~E(x22481,x22482)+E(f837(x22483,x22484,x22485,x22486,x22481),f837(x22483,x22484,x22485,x22486,x22482)) % 154.96/154.58 [2249]~E(x22491,x22492)+E(f779(x22491,x22493),f779(x22492,x22493)) % 154.96/154.58 [2250]~E(x22501,x22502)+E(f779(x22503,x22501),f779(x22503,x22502)) % 154.96/154.58 [2251]~E(x22511,x22512)+E(f801(x22511,x22513,x22514),f801(x22512,x22513,x22514)) % 154.96/154.58 [2252]~E(x22521,x22522)+E(f801(x22523,x22521,x22524),f801(x22523,x22522,x22524)) % 154.96/154.58 [2253]~E(x22531,x22532)+E(f801(x22533,x22534,x22531),f801(x22533,x22534,x22532)) % 154.96/154.58 [2254]~E(x22541,x22542)+E(f438(x22541,x22543,x22544,x22545,x22546),f438(x22542,x22543,x22544,x22545,x22546)) % 154.96/154.58 [2255]~E(x22551,x22552)+E(f438(x22553,x22551,x22554,x22555,x22556),f438(x22553,x22552,x22554,x22555,x22556)) % 154.96/154.58 [2256]~E(x22561,x22562)+E(f438(x22563,x22564,x22561,x22565,x22566),f438(x22563,x22564,x22562,x22565,x22566)) % 154.96/154.58 [2257]~E(x22571,x22572)+E(f438(x22573,x22574,x22575,x22571,x22576),f438(x22573,x22574,x22575,x22572,x22576)) % 154.96/154.58 [2258]~E(x22581,x22582)+E(f438(x22583,x22584,x22585,x22586,x22581),f438(x22583,x22584,x22585,x22586,x22582)) % 154.96/154.58 [2259]~E(x22591,x22592)+E(f216(x22591,x22593,x22594,x22595),f216(x22592,x22593,x22594,x22595)) % 154.96/154.58 [2260]~E(x22601,x22602)+E(f216(x22603,x22601,x22604,x22605),f216(x22603,x22602,x22604,x22605)) % 154.96/154.58 [2261]~E(x22611,x22612)+E(f216(x22613,x22614,x22611,x22615),f216(x22613,x22614,x22612,x22615)) % 154.96/154.58 [2262]~E(x22621,x22622)+E(f216(x22623,x22624,x22625,x22621),f216(x22623,x22624,x22625,x22622)) % 154.96/154.58 [2263]~E(x22631,x22632)+E(f455(x22631,x22633,x22634),f455(x22632,x22633,x22634)) % 154.96/154.58 [2264]~E(x22641,x22642)+E(f455(x22643,x22641,x22644),f455(x22643,x22642,x22644)) % 154.96/154.58 [2265]~E(x22651,x22652)+E(f455(x22653,x22654,x22651),f455(x22653,x22654,x22652)) % 154.96/154.58 [2266]~E(x22661,x22662)+E(f214(x22661,x22663,x22664,x22665,x22666,x22667,x22668),f214(x22662,x22663,x22664,x22665,x22666,x22667,x22668)) % 154.96/154.58 [2267]~E(x22671,x22672)+E(f214(x22673,x22671,x22674,x22675,x22676,x22677,x22678),f214(x22673,x22672,x22674,x22675,x22676,x22677,x22678)) % 154.96/154.58 [2268]~E(x22681,x22682)+E(f214(x22683,x22684,x22681,x22685,x22686,x22687,x22688),f214(x22683,x22684,x22682,x22685,x22686,x22687,x22688)) % 154.96/154.58 [2269]~E(x22691,x22692)+E(f214(x22693,x22694,x22695,x22691,x22696,x22697,x22698),f214(x22693,x22694,x22695,x22692,x22696,x22697,x22698)) % 154.96/154.58 [2270]~E(x22701,x22702)+E(f214(x22703,x22704,x22705,x22706,x22701,x22707,x22708),f214(x22703,x22704,x22705,x22706,x22702,x22707,x22708)) % 154.96/154.58 [2271]~E(x22711,x22712)+E(f214(x22713,x22714,x22715,x22716,x22717,x22711,x22718),f214(x22713,x22714,x22715,x22716,x22717,x22712,x22718)) % 154.96/154.58 [2272]~E(x22721,x22722)+E(f214(x22723,x22724,x22725,x22726,x22727,x22728,x22721),f214(x22723,x22724,x22725,x22726,x22727,x22728,x22722)) % 154.96/154.58 [2273]~E(x22731,x22732)+E(f651(x22731,x22733,x22734,x22735,x22736),f651(x22732,x22733,x22734,x22735,x22736)) % 154.96/154.58 [2274]~E(x22741,x22742)+E(f651(x22743,x22741,x22744,x22745,x22746),f651(x22743,x22742,x22744,x22745,x22746)) % 154.96/154.58 [2275]~E(x22751,x22752)+E(f651(x22753,x22754,x22751,x22755,x22756),f651(x22753,x22754,x22752,x22755,x22756)) % 154.96/154.58 [2276]~E(x22761,x22762)+E(f651(x22763,x22764,x22765,x22761,x22766),f651(x22763,x22764,x22765,x22762,x22766)) % 154.96/154.58 [2277]~E(x22771,x22772)+E(f651(x22773,x22774,x22775,x22776,x22771),f651(x22773,x22774,x22775,x22776,x22772)) % 154.96/154.58 [2278]~E(x22781,x22782)+E(f682(x22781,x22783,x22784),f682(x22782,x22783,x22784)) % 154.96/154.58 [2279]~E(x22791,x22792)+E(f682(x22793,x22791,x22794),f682(x22793,x22792,x22794)) % 154.96/154.58 [2280]~E(x22801,x22802)+E(f682(x22803,x22804,x22801),f682(x22803,x22804,x22802)) % 154.96/154.58 [2281]~E(x22811,x22812)+E(f576(x22811,x22813,x22814,x22815,x22816,x22817),f576(x22812,x22813,x22814,x22815,x22816,x22817)) % 154.96/154.58 [2282]~E(x22821,x22822)+E(f576(x22823,x22821,x22824,x22825,x22826,x22827),f576(x22823,x22822,x22824,x22825,x22826,x22827)) % 154.96/154.58 [2283]~E(x22831,x22832)+E(f576(x22833,x22834,x22831,x22835,x22836,x22837),f576(x22833,x22834,x22832,x22835,x22836,x22837)) % 154.96/154.58 [2284]~E(x22841,x22842)+E(f576(x22843,x22844,x22845,x22841,x22846,x22847),f576(x22843,x22844,x22845,x22842,x22846,x22847)) % 154.96/154.58 [2285]~E(x22851,x22852)+E(f576(x22853,x22854,x22855,x22856,x22851,x22857),f576(x22853,x22854,x22855,x22856,x22852,x22857)) % 154.96/154.58 [2286]~E(x22861,x22862)+E(f576(x22863,x22864,x22865,x22866,x22867,x22861),f576(x22863,x22864,x22865,x22866,x22867,x22862)) % 154.96/154.58 [2287]~E(x22871,x22872)+E(f357(x22871),f357(x22872)) % 154.96/154.58 [2288]~E(x22881,x22882)+E(f334(x22881),f334(x22882)) % 154.96/154.58 [2289]~E(x22891,x22892)+E(f410(x22891),f410(x22892)) % 154.96/154.58 [2290]~E(x22901,x22902)+E(f296(x22901,x22903,x22904,x22905,x22906),f296(x22902,x22903,x22904,x22905,x22906)) % 154.96/154.58 [2291]~E(x22911,x22912)+E(f296(x22913,x22911,x22914,x22915,x22916),f296(x22913,x22912,x22914,x22915,x22916)) % 154.96/154.58 [2292]~E(x22921,x22922)+E(f296(x22923,x22924,x22921,x22925,x22926),f296(x22923,x22924,x22922,x22925,x22926)) % 154.96/154.58 [2293]~E(x22931,x22932)+E(f296(x22933,x22934,x22935,x22931,x22936),f296(x22933,x22934,x22935,x22932,x22936)) % 154.96/154.58 [2294]~E(x22941,x22942)+E(f296(x22943,x22944,x22945,x22946,x22941),f296(x22943,x22944,x22945,x22946,x22942)) % 154.96/154.58 [2295]~E(x22951,x22952)+E(f351(x22951,x22953,x22954,x22955,x22956),f351(x22952,x22953,x22954,x22955,x22956)) % 154.96/154.58 [2296]~E(x22961,x22962)+E(f351(x22963,x22961,x22964,x22965,x22966),f351(x22963,x22962,x22964,x22965,x22966)) % 154.96/154.58 [2297]~E(x22971,x22972)+E(f351(x22973,x22974,x22971,x22975,x22976),f351(x22973,x22974,x22972,x22975,x22976)) % 154.96/154.58 [2298]~E(x22981,x22982)+E(f351(x22983,x22984,x22985,x22981,x22986),f351(x22983,x22984,x22985,x22982,x22986)) % 154.96/154.58 [2299]~E(x22991,x22992)+E(f351(x22993,x22994,x22995,x22996,x22991),f351(x22993,x22994,x22995,x22996,x22992)) % 154.96/154.58 [2300]~E(x23001,x23002)+E(f783(x23001,x23003,x23004),f783(x23002,x23003,x23004)) % 154.96/154.58 [2301]~E(x23011,x23012)+E(f783(x23013,x23011,x23014),f783(x23013,x23012,x23014)) % 154.96/154.58 [2302]~E(x23021,x23022)+E(f783(x23023,x23024,x23021),f783(x23023,x23024,x23022)) % 154.96/154.58 [2303]~E(x23031,x23032)+E(f213(x23031,x23033,x23034,x23035),f213(x23032,x23033,x23034,x23035)) % 154.96/154.58 [2304]~E(x23041,x23042)+E(f213(x23043,x23041,x23044,x23045),f213(x23043,x23042,x23044,x23045)) % 154.96/154.58 [2305]~E(x23051,x23052)+E(f213(x23053,x23054,x23051,x23055),f213(x23053,x23054,x23052,x23055)) % 154.96/154.58 [2306]~E(x23061,x23062)+E(f213(x23063,x23064,x23065,x23061),f213(x23063,x23064,x23065,x23062)) % 154.96/154.58 [2307]~E(x23071,x23072)+E(f722(x23071,x23073,x23074),f722(x23072,x23073,x23074)) % 154.96/154.58 [2308]~E(x23081,x23082)+E(f722(x23083,x23081,x23084),f722(x23083,x23082,x23084)) % 154.96/154.58 [2309]~E(x23091,x23092)+E(f722(x23093,x23094,x23091),f722(x23093,x23094,x23092)) % 154.96/154.58 [2310]~E(x23101,x23102)+E(f853(x23101,x23103,x23104),f853(x23102,x23103,x23104)) % 154.96/154.58 [2311]~E(x23111,x23112)+E(f853(x23113,x23111,x23114),f853(x23113,x23112,x23114)) % 154.96/154.58 [2312]~E(x23121,x23122)+E(f853(x23123,x23124,x23121),f853(x23123,x23124,x23122)) % 154.96/154.58 [2313]~E(x23131,x23132)+E(f387(x23131,x23133,x23134),f387(x23132,x23133,x23134)) % 154.96/154.58 [2314]~E(x23141,x23142)+E(f387(x23143,x23141,x23144),f387(x23143,x23142,x23144)) % 154.96/154.58 [2315]~E(x23151,x23152)+E(f387(x23153,x23154,x23151),f387(x23153,x23154,x23152)) % 154.96/154.58 [2316]~E(x23161,x23162)+E(f483(x23161,x23163),f483(x23162,x23163)) % 154.96/154.58 [2317]~E(x23171,x23172)+E(f483(x23173,x23171),f483(x23173,x23172)) % 154.96/154.58 [2318]~E(x23181,x23182)+E(f744(x23181,x23183),f744(x23182,x23183)) % 154.96/154.58 [2319]~E(x23191,x23192)+E(f744(x23193,x23191),f744(x23193,x23192)) % 154.96/154.58 [2320]~E(x23201,x23202)+E(f756(x23201,x23203,x23204,x23205,x23206),f756(x23202,x23203,x23204,x23205,x23206)) % 154.96/154.58 [2321]~E(x23211,x23212)+E(f756(x23213,x23211,x23214,x23215,x23216),f756(x23213,x23212,x23214,x23215,x23216)) % 154.96/154.58 [2322]~E(x23221,x23222)+E(f756(x23223,x23224,x23221,x23225,x23226),f756(x23223,x23224,x23222,x23225,x23226)) % 154.96/154.58 [2323]~E(x23231,x23232)+E(f756(x23233,x23234,x23235,x23231,x23236),f756(x23233,x23234,x23235,x23232,x23236)) % 154.96/154.58 [2324]~E(x23241,x23242)+E(f756(x23243,x23244,x23245,x23246,x23241),f756(x23243,x23244,x23245,x23246,x23242)) % 154.96/154.58 [2325]~E(x23251,x23252)+E(f309(x23251,x23253),f309(x23252,x23253)) % 154.96/154.58 [2326]~E(x23261,x23262)+E(f309(x23263,x23261),f309(x23263,x23262)) % 154.96/154.58 [2327]~E(x23271,x23272)+E(f474(x23271,x23273,x23274),f474(x23272,x23273,x23274)) % 154.96/154.58 [2328]~E(x23281,x23282)+E(f474(x23283,x23281,x23284),f474(x23283,x23282,x23284)) % 154.96/154.58 [2329]~E(x23291,x23292)+E(f474(x23293,x23294,x23291),f474(x23293,x23294,x23292)) % 154.96/154.58 [2330]~E(x23301,x23302)+E(f604(x23301,x23303,x23304),f604(x23302,x23303,x23304)) % 154.96/154.58 [2331]~E(x23311,x23312)+E(f604(x23313,x23311,x23314),f604(x23313,x23312,x23314)) % 154.96/154.58 [2332]~E(x23321,x23322)+E(f604(x23323,x23324,x23321),f604(x23323,x23324,x23322)) % 154.96/154.58 [2333]~E(x23331,x23332)+E(f232(x23331,x23333,x23334),f232(x23332,x23333,x23334)) % 154.96/154.58 [2334]~E(x23341,x23342)+E(f232(x23343,x23341,x23344),f232(x23343,x23342,x23344)) % 154.96/154.58 [2335]~E(x23351,x23352)+E(f232(x23353,x23354,x23351),f232(x23353,x23354,x23352)) % 154.96/154.58 [2336]~E(x23361,x23362)+E(f735(x23361,x23363,x23364,x23365),f735(x23362,x23363,x23364,x23365)) % 154.96/154.58 [2337]~E(x23371,x23372)+E(f735(x23373,x23371,x23374,x23375),f735(x23373,x23372,x23374,x23375)) % 154.96/154.58 [2338]~E(x23381,x23382)+E(f735(x23383,x23384,x23381,x23385),f735(x23383,x23384,x23382,x23385)) % 154.96/154.58 [2339]~E(x23391,x23392)+E(f735(x23393,x23394,x23395,x23391),f735(x23393,x23394,x23395,x23392)) % 154.96/154.58 [2340]~E(x23401,x23402)+E(f384(x23401,x23403),f384(x23402,x23403)) % 154.96/154.58 [2341]~E(x23411,x23412)+E(f384(x23413,x23411),f384(x23413,x23412)) % 154.96/154.58 [2342]~E(x23421,x23422)+E(f511(x23421,x23423),f511(x23422,x23423)) % 154.96/154.58 [2343]~E(x23431,x23432)+E(f511(x23433,x23431),f511(x23433,x23432)) % 154.96/154.58 [2344]~E(x23441,x23442)+E(f124(x23441),f124(x23442)) % 154.96/154.58 [2345]~E(x23451,x23452)+E(f385(x23451,x23453,x23454),f385(x23452,x23453,x23454)) % 154.96/154.58 [2346]~E(x23461,x23462)+E(f385(x23463,x23461,x23464),f385(x23463,x23462,x23464)) % 154.96/154.58 [2347]~E(x23471,x23472)+E(f385(x23473,x23474,x23471),f385(x23473,x23474,x23472)) % 154.96/154.58 [2348]~E(x23481,x23482)+E(f201(x23481,x23483,x23484,x23485),f201(x23482,x23483,x23484,x23485)) % 154.96/154.58 [2349]~E(x23491,x23492)+E(f201(x23493,x23491,x23494,x23495),f201(x23493,x23492,x23494,x23495)) % 154.96/154.58 [2350]~E(x23501,x23502)+E(f201(x23503,x23504,x23501,x23505),f201(x23503,x23504,x23502,x23505)) % 154.96/154.58 [2351]~E(x23511,x23512)+E(f201(x23513,x23514,x23515,x23511),f201(x23513,x23514,x23515,x23512)) % 154.96/154.58 [2352]~E(x23521,x23522)+E(f867(x23521,x23523,x23524,x23525,x23526),f867(x23522,x23523,x23524,x23525,x23526)) % 154.96/154.58 [2353]~E(x23531,x23532)+E(f867(x23533,x23531,x23534,x23535,x23536),f867(x23533,x23532,x23534,x23535,x23536)) % 154.96/154.58 [2354]~E(x23541,x23542)+E(f867(x23543,x23544,x23541,x23545,x23546),f867(x23543,x23544,x23542,x23545,x23546)) % 154.96/154.58 [2355]~E(x23551,x23552)+E(f867(x23553,x23554,x23555,x23551,x23556),f867(x23553,x23554,x23555,x23552,x23556)) % 154.96/154.58 [2356]~E(x23561,x23562)+E(f867(x23563,x23564,x23565,x23566,x23561),f867(x23563,x23564,x23565,x23566,x23562)) % 154.96/154.58 [2357]~E(x23571,x23572)+E(f585(x23571,x23573),f585(x23572,x23573)) % 154.96/154.58 [2358]~E(x23581,x23582)+E(f585(x23583,x23581),f585(x23583,x23582)) % 154.96/154.58 [2359]~E(x23591,x23592)+E(f626(x23591,x23593,x23594),f626(x23592,x23593,x23594)) % 154.96/154.58 [2360]~E(x23601,x23602)+E(f626(x23603,x23601,x23604),f626(x23603,x23602,x23604)) % 154.96/154.58 [2361]~E(x23611,x23612)+E(f626(x23613,x23614,x23611),f626(x23613,x23614,x23612)) % 154.96/154.58 [2362]~E(x23621,x23622)+E(f633(x23621,x23623,x23624),f633(x23622,x23623,x23624)) % 154.96/154.58 [2363]~E(x23631,x23632)+E(f633(x23633,x23631,x23634),f633(x23633,x23632,x23634)) % 154.96/154.58 [2364]~E(x23641,x23642)+E(f633(x23643,x23644,x23641),f633(x23643,x23644,x23642)) % 154.96/154.58 [2365]~E(x23651,x23652)+E(f499(x23651,x23653,x23654,x23655,x23656),f499(x23652,x23653,x23654,x23655,x23656)) % 154.96/154.58 [2366]~E(x23661,x23662)+E(f499(x23663,x23661,x23664,x23665,x23666),f499(x23663,x23662,x23664,x23665,x23666)) % 154.96/154.58 [2367]~E(x23671,x23672)+E(f499(x23673,x23674,x23671,x23675,x23676),f499(x23673,x23674,x23672,x23675,x23676)) % 154.96/154.58 [2368]~E(x23681,x23682)+E(f499(x23683,x23684,x23685,x23681,x23686),f499(x23683,x23684,x23685,x23682,x23686)) % 154.96/154.58 [2369]~E(x23691,x23692)+E(f499(x23693,x23694,x23695,x23696,x23691),f499(x23693,x23694,x23695,x23696,x23692)) % 154.96/154.58 [2370]~E(x23701,x23702)+E(f540(x23701,x23703,x23704),f540(x23702,x23703,x23704)) % 154.96/154.58 [2371]~E(x23711,x23712)+E(f540(x23713,x23711,x23714),f540(x23713,x23712,x23714)) % 154.96/154.58 [2372]~E(x23721,x23722)+E(f540(x23723,x23724,x23721),f540(x23723,x23724,x23722)) % 154.96/154.58 [2373]~E(x23731,x23732)+E(f612(x23731,x23733,x23734),f612(x23732,x23733,x23734)) % 154.96/154.58 [2374]~E(x23741,x23742)+E(f612(x23743,x23741,x23744),f612(x23743,x23742,x23744)) % 154.96/154.58 [2375]~E(x23751,x23752)+E(f612(x23753,x23754,x23751),f612(x23753,x23754,x23752)) % 154.96/154.58 [2376]~E(x23761,x23762)+E(f470(x23761,x23763,x23764),f470(x23762,x23763,x23764)) % 154.96/154.58 [2377]~E(x23771,x23772)+E(f470(x23773,x23771,x23774),f470(x23773,x23772,x23774)) % 154.96/154.58 [2378]~E(x23781,x23782)+E(f470(x23783,x23784,x23781),f470(x23783,x23784,x23782)) % 154.96/154.58 [2379]~E(x23791,x23792)+E(f244(x23791,x23793),f244(x23792,x23793)) % 154.96/154.58 [2380]~E(x23801,x23802)+E(f244(x23803,x23801),f244(x23803,x23802)) % 154.96/154.58 [2381]~E(x23811,x23812)+E(f710(x23811,x23813,x23814,x23815,x23816),f710(x23812,x23813,x23814,x23815,x23816)) % 154.96/154.58 [2382]~E(x23821,x23822)+E(f710(x23823,x23821,x23824,x23825,x23826),f710(x23823,x23822,x23824,x23825,x23826)) % 154.96/154.58 [2383]~E(x23831,x23832)+E(f710(x23833,x23834,x23831,x23835,x23836),f710(x23833,x23834,x23832,x23835,x23836)) % 154.96/154.58 [2384]~E(x23841,x23842)+E(f710(x23843,x23844,x23845,x23841,x23846),f710(x23843,x23844,x23845,x23842,x23846)) % 154.96/154.58 [2385]~E(x23851,x23852)+E(f710(x23853,x23854,x23855,x23856,x23851),f710(x23853,x23854,x23855,x23856,x23852)) % 154.96/154.58 [2386]~E(x23861,x23862)+E(f468(x23861,x23863,x23864),f468(x23862,x23863,x23864)) % 154.96/154.58 [2387]~E(x23871,x23872)+E(f468(x23873,x23871,x23874),f468(x23873,x23872,x23874)) % 154.96/154.58 [2388]~E(x23881,x23882)+E(f468(x23883,x23884,x23881),f468(x23883,x23884,x23882)) % 154.96/154.58 [2389]~E(x23891,x23892)+E(f376(x23891,x23893),f376(x23892,x23893)) % 154.96/154.58 [2390]~E(x23901,x23902)+E(f376(x23903,x23901),f376(x23903,x23902)) % 154.96/154.58 [2391]~E(x23911,x23912)+E(f844(x23911,x23913,x23914,x23915,x23916),f844(x23912,x23913,x23914,x23915,x23916)) % 154.96/154.58 [2392]~E(x23921,x23922)+E(f844(x23923,x23921,x23924,x23925,x23926),f844(x23923,x23922,x23924,x23925,x23926)) % 154.96/154.58 [2393]~E(x23931,x23932)+E(f844(x23933,x23934,x23931,x23935,x23936),f844(x23933,x23934,x23932,x23935,x23936)) % 154.96/154.58 [2394]~E(x23941,x23942)+E(f844(x23943,x23944,x23945,x23941,x23946),f844(x23943,x23944,x23945,x23942,x23946)) % 154.96/154.58 [2395]~E(x23951,x23952)+E(f844(x23953,x23954,x23955,x23956,x23951),f844(x23953,x23954,x23955,x23956,x23952)) % 154.96/154.58 [2396]~E(x23961,x23962)+E(f346(x23961,x23963,x23964),f346(x23962,x23963,x23964)) % 154.96/154.58 [2397]~E(x23971,x23972)+E(f346(x23973,x23971,x23974),f346(x23973,x23972,x23974)) % 154.96/154.58 [2398]~E(x23981,x23982)+E(f346(x23983,x23984,x23981),f346(x23983,x23984,x23982)) % 154.96/154.58 [2399]~E(x23991,x23992)+E(f389(x23991),f389(x23992)) % 154.96/154.58 [2400]~E(x24001,x24002)+E(f717(x24001,x24003),f717(x24002,x24003)) % 154.96/154.58 [2401]~E(x24011,x24012)+E(f717(x24013,x24011),f717(x24013,x24012)) % 154.96/154.58 [2402]~E(x24021,x24022)+E(f362(x24021,x24023,x24024,x24025,x24026),f362(x24022,x24023,x24024,x24025,x24026)) % 154.96/154.58 [2403]~E(x24031,x24032)+E(f362(x24033,x24031,x24034,x24035,x24036),f362(x24033,x24032,x24034,x24035,x24036)) % 154.96/154.58 [2404]~E(x24041,x24042)+E(f362(x24043,x24044,x24041,x24045,x24046),f362(x24043,x24044,x24042,x24045,x24046)) % 154.96/154.58 [2405]~E(x24051,x24052)+E(f362(x24053,x24054,x24055,x24051,x24056),f362(x24053,x24054,x24055,x24052,x24056)) % 154.96/154.58 [2406]~E(x24061,x24062)+E(f362(x24063,x24064,x24065,x24066,x24061),f362(x24063,x24064,x24065,x24066,x24062)) % 154.96/154.58 [2407]~E(x24071,x24072)+E(f99(x24071,x24073,x24074,x24075),f99(x24072,x24073,x24074,x24075)) % 154.96/154.58 [2408]~E(x24081,x24082)+E(f99(x24083,x24081,x24084,x24085),f99(x24083,x24082,x24084,x24085)) % 154.96/154.58 [2409]~E(x24091,x24092)+E(f99(x24093,x24094,x24091,x24095),f99(x24093,x24094,x24092,x24095)) % 154.96/154.58 [2410]~E(x24101,x24102)+E(f99(x24103,x24104,x24105,x24101),f99(x24103,x24104,x24105,x24102)) % 154.96/154.58 [2411]~E(x24111,x24112)+E(f634(x24111,x24113),f634(x24112,x24113)) % 154.96/154.58 [2412]~E(x24121,x24122)+E(f634(x24123,x24121),f634(x24123,x24122)) % 154.96/154.58 [2413]~E(x24131,x24132)+E(f340(x24131,x24133),f340(x24132,x24133)) % 154.96/154.58 [2414]~E(x24141,x24142)+E(f340(x24143,x24141),f340(x24143,x24142)) % 154.96/154.58 [2415]~E(x24151,x24152)+E(f212(x24151,x24153,x24154,x24155),f212(x24152,x24153,x24154,x24155)) % 154.96/154.58 [2416]~E(x24161,x24162)+E(f212(x24163,x24161,x24164,x24165),f212(x24163,x24162,x24164,x24165)) % 154.96/154.58 [2417]~E(x24171,x24172)+E(f212(x24173,x24174,x24171,x24175),f212(x24173,x24174,x24172,x24175)) % 154.96/154.58 [2418]~E(x24181,x24182)+E(f212(x24183,x24184,x24185,x24181),f212(x24183,x24184,x24185,x24182)) % 154.96/154.58 [2419]~E(x24191,x24192)+E(f730(x24191,x24193),f730(x24192,x24193)) % 154.96/154.58 [2420]~E(x24201,x24202)+E(f730(x24203,x24201),f730(x24203,x24202)) % 154.96/154.58 [2421]~E(x24211,x24212)+E(f721(x24211,x24213,x24214),f721(x24212,x24213,x24214)) % 154.96/154.58 [2422]~E(x24221,x24222)+E(f721(x24223,x24221,x24224),f721(x24223,x24222,x24224)) % 154.96/154.58 [2423]~E(x24231,x24232)+E(f721(x24233,x24234,x24231),f721(x24233,x24234,x24232)) % 154.96/154.58 [2424]~E(x24241,x24242)+E(f533(x24241,x24243,x24244),f533(x24242,x24243,x24244)) % 154.96/154.58 [2425]~E(x24251,x24252)+E(f533(x24253,x24251,x24254),f533(x24253,x24252,x24254)) % 154.96/154.58 [2426]~E(x24261,x24262)+E(f533(x24263,x24264,x24261),f533(x24263,x24264,x24262)) % 154.96/154.58 [2427]~E(x24271,x24272)+E(f555(x24271,x24273,x24274,x24275),f555(x24272,x24273,x24274,x24275)) % 154.96/154.58 [2428]~E(x24281,x24282)+E(f555(x24283,x24281,x24284,x24285),f555(x24283,x24282,x24284,x24285)) % 154.96/154.58 [2429]~E(x24291,x24292)+E(f555(x24293,x24294,x24291,x24295),f555(x24293,x24294,x24292,x24295)) % 154.96/154.58 [2430]~E(x24301,x24302)+E(f555(x24303,x24304,x24305,x24301),f555(x24303,x24304,x24305,x24302)) % 154.96/154.58 [2431]~E(x24311,x24312)+E(f646(x24311,x24313,x24314,x24315,x24316),f646(x24312,x24313,x24314,x24315,x24316)) % 154.96/154.58 [2432]~E(x24321,x24322)+E(f646(x24323,x24321,x24324,x24325,x24326),f646(x24323,x24322,x24324,x24325,x24326)) % 154.96/154.58 [2433]~E(x24331,x24332)+E(f646(x24333,x24334,x24331,x24335,x24336),f646(x24333,x24334,x24332,x24335,x24336)) % 154.96/154.58 [2434]~E(x24341,x24342)+E(f646(x24343,x24344,x24345,x24341,x24346),f646(x24343,x24344,x24345,x24342,x24346)) % 154.96/154.58 [2435]~E(x24351,x24352)+E(f646(x24353,x24354,x24355,x24356,x24351),f646(x24353,x24354,x24355,x24356,x24352)) % 154.96/154.58 [2436]~E(x24361,x24362)+E(f354(x24361,x24363,x24364,x24365),f354(x24362,x24363,x24364,x24365)) % 154.96/154.58 [2437]~E(x24371,x24372)+E(f354(x24373,x24371,x24374,x24375),f354(x24373,x24372,x24374,x24375)) % 154.96/154.58 [2438]~E(x24381,x24382)+E(f354(x24383,x24384,x24381,x24385),f354(x24383,x24384,x24382,x24385)) % 154.96/154.58 [2439]~E(x24391,x24392)+E(f354(x24393,x24394,x24395,x24391),f354(x24393,x24394,x24395,x24392)) % 154.96/154.58 [2440]~E(x24401,x24402)+E(f454(x24401),f454(x24402)) % 154.96/154.58 [2441]~E(x24411,x24412)+E(f342(x24411),f342(x24412)) % 154.96/154.58 [2442]~E(x24421,x24422)+E(f802(x24421,x24423,x24424),f802(x24422,x24423,x24424)) % 154.96/154.58 [2443]~E(x24431,x24432)+E(f802(x24433,x24431,x24434),f802(x24433,x24432,x24434)) % 154.96/154.58 [2444]~E(x24441,x24442)+E(f802(x24443,x24444,x24441),f802(x24443,x24444,x24442)) % 154.96/154.58 [2445]~E(x24451,x24452)+E(f416(x24451,x24453,x24454,x24455),f416(x24452,x24453,x24454,x24455)) % 154.96/154.58 [2446]~E(x24461,x24462)+E(f416(x24463,x24461,x24464,x24465),f416(x24463,x24462,x24464,x24465)) % 154.96/154.58 [2447]~E(x24471,x24472)+E(f416(x24473,x24474,x24471,x24475),f416(x24473,x24474,x24472,x24475)) % 154.96/154.58 [2448]~E(x24481,x24482)+E(f416(x24483,x24484,x24485,x24481),f416(x24483,x24484,x24485,x24482)) % 154.96/154.58 [2449]~E(x24491,x24492)+E(f358(x24491,x24493,x24494,x24495),f358(x24492,x24493,x24494,x24495)) % 154.96/154.58 [2450]~E(x24501,x24502)+E(f358(x24503,x24501,x24504,x24505),f358(x24503,x24502,x24504,x24505)) % 154.96/154.58 [2451]~E(x24511,x24512)+E(f358(x24513,x24514,x24511,x24515),f358(x24513,x24514,x24512,x24515)) % 154.96/154.58 [2452]~E(x24521,x24522)+E(f358(x24523,x24524,x24525,x24521),f358(x24523,x24524,x24525,x24522)) % 154.96/154.58 [2453]~E(x24531,x24532)+E(f545(x24531,x24533,x24534,x24535,x24536,x24537,x24538),f545(x24532,x24533,x24534,x24535,x24536,x24537,x24538)) % 154.96/154.58 [2454]~E(x24541,x24542)+E(f545(x24543,x24541,x24544,x24545,x24546,x24547,x24548),f545(x24543,x24542,x24544,x24545,x24546,x24547,x24548)) % 154.96/154.58 [2455]~E(x24551,x24552)+E(f545(x24553,x24554,x24551,x24555,x24556,x24557,x24558),f545(x24553,x24554,x24552,x24555,x24556,x24557,x24558)) % 154.96/154.58 [2456]~E(x24561,x24562)+E(f545(x24563,x24564,x24565,x24561,x24566,x24567,x24568),f545(x24563,x24564,x24565,x24562,x24566,x24567,x24568)) % 154.96/154.58 [2457]~E(x24571,x24572)+E(f545(x24573,x24574,x24575,x24576,x24571,x24577,x24578),f545(x24573,x24574,x24575,x24576,x24572,x24577,x24578)) % 154.96/154.58 [2458]~E(x24581,x24582)+E(f545(x24583,x24584,x24585,x24586,x24587,x24581,x24588),f545(x24583,x24584,x24585,x24586,x24587,x24582,x24588)) % 154.96/154.58 [2459]~E(x24591,x24592)+E(f545(x24593,x24594,x24595,x24596,x24597,x24598,x24591),f545(x24593,x24594,x24595,x24596,x24597,x24598,x24592)) % 154.96/154.58 [2460]~E(x24601,x24602)+E(f270(x24601,x24603,x24604,x24605,x24606),f270(x24602,x24603,x24604,x24605,x24606)) % 154.96/154.58 [2461]~E(x24611,x24612)+E(f270(x24613,x24611,x24614,x24615,x24616),f270(x24613,x24612,x24614,x24615,x24616)) % 154.96/154.58 [2462]~E(x24621,x24622)+E(f270(x24623,x24624,x24621,x24625,x24626),f270(x24623,x24624,x24622,x24625,x24626)) % 154.96/154.58 [2463]~E(x24631,x24632)+E(f270(x24633,x24634,x24635,x24631,x24636),f270(x24633,x24634,x24635,x24632,x24636)) % 154.96/154.58 [2464]~E(x24641,x24642)+E(f270(x24643,x24644,x24645,x24646,x24641),f270(x24643,x24644,x24645,x24646,x24642)) % 154.96/154.58 [2465]~E(x24651,x24652)+E(f160(x24651,x24653,x24654,x24655),f160(x24652,x24653,x24654,x24655)) % 154.96/154.58 [2466]~E(x24661,x24662)+E(f160(x24663,x24661,x24664,x24665),f160(x24663,x24662,x24664,x24665)) % 154.96/154.58 [2467]~E(x24671,x24672)+E(f160(x24673,x24674,x24671,x24675),f160(x24673,x24674,x24672,x24675)) % 154.96/154.58 [2468]~E(x24681,x24682)+E(f160(x24683,x24684,x24685,x24681),f160(x24683,x24684,x24685,x24682)) % 154.96/154.58 [2469]~E(x24691,x24692)+E(f606(x24691,x24693,x24694),f606(x24692,x24693,x24694)) % 154.96/154.58 [2470]~E(x24701,x24702)+E(f606(x24703,x24701,x24704),f606(x24703,x24702,x24704)) % 154.96/154.58 [2471]~E(x24711,x24712)+E(f606(x24713,x24714,x24711),f606(x24713,x24714,x24712)) % 154.96/154.58 [2472]~E(x24721,x24722)+E(f740(x24721,x24723),f740(x24722,x24723)) % 154.96/154.58 [2473]~E(x24731,x24732)+E(f740(x24733,x24731),f740(x24733,x24732)) % 154.96/154.58 [2474]~E(x24741,x24742)+E(f798(x24741,x24743,x24744),f798(x24742,x24743,x24744)) % 154.96/154.58 [2475]~E(x24751,x24752)+E(f798(x24753,x24751,x24754),f798(x24753,x24752,x24754)) % 154.96/154.58 [2476]~E(x24761,x24762)+E(f798(x24763,x24764,x24761),f798(x24763,x24764,x24762)) % 154.96/154.58 [2477]~E(x24771,x24772)+E(f392(x24771,x24773,x24774,x24775,x24776,x24777),f392(x24772,x24773,x24774,x24775,x24776,x24777)) % 154.96/154.58 [2478]~E(x24781,x24782)+E(f392(x24783,x24781,x24784,x24785,x24786,x24787),f392(x24783,x24782,x24784,x24785,x24786,x24787)) % 154.96/154.58 [2479]~E(x24791,x24792)+E(f392(x24793,x24794,x24791,x24795,x24796,x24797),f392(x24793,x24794,x24792,x24795,x24796,x24797)) % 154.96/154.58 [2480]~E(x24801,x24802)+E(f392(x24803,x24804,x24805,x24801,x24806,x24807),f392(x24803,x24804,x24805,x24802,x24806,x24807)) % 154.96/154.58 [2481]~E(x24811,x24812)+E(f392(x24813,x24814,x24815,x24816,x24811,x24817),f392(x24813,x24814,x24815,x24816,x24812,x24817)) % 154.96/154.58 [2482]~E(x24821,x24822)+E(f392(x24823,x24824,x24825,x24826,x24827,x24821),f392(x24823,x24824,x24825,x24826,x24827,x24822)) % 154.96/154.58 [2483]~E(x24831,x24832)+E(f796(x24831,x24833,x24834),f796(x24832,x24833,x24834)) % 154.96/154.58 [2484]~E(x24841,x24842)+E(f796(x24843,x24841,x24844),f796(x24843,x24842,x24844)) % 154.96/154.58 [2485]~E(x24851,x24852)+E(f796(x24853,x24854,x24851),f796(x24853,x24854,x24852)) % 154.96/154.58 [2486]~E(x24861,x24862)+E(f496(x24861,x24863,x24864),f496(x24862,x24863,x24864)) % 154.96/154.58 [2487]~E(x24871,x24872)+E(f496(x24873,x24871,x24874),f496(x24873,x24872,x24874)) % 154.96/154.58 [2488]~E(x24881,x24882)+E(f496(x24883,x24884,x24881),f496(x24883,x24884,x24882)) % 154.96/154.58 [2489]~E(x24891,x24892)+E(f578(x24891,x24893),f578(x24892,x24893)) % 154.96/154.58 [2490]~E(x24901,x24902)+E(f578(x24903,x24901),f578(x24903,x24902)) % 154.96/154.58 [2491]~E(x24911,x24912)+E(f229(x24911,x24913,x24914,x24915),f229(x24912,x24913,x24914,x24915)) % 154.96/154.58 [2492]~E(x24921,x24922)+E(f229(x24923,x24921,x24924,x24925),f229(x24923,x24922,x24924,x24925)) % 154.96/154.58 [2493]~E(x24931,x24932)+E(f229(x24933,x24934,x24931,x24935),f229(x24933,x24934,x24932,x24935)) % 154.96/154.58 [2494]~E(x24941,x24942)+E(f229(x24943,x24944,x24945,x24941),f229(x24943,x24944,x24945,x24942)) % 154.96/154.58 [2495]~E(x24951,x24952)+E(f526(x24951,x24953,x24954),f526(x24952,x24953,x24954)) % 154.96/154.58 [2496]~E(x24961,x24962)+E(f526(x24963,x24961,x24964),f526(x24963,x24962,x24964)) % 154.96/154.58 [2497]~E(x24971,x24972)+E(f526(x24973,x24974,x24971),f526(x24973,x24974,x24972)) % 154.96/154.58 [2498]~E(x24981,x24982)+E(f835(x24981,x24983,x24984,x24985),f835(x24982,x24983,x24984,x24985)) % 154.96/154.58 [2499]~E(x24991,x24992)+E(f835(x24993,x24991,x24994,x24995),f835(x24993,x24992,x24994,x24995)) % 154.96/154.58 [2500]~E(x25001,x25002)+E(f835(x25003,x25004,x25001,x25005),f835(x25003,x25004,x25002,x25005)) % 154.96/154.58 [2501]~E(x25011,x25012)+E(f835(x25013,x25014,x25015,x25011),f835(x25013,x25014,x25015,x25012)) % 154.96/154.58 [2502]~E(x25021,x25022)+E(f747(x25021,x25023,x25024),f747(x25022,x25023,x25024)) % 154.96/154.58 [2503]~E(x25031,x25032)+E(f747(x25033,x25031,x25034),f747(x25033,x25032,x25034)) % 154.96/154.58 [2504]~E(x25041,x25042)+E(f747(x25043,x25044,x25041),f747(x25043,x25044,x25042)) % 154.96/154.58 [2505]~E(x25051,x25052)+E(f605(x25051,x25053,x25054,x25055),f605(x25052,x25053,x25054,x25055)) % 154.96/154.58 [2506]~E(x25061,x25062)+E(f605(x25063,x25061,x25064,x25065),f605(x25063,x25062,x25064,x25065)) % 154.96/154.58 [2507]~E(x25071,x25072)+E(f605(x25073,x25074,x25071,x25075),f605(x25073,x25074,x25072,x25075)) % 154.96/154.58 [2508]~E(x25081,x25082)+E(f605(x25083,x25084,x25085,x25081),f605(x25083,x25084,x25085,x25082)) % 154.96/154.58 [2509]~E(x25091,x25092)+E(f758(x25091,x25093,x25094),f758(x25092,x25093,x25094)) % 154.96/154.58 [2510]~E(x25101,x25102)+E(f758(x25103,x25101,x25104),f758(x25103,x25102,x25104)) % 154.96/154.58 [2511]~E(x25111,x25112)+E(f758(x25113,x25114,x25111),f758(x25113,x25114,x25112)) % 154.96/154.58 [2512]~E(x25121,x25122)+E(f572(x25121,x25123),f572(x25122,x25123)) % 154.96/154.58 [2513]~E(x25131,x25132)+E(f572(x25133,x25131),f572(x25133,x25132)) % 154.96/154.58 [2514]~E(x25141,x25142)+E(f516(x25141,x25143,x25144),f516(x25142,x25143,x25144)) % 154.96/154.58 [2515]~E(x25151,x25152)+E(f516(x25153,x25151,x25154),f516(x25153,x25152,x25154)) % 154.96/154.58 [2516]~E(x25161,x25162)+E(f516(x25163,x25164,x25161),f516(x25163,x25164,x25162)) % 154.96/154.58 [2517]~E(x25171,x25172)+E(f407(x25171,x25173,x25174,x25175),f407(x25172,x25173,x25174,x25175)) % 154.96/154.58 [2518]~E(x25181,x25182)+E(f407(x25183,x25181,x25184,x25185),f407(x25183,x25182,x25184,x25185)) % 154.96/154.58 [2519]~E(x25191,x25192)+E(f407(x25193,x25194,x25191,x25195),f407(x25193,x25194,x25192,x25195)) % 154.96/154.58 [2520]~E(x25201,x25202)+E(f407(x25203,x25204,x25205,x25201),f407(x25203,x25204,x25205,x25202)) % 154.96/154.58 [2521]~E(x25211,x25212)+E(f584(x25211),f584(x25212)) % 154.96/154.58 [2522]~E(x25221,x25222)+E(f569(x25221,x25223),f569(x25222,x25223)) % 154.96/154.58 [2523]~E(x25231,x25232)+E(f569(x25233,x25231),f569(x25233,x25232)) % 154.96/154.58 [2524]~E(x25241,x25242)+E(f751(x25241,x25243,x25244),f751(x25242,x25243,x25244)) % 154.96/154.58 [2525]~E(x25251,x25252)+E(f751(x25253,x25251,x25254),f751(x25253,x25252,x25254)) % 154.96/154.58 [2526]~E(x25261,x25262)+E(f751(x25263,x25264,x25261),f751(x25263,x25264,x25262)) % 154.96/154.58 [2527]~E(x25271,x25272)+E(f445(x25271,x25273,x25274,x25275,x25276,x25277,x25278,x25279),f445(x25272,x25273,x25274,x25275,x25276,x25277,x25278,x25279)) % 154.96/154.58 [2528]~E(x25281,x25282)+E(f445(x25283,x25281,x25284,x25285,x25286,x25287,x25288,x25289),f445(x25283,x25282,x25284,x25285,x25286,x25287,x25288,x25289)) % 154.96/154.58 [2529]~E(x25291,x25292)+E(f445(x25293,x25294,x25291,x25295,x25296,x25297,x25298,x25299),f445(x25293,x25294,x25292,x25295,x25296,x25297,x25298,x25299)) % 154.96/154.58 [2530]~E(x25301,x25302)+E(f445(x25303,x25304,x25305,x25301,x25306,x25307,x25308,x25309),f445(x25303,x25304,x25305,x25302,x25306,x25307,x25308,x25309)) % 154.96/154.58 [2531]~E(x25311,x25312)+E(f445(x25313,x25314,x25315,x25316,x25311,x25317,x25318,x25319),f445(x25313,x25314,x25315,x25316,x25312,x25317,x25318,x25319)) % 154.96/154.58 [2532]~E(x25321,x25322)+E(f445(x25323,x25324,x25325,x25326,x25327,x25321,x25328,x25329),f445(x25323,x25324,x25325,x25326,x25327,x25322,x25328,x25329)) % 154.96/154.58 [2533]~E(x25331,x25332)+E(f445(x25333,x25334,x25335,x25336,x25337,x25338,x25331,x25339),f445(x25333,x25334,x25335,x25336,x25337,x25338,x25332,x25339)) % 154.96/154.58 [2534]~E(x25341,x25342)+E(f445(x25343,x25344,x25345,x25346,x25347,x25348,x25349,x25341),f445(x25343,x25344,x25345,x25346,x25347,x25348,x25349,x25342)) % 154.96/154.58 [2535]~E(x25351,x25352)+E(f367(x25351),f367(x25352)) % 154.96/154.58 [2536]~E(x25361,x25362)+E(f547(x25361,x25363,x25364,x25365,x25366,x25367,x25368),f547(x25362,x25363,x25364,x25365,x25366,x25367,x25368)) % 154.96/154.58 [2537]~E(x25371,x25372)+E(f547(x25373,x25371,x25374,x25375,x25376,x25377,x25378),f547(x25373,x25372,x25374,x25375,x25376,x25377,x25378)) % 154.96/154.58 [2538]~E(x25381,x25382)+E(f547(x25383,x25384,x25381,x25385,x25386,x25387,x25388),f547(x25383,x25384,x25382,x25385,x25386,x25387,x25388)) % 154.96/154.58 [2539]~E(x25391,x25392)+E(f547(x25393,x25394,x25395,x25391,x25396,x25397,x25398),f547(x25393,x25394,x25395,x25392,x25396,x25397,x25398)) % 154.96/154.58 [2540]~E(x25401,x25402)+E(f547(x25403,x25404,x25405,x25406,x25401,x25407,x25408),f547(x25403,x25404,x25405,x25406,x25402,x25407,x25408)) % 154.96/154.58 [2541]~E(x25411,x25412)+E(f547(x25413,x25414,x25415,x25416,x25417,x25411,x25418),f547(x25413,x25414,x25415,x25416,x25417,x25412,x25418)) % 154.96/154.58 [2542]~E(x25421,x25422)+E(f547(x25423,x25424,x25425,x25426,x25427,x25428,x25421),f547(x25423,x25424,x25425,x25426,x25427,x25428,x25422)) % 154.96/154.58 [2543]~E(x25431,x25432)+E(f806(x25431),f806(x25432)) % 154.96/154.58 [2544]~E(x25441,x25442)+E(f750(x25441,x25443,x25444),f750(x25442,x25443,x25444)) % 154.96/154.58 [2545]~E(x25451,x25452)+E(f750(x25453,x25451,x25454),f750(x25453,x25452,x25454)) % 154.96/154.58 [2546]~E(x25461,x25462)+E(f750(x25463,x25464,x25461),f750(x25463,x25464,x25462)) % 154.96/154.58 [2547]~E(x25471,x25472)+E(f635(x25471,x25473,x25474),f635(x25472,x25473,x25474)) % 154.96/154.58 [2548]~E(x25481,x25482)+E(f635(x25483,x25481,x25484),f635(x25483,x25482,x25484)) % 154.96/154.58 [2549]~E(x25491,x25492)+E(f635(x25493,x25494,x25491),f635(x25493,x25494,x25492)) % 154.96/154.58 [2550]~E(x25501,x25502)+E(f532(x25501,x25503,x25504),f532(x25502,x25503,x25504)) % 154.96/154.58 [2551]~E(x25511,x25512)+E(f532(x25513,x25511,x25514),f532(x25513,x25512,x25514)) % 154.96/154.58 [2552]~E(x25521,x25522)+E(f532(x25523,x25524,x25521),f532(x25523,x25524,x25522)) % 154.96/154.58 [2553]~E(x25531,x25532)+E(f596(x25531),f596(x25532)) % 154.96/154.58 [2554]~E(x25541,x25542)+E(f680(x25541,x25543,x25544),f680(x25542,x25543,x25544)) % 154.96/154.58 [2555]~E(x25551,x25552)+E(f680(x25553,x25551,x25554),f680(x25553,x25552,x25554)) % 154.96/154.58 [2556]~E(x25561,x25562)+E(f680(x25563,x25564,x25561),f680(x25563,x25564,x25562)) % 154.96/154.58 [2557]~E(x25571,x25572)+E(f365(x25571,x25573),f365(x25572,x25573)) % 154.96/154.58 [2558]~E(x25581,x25582)+E(f365(x25583,x25581),f365(x25583,x25582)) % 154.96/154.58 [2559]~E(x25591,x25592)+E(f409(x25591,x25593),f409(x25592,x25593)) % 154.96/154.58 [2560]~E(x25601,x25602)+E(f409(x25603,x25601),f409(x25603,x25602)) % 154.96/154.58 [2561]~E(x25611,x25612)+E(f861(x25611,x25613,x25614,x25615,x25616),f861(x25612,x25613,x25614,x25615,x25616)) % 154.96/154.58 [2562]~E(x25621,x25622)+E(f861(x25623,x25621,x25624,x25625,x25626),f861(x25623,x25622,x25624,x25625,x25626)) % 154.96/154.58 [2563]~E(x25631,x25632)+E(f861(x25633,x25634,x25631,x25635,x25636),f861(x25633,x25634,x25632,x25635,x25636)) % 154.96/154.58 [2564]~E(x25641,x25642)+E(f861(x25643,x25644,x25645,x25641,x25646),f861(x25643,x25644,x25645,x25642,x25646)) % 154.96/154.58 [2565]~E(x25651,x25652)+E(f861(x25653,x25654,x25655,x25656,x25651),f861(x25653,x25654,x25655,x25656,x25652)) % 154.96/154.58 [2566]~E(x25661,x25662)+E(f708(x25661,x25663,x25664),f708(x25662,x25663,x25664)) % 154.96/154.58 [2567]~E(x25671,x25672)+E(f708(x25673,x25671,x25674),f708(x25673,x25672,x25674)) % 154.96/154.58 [2568]~E(x25681,x25682)+E(f708(x25683,x25684,x25681),f708(x25683,x25684,x25682)) % 154.96/154.58 [2569]~E(x25691,x25692)+E(f360(x25691,x25693,x25694,x25695,x25696),f360(x25692,x25693,x25694,x25695,x25696)) % 154.96/154.58 [2570]~E(x25701,x25702)+E(f360(x25703,x25701,x25704,x25705,x25706),f360(x25703,x25702,x25704,x25705,x25706)) % 154.96/154.58 [2571]~E(x25711,x25712)+E(f360(x25713,x25714,x25711,x25715,x25716),f360(x25713,x25714,x25712,x25715,x25716)) % 154.96/154.58 [2572]~E(x25721,x25722)+E(f360(x25723,x25724,x25725,x25721,x25726),f360(x25723,x25724,x25725,x25722,x25726)) % 154.96/154.58 [2573]~E(x25731,x25732)+E(f360(x25733,x25734,x25735,x25736,x25731),f360(x25733,x25734,x25735,x25736,x25732)) % 154.96/154.58 [2574]~E(x25741,x25742)+E(f838(x25741,x25743,x25744,x25745,x25746,x25747,x25748),f838(x25742,x25743,x25744,x25745,x25746,x25747,x25748)) % 154.96/154.58 [2575]~E(x25751,x25752)+E(f838(x25753,x25751,x25754,x25755,x25756,x25757,x25758),f838(x25753,x25752,x25754,x25755,x25756,x25757,x25758)) % 154.96/154.58 [2576]~E(x25761,x25762)+E(f838(x25763,x25764,x25761,x25765,x25766,x25767,x25768),f838(x25763,x25764,x25762,x25765,x25766,x25767,x25768)) % 154.96/154.58 [2577]~E(x25771,x25772)+E(f838(x25773,x25774,x25775,x25771,x25776,x25777,x25778),f838(x25773,x25774,x25775,x25772,x25776,x25777,x25778)) % 154.96/154.58 [2578]~E(x25781,x25782)+E(f838(x25783,x25784,x25785,x25786,x25781,x25787,x25788),f838(x25783,x25784,x25785,x25786,x25782,x25787,x25788)) % 154.96/154.58 [2579]~E(x25791,x25792)+E(f838(x25793,x25794,x25795,x25796,x25797,x25791,x25798),f838(x25793,x25794,x25795,x25796,x25797,x25792,x25798)) % 154.96/154.58 [2580]~E(x25801,x25802)+E(f838(x25803,x25804,x25805,x25806,x25807,x25808,x25801),f838(x25803,x25804,x25805,x25806,x25807,x25808,x25802)) % 154.96/154.58 [2581]~E(x25811,x25812)+E(f724(x25811,x25813,x25814,x25815),f724(x25812,x25813,x25814,x25815)) % 154.96/154.58 [2582]~E(x25821,x25822)+E(f724(x25823,x25821,x25824,x25825),f724(x25823,x25822,x25824,x25825)) % 154.96/154.58 [2583]~E(x25831,x25832)+E(f724(x25833,x25834,x25831,x25835),f724(x25833,x25834,x25832,x25835)) % 154.96/154.58 [2584]~E(x25841,x25842)+E(f724(x25843,x25844,x25845,x25841),f724(x25843,x25844,x25845,x25842)) % 154.96/154.58 [2585]~E(x25851,x25852)+E(f832(x25851,x25853,x25854,x25855,x25856,x25857,x25858),f832(x25852,x25853,x25854,x25855,x25856,x25857,x25858)) % 154.96/154.58 [2586]~E(x25861,x25862)+E(f832(x25863,x25861,x25864,x25865,x25866,x25867,x25868),f832(x25863,x25862,x25864,x25865,x25866,x25867,x25868)) % 154.96/154.58 [2587]~E(x25871,x25872)+E(f832(x25873,x25874,x25871,x25875,x25876,x25877,x25878),f832(x25873,x25874,x25872,x25875,x25876,x25877,x25878)) % 154.96/154.58 [2588]~E(x25881,x25882)+E(f832(x25883,x25884,x25885,x25881,x25886,x25887,x25888),f832(x25883,x25884,x25885,x25882,x25886,x25887,x25888)) % 154.96/154.58 [2589]~E(x25891,x25892)+E(f832(x25893,x25894,x25895,x25896,x25891,x25897,x25898),f832(x25893,x25894,x25895,x25896,x25892,x25897,x25898)) % 154.96/154.58 [2590]~E(x25901,x25902)+E(f832(x25903,x25904,x25905,x25906,x25907,x25901,x25908),f832(x25903,x25904,x25905,x25906,x25907,x25902,x25908)) % 154.96/154.58 [2591]~E(x25911,x25912)+E(f832(x25913,x25914,x25915,x25916,x25917,x25918,x25911),f832(x25913,x25914,x25915,x25916,x25917,x25918,x25912)) % 154.96/154.58 [2592]~E(x25921,x25922)+E(f849(x25921,x25923,x25924,x25925,x25926),f849(x25922,x25923,x25924,x25925,x25926)) % 154.96/154.58 [2593]~E(x25931,x25932)+E(f849(x25933,x25931,x25934,x25935,x25936),f849(x25933,x25932,x25934,x25935,x25936)) % 154.96/154.58 [2594]~E(x25941,x25942)+E(f849(x25943,x25944,x25941,x25945,x25946),f849(x25943,x25944,x25942,x25945,x25946)) % 154.96/154.58 [2595]~E(x25951,x25952)+E(f849(x25953,x25954,x25955,x25951,x25956),f849(x25953,x25954,x25955,x25952,x25956)) % 154.96/154.58 [2596]~E(x25961,x25962)+E(f849(x25963,x25964,x25965,x25966,x25961),f849(x25963,x25964,x25965,x25966,x25962)) % 154.96/154.58 [2597]~E(x25971,x25972)+E(f763(x25971,x25973,x25974),f763(x25972,x25973,x25974)) % 154.96/154.58 [2598]~E(x25981,x25982)+E(f763(x25983,x25981,x25984),f763(x25983,x25982,x25984)) % 154.96/154.58 [2599]~E(x25991,x25992)+E(f763(x25993,x25994,x25991),f763(x25993,x25994,x25992)) % 154.96/154.58 [2600]~E(x26001,x26002)+E(f128(x26001),f128(x26002)) % 154.96/154.58 [2601]~E(x26011,x26012)+E(f818(x26011,x26013,x26014,x26015),f818(x26012,x26013,x26014,x26015)) % 154.96/154.58 [2602]~E(x26021,x26022)+E(f818(x26023,x26021,x26024,x26025),f818(x26023,x26022,x26024,x26025)) % 154.96/154.58 [2603]~E(x26031,x26032)+E(f818(x26033,x26034,x26031,x26035),f818(x26033,x26034,x26032,x26035)) % 154.96/154.58 [2604]~E(x26041,x26042)+E(f818(x26043,x26044,x26045,x26041),f818(x26043,x26044,x26045,x26042)) % 154.96/154.58 [2605]~E(x26051,x26052)+E(f453(x26051,x26053),f453(x26052,x26053)) % 154.96/154.58 [2606]~E(x26061,x26062)+E(f453(x26063,x26061),f453(x26063,x26062)) % 154.96/154.58 [2607]~E(x26071,x26072)+E(f482(x26071,x26073),f482(x26072,x26073)) % 154.96/154.58 [2608]~E(x26081,x26082)+E(f482(x26083,x26081),f482(x26083,x26082)) % 154.96/154.58 [2609]~E(x26091,x26092)+E(f97(x26091,x26093,x26094),f97(x26092,x26093,x26094)) % 154.96/154.58 [2610]~E(x26101,x26102)+E(f97(x26103,x26101,x26104),f97(x26103,x26102,x26104)) % 154.96/154.58 [2611]~E(x26111,x26112)+E(f97(x26113,x26114,x26111),f97(x26113,x26114,x26112)) % 154.96/154.58 [2612]~E(x26121,x26122)+E(f719(x26121,x26123),f719(x26122,x26123)) % 154.96/154.58 [2613]~E(x26131,x26132)+E(f719(x26133,x26131),f719(x26133,x26132)) % 154.96/154.58 [2614]~E(x26141,x26142)+E(f553(x26141,x26143),f553(x26142,x26143)) % 154.96/154.58 [2615]~E(x26151,x26152)+E(f553(x26153,x26151),f553(x26153,x26152)) % 154.96/154.58 [2616]~E(x26161,x26162)+E(f568(x26161,x26163,x26164,x26165),f568(x26162,x26163,x26164,x26165)) % 154.96/154.58 [2617]~E(x26171,x26172)+E(f568(x26173,x26171,x26174,x26175),f568(x26173,x26172,x26174,x26175)) % 154.96/154.58 [2618]~E(x26181,x26182)+E(f568(x26183,x26184,x26181,x26185),f568(x26183,x26184,x26182,x26185)) % 154.96/154.58 [2619]~E(x26191,x26192)+E(f568(x26193,x26194,x26195,x26191),f568(x26193,x26194,x26195,x26192)) % 154.96/154.58 [2620]~E(x26201,x26202)+E(f370(x26201),f370(x26202)) % 154.96/154.58 [2621]~P1(x26211)+P1(x26212)+~E(x26211,x26212) % 154.96/154.58 [2622]~P2(x26221)+P2(x26222)+~E(x26221,x26222) % 154.96/154.58 [2623]P16(x26232,x26233)+~E(x26231,x26232)+~P16(x26231,x26233) % 154.96/154.58 [2624]P16(x26243,x26242)+~E(x26241,x26242)+~P16(x26243,x26241) % 154.96/154.58 [2625]P144(x26252,x26253,x26254)+~E(x26251,x26252)+~P144(x26251,x26253,x26254) % 154.96/154.58 [2626]P144(x26263,x26262,x26264)+~E(x26261,x26262)+~P144(x26263,x26261,x26264) % 154.96/154.58 [2627]P144(x26273,x26274,x26272)+~E(x26271,x26272)+~P144(x26273,x26274,x26271) % 154.96/154.58 [2628]~P98(x26281)+P98(x26282)+~E(x26281,x26282) % 154.96/154.58 [2629]~P105(x26291)+P105(x26292)+~E(x26291,x26292) % 154.96/154.58 [2630]~P99(x26301)+P99(x26302)+~E(x26301,x26302) % 154.96/154.58 [2631]~P5(x26311)+P5(x26312)+~E(x26311,x26312) % 154.96/154.58 [2632]~P121(x26321)+P121(x26322)+~E(x26321,x26322) % 154.96/154.58 [2633]~P3(x26331)+P3(x26332)+~E(x26331,x26332) % 154.96/154.58 [2634]~P4(x26341)+P4(x26342)+~E(x26341,x26342) % 154.96/154.58 [2635]~P81(x26351)+P81(x26352)+~E(x26351,x26352) % 154.96/154.58 [2636]~P64(x26361)+P64(x26362)+~E(x26361,x26362) % 154.96/154.58 [2637]~P62(x26371)+P62(x26372)+~E(x26371,x26372) % 154.96/154.58 [2638]~P114(x26381)+P114(x26382)+~E(x26381,x26382) % 154.96/154.58 [2639]P41(x26392,x26393,x26394)+~E(x26391,x26392)+~P41(x26391,x26393,x26394) % 154.96/154.58 [2640]P41(x26403,x26402,x26404)+~E(x26401,x26402)+~P41(x26403,x26401,x26404) % 154.96/154.58 [2641]P41(x26413,x26414,x26412)+~E(x26411,x26412)+~P41(x26413,x26414,x26411) % 154.96/154.58 [2642]~P103(x26421)+P103(x26422)+~E(x26421,x26422) % 154.96/154.58 [2643]~P65(x26431)+P65(x26432)+~E(x26431,x26432) % 154.96/154.58 [2644]~P100(x26441)+P100(x26442)+~E(x26441,x26442) % 154.96/154.58 [2645]~P108(x26451)+P108(x26452)+~E(x26451,x26452) % 154.96/154.58 [2646]P27(x26462,x26463,x26464,x26465)+~E(x26461,x26462)+~P27(x26461,x26463,x26464,x26465) % 154.96/154.58 [2647]P27(x26473,x26472,x26474,x26475)+~E(x26471,x26472)+~P27(x26473,x26471,x26474,x26475) % 154.96/154.58 [2648]P27(x26483,x26484,x26482,x26485)+~E(x26481,x26482)+~P27(x26483,x26484,x26481,x26485) % 154.96/154.58 [2649]P27(x26493,x26494,x26495,x26492)+~E(x26491,x26492)+~P27(x26493,x26494,x26495,x26491) % 154.96/154.58 [2650]~P66(x26501)+P66(x26502)+~E(x26501,x26502) % 154.96/154.58 [2651]P33(x26512,x26513,x26514)+~E(x26511,x26512)+~P33(x26511,x26513,x26514) % 154.96/154.58 [2652]P33(x26523,x26522,x26524)+~E(x26521,x26522)+~P33(x26523,x26521,x26524) % 154.96/154.58 [2653]P33(x26533,x26534,x26532)+~E(x26531,x26532)+~P33(x26533,x26534,x26531) % 154.96/154.58 [2654]~P91(x26541)+P91(x26542)+~E(x26541,x26542) % 154.96/154.58 [2655]~P96(x26551)+P96(x26552)+~E(x26551,x26552) % 154.96/154.58 [2656]P22(x26562,x26563,x26564,x26565)+~E(x26561,x26562)+~P22(x26561,x26563,x26564,x26565) % 154.96/154.58 [2657]P22(x26573,x26572,x26574,x26575)+~E(x26571,x26572)+~P22(x26573,x26571,x26574,x26575) % 154.96/154.58 [2658]P22(x26583,x26584,x26582,x26585)+~E(x26581,x26582)+~P22(x26583,x26584,x26581,x26585) % 154.96/154.58 [2659]P22(x26593,x26594,x26595,x26592)+~E(x26591,x26592)+~P22(x26593,x26594,x26595,x26591) % 154.96/154.58 [2660]P143(x26602,x26603,x26604)+~E(x26601,x26602)+~P143(x26601,x26603,x26604) % 154.96/154.58 [2661]P143(x26613,x26612,x26614)+~E(x26611,x26612)+~P143(x26613,x26611,x26614) % 154.96/154.58 [2662]P143(x26623,x26624,x26622)+~E(x26621,x26622)+~P143(x26623,x26624,x26621) % 154.96/154.58 [2663]~P72(x26631)+P72(x26632)+~E(x26631,x26632) % 154.96/154.58 [2664]P12(x26642,x26643,x26644)+~E(x26641,x26642)+~P12(x26641,x26643,x26644) % 154.96/154.58 [2665]P12(x26653,x26652,x26654)+~E(x26651,x26652)+~P12(x26653,x26651,x26654) % 154.96/154.58 [2666]P12(x26663,x26664,x26662)+~E(x26661,x26662)+~P12(x26663,x26664,x26661) % 154.96/154.58 [2667]~P67(x26671)+P67(x26672)+~E(x26671,x26672) % 154.96/154.58 [2668]P36(x26682,x26683,x26684,x26685,x26686)+~E(x26681,x26682)+~P36(x26681,x26683,x26684,x26685,x26686) % 154.96/154.58 [2669]P36(x26693,x26692,x26694,x26695,x26696)+~E(x26691,x26692)+~P36(x26693,x26691,x26694,x26695,x26696) % 154.96/154.58 [2670]P36(x26703,x26704,x26702,x26705,x26706)+~E(x26701,x26702)+~P36(x26703,x26704,x26701,x26705,x26706) % 154.96/154.58 [2671]P36(x26713,x26714,x26715,x26712,x26716)+~E(x26711,x26712)+~P36(x26713,x26714,x26715,x26711,x26716) % 154.96/154.58 [2672]P36(x26723,x26724,x26725,x26726,x26722)+~E(x26721,x26722)+~P36(x26723,x26724,x26725,x26726,x26721) % 154.96/154.58 [2673]~P109(x26731)+P109(x26732)+~E(x26731,x26732) % 154.96/154.58 [2674]~P68(x26741)+P68(x26742)+~E(x26741,x26742) % 154.96/154.58 [2675]P52(x26752,x26753,x26754)+~E(x26751,x26752)+~P52(x26751,x26753,x26754) % 154.96/154.58 [2676]P52(x26763,x26762,x26764)+~E(x26761,x26762)+~P52(x26763,x26761,x26764) % 154.96/154.58 [2677]P52(x26773,x26774,x26772)+~E(x26771,x26772)+~P52(x26773,x26774,x26771) % 154.96/154.58 [2678]~P107(x26781)+P107(x26782)+~E(x26781,x26782) % 154.96/154.58 [2679]~P69(x26791)+P69(x26792)+~E(x26791,x26792) % 154.96/154.58 [2680]~P60(x26801)+P60(x26802)+~E(x26801,x26802) % 154.96/154.58 [2681]P32(x26812,x26813)+~E(x26811,x26812)+~P32(x26811,x26813) % 154.96/154.58 [2682]P32(x26823,x26822)+~E(x26821,x26822)+~P32(x26823,x26821) % 154.96/154.58 [2683]~P76(x26831)+P76(x26832)+~E(x26831,x26832) % 154.96/154.58 [2684]~P122(x26841)+P122(x26842)+~E(x26841,x26842) % 154.96/154.58 [2685]P39(x26852,x26853)+~E(x26851,x26852)+~P39(x26851,x26853) % 154.96/154.58 [2686]P39(x26863,x26862)+~E(x26861,x26862)+~P39(x26863,x26861) % 154.96/154.58 [2687]~P104(x26871)+P104(x26872)+~E(x26871,x26872) % 154.96/154.58 [2688]~P77(x26881)+P77(x26882)+~E(x26881,x26882) % 154.96/154.58 [2689]~P63(x26891)+P63(x26892)+~E(x26891,x26892) % 154.96/154.58 [2690]~P83(x26901)+P83(x26902)+~E(x26901,x26902) % 154.96/154.58 [2691]~P74(x26911)+P74(x26912)+~E(x26911,x26912) % 154.96/154.58 [2692]~P97(x26921)+P97(x26922)+~E(x26921,x26922) % 154.96/154.58 [2693]~P78(x26931)+P78(x26932)+~E(x26931,x26932) % 154.96/154.58 [2694]P23(x26942,x26943,x26944,x26945,x26946)+~E(x26941,x26942)+~P23(x26941,x26943,x26944,x26945,x26946) % 154.96/154.58 [2695]P23(x26953,x26952,x26954,x26955,x26956)+~E(x26951,x26952)+~P23(x26953,x26951,x26954,x26955,x26956) % 154.96/154.58 [2696]P23(x26963,x26964,x26962,x26965,x26966)+~E(x26961,x26962)+~P23(x26963,x26964,x26961,x26965,x26966) % 154.96/154.58 [2697]P23(x26973,x26974,x26975,x26972,x26976)+~E(x26971,x26972)+~P23(x26973,x26974,x26975,x26971,x26976) % 154.96/154.58 [2698]P23(x26983,x26984,x26985,x26986,x26982)+~E(x26981,x26982)+~P23(x26983,x26984,x26985,x26986,x26981) % 154.96/154.58 [2699]~P120(x26991)+P120(x26992)+~E(x26991,x26992) % 154.96/154.58 [2700]~P134(x27001)+P134(x27002)+~E(x27001,x27002) % 154.96/154.58 [2701]P21(x27012,x27013,x27014,x27015)+~E(x27011,x27012)+~P21(x27011,x27013,x27014,x27015) % 154.96/154.58 [2702]P21(x27023,x27022,x27024,x27025)+~E(x27021,x27022)+~P21(x27023,x27021,x27024,x27025) % 154.96/154.58 [2703]P21(x27033,x27034,x27032,x27035)+~E(x27031,x27032)+~P21(x27033,x27034,x27031,x27035) % 154.96/154.58 [2704]P21(x27043,x27044,x27045,x27042)+~E(x27041,x27042)+~P21(x27043,x27044,x27045,x27041) % 154.96/154.58 [2705]P14(x27052,x27053,x27054,x27055)+~E(x27051,x27052)+~P14(x27051,x27053,x27054,x27055) % 154.96/154.58 [2706]P14(x27063,x27062,x27064,x27065)+~E(x27061,x27062)+~P14(x27063,x27061,x27064,x27065) % 154.96/154.58 [2707]P14(x27073,x27074,x27072,x27075)+~E(x27071,x27072)+~P14(x27073,x27074,x27071,x27075) % 154.96/154.58 [2708]P14(x27083,x27084,x27085,x27082)+~E(x27081,x27082)+~P14(x27083,x27084,x27085,x27081) % 154.96/154.58 [2709]~P135(x27091)+P135(x27092)+~E(x27091,x27092) % 154.96/154.58 [2710]~P123(x27101)+P123(x27102)+~E(x27101,x27102) % 154.96/154.58 [2711]~P40(x27111)+P40(x27112)+~E(x27111,x27112) % 154.96/154.58 [2712]~P141(x27121)+P141(x27122)+~E(x27121,x27122) % 154.96/154.58 [2713]P44(x27132,x27133,x27134,x27135,x27136,x27137)+~E(x27131,x27132)+~P44(x27131,x27133,x27134,x27135,x27136,x27137) % 154.96/154.58 [2714]P44(x27143,x27142,x27144,x27145,x27146,x27147)+~E(x27141,x27142)+~P44(x27143,x27141,x27144,x27145,x27146,x27147) % 154.96/154.58 [2715]P44(x27153,x27154,x27152,x27155,x27156,x27157)+~E(x27151,x27152)+~P44(x27153,x27154,x27151,x27155,x27156,x27157) % 154.96/154.58 [2716]P44(x27163,x27164,x27165,x27162,x27166,x27167)+~E(x27161,x27162)+~P44(x27163,x27164,x27165,x27161,x27166,x27167) % 154.96/154.58 [2717]P44(x27173,x27174,x27175,x27176,x27172,x27177)+~E(x27171,x27172)+~P44(x27173,x27174,x27175,x27176,x27171,x27177) % 154.96/154.58 [2718]P44(x27183,x27184,x27185,x27186,x27187,x27182)+~E(x27181,x27182)+~P44(x27183,x27184,x27185,x27186,x27187,x27181) % 154.96/154.58 [2719]~P73(x27191)+P73(x27192)+~E(x27191,x27192) % 154.96/154.58 [2720]~P61(x27201)+P61(x27202)+~E(x27201,x27202) % 154.96/154.58 [2721]~P59(x27211)+P59(x27212)+~E(x27211,x27212) % 154.96/154.58 [2722]~P89(x27221)+P89(x27222)+~E(x27221,x27222) % 154.96/154.58 [2723]~P85(x27231)+P85(x27232)+~E(x27231,x27232) % 154.96/154.58 [2724]~P115(x27241)+P115(x27242)+~E(x27241,x27242) % 154.96/154.58 [2725]~P57(x27251)+P57(x27252)+~E(x27251,x27252) % 154.96/154.58 [2726]P8(x27262,x27263,x27264)+~E(x27261,x27262)+~P8(x27261,x27263,x27264) % 154.96/154.58 [2727]P8(x27273,x27272,x27274)+~E(x27271,x27272)+~P8(x27273,x27271,x27274) % 154.96/154.58 [2728]P8(x27283,x27284,x27282)+~E(x27281,x27282)+~P8(x27283,x27284,x27281) % 154.96/154.58 [2729]~P90(x27291)+P90(x27292)+~E(x27291,x27292) % 154.96/154.58 [2730]P26(x27302,x27303,x27304)+~E(x27301,x27302)+~P26(x27301,x27303,x27304) % 154.96/154.58 [2731]P26(x27313,x27312,x27314)+~E(x27311,x27312)+~P26(x27313,x27311,x27314) % 154.96/154.58 [2732]P26(x27323,x27324,x27322)+~E(x27321,x27322)+~P26(x27323,x27324,x27321) % 154.96/154.58 [2733]~P140(x27331)+P140(x27332)+~E(x27331,x27332) % 154.96/154.58 [2734]P11(x27342,x27343,x27344,x27345,x27346)+~E(x27341,x27342)+~P11(x27341,x27343,x27344,x27345,x27346) % 154.96/154.58 [2735]P11(x27353,x27352,x27354,x27355,x27356)+~E(x27351,x27352)+~P11(x27353,x27351,x27354,x27355,x27356) % 154.96/154.58 [2736]P11(x27363,x27364,x27362,x27365,x27366)+~E(x27361,x27362)+~P11(x27363,x27364,x27361,x27365,x27366) % 154.96/154.58 [2737]P11(x27373,x27374,x27375,x27372,x27376)+~E(x27371,x27372)+~P11(x27373,x27374,x27375,x27371,x27376) % 154.96/154.58 [2738]P11(x27383,x27384,x27385,x27386,x27382)+~E(x27381,x27382)+~P11(x27383,x27384,x27385,x27386,x27381) % 154.96/154.58 [2739]P10(x27392,x27393,x27394)+~E(x27391,x27392)+~P10(x27391,x27393,x27394) % 154.96/154.58 [2740]P10(x27403,x27402,x27404)+~E(x27401,x27402)+~P10(x27403,x27401,x27404) % 154.96/154.58 [2741]P10(x27413,x27414,x27412)+~E(x27411,x27412)+~P10(x27413,x27414,x27411) % 154.96/154.58 [2742]~P137(x27421)+P137(x27422)+~E(x27421,x27422) % 154.96/154.58 [2743]P20(x27432,x27433,x27434)+~E(x27431,x27432)+~P20(x27431,x27433,x27434) % 154.96/154.58 [2744]P20(x27443,x27442,x27444)+~E(x27441,x27442)+~P20(x27443,x27441,x27444) % 154.96/154.58 [2745]P20(x27453,x27454,x27452)+~E(x27451,x27452)+~P20(x27453,x27454,x27451) % 154.96/154.58 [2746]P34(x27462,x27463,x27464,x27465)+~E(x27461,x27462)+~P34(x27461,x27463,x27464,x27465) % 154.96/154.58 [2747]P34(x27473,x27472,x27474,x27475)+~E(x27471,x27472)+~P34(x27473,x27471,x27474,x27475) % 154.96/154.58 [2748]P34(x27483,x27484,x27482,x27485)+~E(x27481,x27482)+~P34(x27483,x27484,x27481,x27485) % 154.96/154.58 [2749]P34(x27493,x27494,x27495,x27492)+~E(x27491,x27492)+~P34(x27493,x27494,x27495,x27491) % 154.96/154.58 [2750]~P117(x27501)+P117(x27502)+~E(x27501,x27502) % 154.96/154.58 [2751]P13(x27512,x27513,x27514)+~E(x27511,x27512)+~P13(x27511,x27513,x27514) % 154.96/154.58 [2752]P13(x27523,x27522,x27524)+~E(x27521,x27522)+~P13(x27523,x27521,x27524) % 154.96/154.58 [2753]P13(x27533,x27534,x27532)+~E(x27531,x27532)+~P13(x27533,x27534,x27531) % 154.96/154.58 [2754]P19(x27542,x27543,x27544)+~E(x27541,x27542)+~P19(x27541,x27543,x27544) % 154.96/154.58 [2755]P19(x27553,x27552,x27554)+~E(x27551,x27552)+~P19(x27553,x27551,x27554) % 154.96/154.58 [2756]P19(x27563,x27564,x27562)+~E(x27561,x27562)+~P19(x27563,x27564,x27561) % 154.96/154.58 [2757]~P80(x27571)+P80(x27572)+~E(x27571,x27572) % 154.96/154.58 [2758]~P106(x27581)+P106(x27582)+~E(x27581,x27582) % 154.96/154.58 [2759]P7(x27592,x27593)+~E(x27591,x27592)+~P7(x27591,x27593) % 154.96/154.58 [2760]P7(x27603,x27602)+~E(x27601,x27602)+~P7(x27603,x27601) % 154.96/154.58 [2761]P55(x27612,x27613,x27614,x27615)+~E(x27611,x27612)+~P55(x27611,x27613,x27614,x27615) % 154.96/154.58 [2762]P55(x27623,x27622,x27624,x27625)+~E(x27621,x27622)+~P55(x27623,x27621,x27624,x27625) % 154.96/154.58 [2763]P55(x27633,x27634,x27632,x27635)+~E(x27631,x27632)+~P55(x27633,x27634,x27631,x27635) % 154.96/154.58 [2764]P55(x27643,x27644,x27645,x27642)+~E(x27641,x27642)+~P55(x27643,x27644,x27645,x27641) % 154.96/154.58 [2765]P29(x27652,x27653,x27654)+~E(x27651,x27652)+~P29(x27651,x27653,x27654) % 154.96/154.58 [2766]P29(x27663,x27662,x27664)+~E(x27661,x27662)+~P29(x27663,x27661,x27664) % 154.96/154.58 [2767]P29(x27673,x27674,x27672)+~E(x27671,x27672)+~P29(x27673,x27674,x27671) % 154.96/154.58 [2768]~P82(x27681)+P82(x27682)+~E(x27681,x27682) % 154.96/154.58 [2769]P37(x27692,x27693,x27694)+~E(x27691,x27692)+~P37(x27691,x27693,x27694) % 154.96/154.58 [2770]P37(x27703,x27702,x27704)+~E(x27701,x27702)+~P37(x27703,x27701,x27704) % 154.96/154.58 [2771]P37(x27713,x27714,x27712)+~E(x27711,x27712)+~P37(x27713,x27714,x27711) % 154.96/154.58 [2772]P43(x27722,x27723)+~E(x27721,x27722)+~P43(x27721,x27723) % 154.96/154.58 [2773]P43(x27733,x27732)+~E(x27731,x27732)+~P43(x27733,x27731) % 154.96/154.58 [2774]P56(x27742,x27743)+~E(x27741,x27742)+~P56(x27741,x27743) % 154.96/154.58 [2775]P56(x27753,x27752)+~E(x27751,x27752)+~P56(x27753,x27751) % 154.96/154.58 [2776]~P127(x27761)+P127(x27762)+~E(x27761,x27762) % 154.96/154.58 [2777]~P79(x27771)+P79(x27772)+~E(x27771,x27772) % 154.96/154.58 [2778]~P58(x27781)+P58(x27782)+~E(x27781,x27782) % 154.96/154.58 [2779]P49(x27792,x27793,x27794)+~E(x27791,x27792)+~P49(x27791,x27793,x27794) % 154.96/154.58 [2780]P49(x27803,x27802,x27804)+~E(x27801,x27802)+~P49(x27803,x27801,x27804) % 154.96/154.58 [2781]P49(x27813,x27814,x27812)+~E(x27811,x27812)+~P49(x27813,x27814,x27811) % 154.96/154.58 [2782]~P70(x27821)+P70(x27822)+~E(x27821,x27822) % 154.96/154.58 [2783]~P139(x27831)+P139(x27832)+~E(x27831,x27832) % 154.96/154.58 [2784]~P112(x27841)+P112(x27842)+~E(x27841,x27842) % 154.96/154.58 [2785]~P92(x27851)+P92(x27852)+~E(x27851,x27852) % 154.96/154.58 [2786]~P128(x27861)+P128(x27862)+~E(x27861,x27862) % 154.96/154.58 [2787]~P93(x27871)+P93(x27872)+~E(x27871,x27872) % 154.96/154.58 [2788]P54(x27882,x27883)+~E(x27881,x27882)+~P54(x27881,x27883) % 154.96/154.58 [2789]P54(x27893,x27892)+~E(x27891,x27892)+~P54(x27893,x27891) % 154.96/154.58 [2790]~P136(x27901)+P136(x27902)+~E(x27901,x27902) % 154.96/154.58 [2791]~P129(x27911)+P129(x27912)+~E(x27911,x27912) % 154.96/154.58 [2792]P53(x27922,x27923,x27924,x27925,x27926)+~E(x27921,x27922)+~P53(x27921,x27923,x27924,x27925,x27926) % 154.96/154.58 [2793]P53(x27933,x27932,x27934,x27935,x27936)+~E(x27931,x27932)+~P53(x27933,x27931,x27934,x27935,x27936) % 154.96/154.58 [2794]P53(x27943,x27944,x27942,x27945,x27946)+~E(x27941,x27942)+~P53(x27943,x27944,x27941,x27945,x27946) % 154.96/154.58 [2795]P53(x27953,x27954,x27955,x27952,x27956)+~E(x27951,x27952)+~P53(x27953,x27954,x27955,x27951,x27956) % 154.96/154.58 [2796]P53(x27963,x27964,x27965,x27966,x27962)+~E(x27961,x27962)+~P53(x27963,x27964,x27965,x27966,x27961) % 154.96/154.58 [2797]P35(x27972,x27973,x27974)+~E(x27971,x27972)+~P35(x27971,x27973,x27974) % 154.96/154.58 [2798]P35(x27983,x27982,x27984)+~E(x27981,x27982)+~P35(x27983,x27981,x27984) % 154.96/154.58 [2799]P35(x27993,x27994,x27992)+~E(x27991,x27992)+~P35(x27993,x27994,x27991) % 154.96/154.58 [2800]~P138(x28001)+P138(x28002)+~E(x28001,x28002) % 154.96/154.58 [2801]~P142(x28011)+P142(x28012)+~E(x28011,x28012) % 154.96/154.58 [2802]~P9(x28021)+P9(x28022)+~E(x28021,x28022) % 154.96/154.58 [2803]~P110(x28031)+P110(x28032)+~E(x28031,x28032) % 154.96/154.58 [2804]P18(x28042,x28043,x28044)+~E(x28041,x28042)+~P18(x28041,x28043,x28044) % 154.96/154.58 [2805]P18(x28053,x28052,x28054)+~E(x28051,x28052)+~P18(x28053,x28051,x28054) % 154.96/154.58 [2806]P18(x28063,x28064,x28062)+~E(x28061,x28062)+~P18(x28063,x28064,x28061) % 154.96/154.58 [2807]~P6(x28071)+P6(x28072)+~E(x28071,x28072) % 154.96/154.58 [2808]P50(x28082,x28083)+~E(x28081,x28082)+~P50(x28081,x28083) % 154.96/154.58 [2809]P50(x28093,x28092)+~E(x28091,x28092)+~P50(x28093,x28091) % 154.96/154.58 [2810]P30(x28102,x28103,x28104)+~E(x28101,x28102)+~P30(x28101,x28103,x28104) % 154.96/154.58 [2811]P30(x28113,x28112,x28114)+~E(x28111,x28112)+~P30(x28113,x28111,x28114) % 154.96/154.58 [2812]P30(x28123,x28124,x28122)+~E(x28121,x28122)+~P30(x28123,x28124,x28121) % 154.96/154.58 [2813]P25(x28132,x28133,x28134,x28135,x28136,x28137)+~E(x28131,x28132)+~P25(x28131,x28133,x28134,x28135,x28136,x28137) % 154.96/154.58 [2814]P25(x28143,x28142,x28144,x28145,x28146,x28147)+~E(x28141,x28142)+~P25(x28143,x28141,x28144,x28145,x28146,x28147) % 154.96/154.58 [2815]P25(x28153,x28154,x28152,x28155,x28156,x28157)+~E(x28151,x28152)+~P25(x28153,x28154,x28151,x28155,x28156,x28157) % 154.96/154.58 [2816]P25(x28163,x28164,x28165,x28162,x28166,x28167)+~E(x28161,x28162)+~P25(x28163,x28164,x28165,x28161,x28166,x28167) % 154.96/154.58 [2817]P25(x28173,x28174,x28175,x28176,x28172,x28177)+~E(x28171,x28172)+~P25(x28173,x28174,x28175,x28176,x28171,x28177) % 154.96/154.58 [2818]P25(x28183,x28184,x28185,x28186,x28187,x28182)+~E(x28181,x28182)+~P25(x28183,x28184,x28185,x28186,x28187,x28181) % 154.96/154.58 [2819]~P84(x28191)+P84(x28192)+~E(x28191,x28192) % 154.96/154.58 [2820]~P113(x28201)+P113(x28202)+~E(x28201,x28202) % 154.96/154.58 [2821]P17(x28212,x28213,x28214)+~E(x28211,x28212)+~P17(x28211,x28213,x28214) % 154.96/154.58 [2822]P17(x28223,x28222,x28224)+~E(x28221,x28222)+~P17(x28223,x28221,x28224) % 154.96/154.58 [2823]P17(x28233,x28234,x28232)+~E(x28231,x28232)+~P17(x28233,x28234,x28231) % 154.96/154.58 [2824]~P31(x28241)+P31(x28242)+~E(x28241,x28242) % 154.96/154.58 [2825]P51(x28252,x28253,x28254)+~E(x28251,x28252)+~P51(x28251,x28253,x28254) % 154.96/154.58 [2826]P51(x28263,x28262,x28264)+~E(x28261,x28262)+~P51(x28263,x28261,x28264) % 154.96/154.58 [2827]P51(x28273,x28274,x28272)+~E(x28271,x28272)+~P51(x28273,x28274,x28271) % 154.96/154.58 [2828]P48(x28282,x28283,x28284)+~E(x28281,x28282)+~P48(x28281,x28283,x28284) % 154.96/154.58 [2829]P48(x28293,x28292,x28294)+~E(x28291,x28292)+~P48(x28293,x28291,x28294) % 154.96/154.58 [2830]P48(x28303,x28304,x28302)+~E(x28301,x28302)+~P48(x28303,x28304,x28301) % 154.96/154.58 [2831]~P118(x28311)+P118(x28312)+~E(x28311,x28312) % 154.96/154.58 [2832]~P95(x28321)+P95(x28322)+~E(x28321,x28322) % 154.96/154.58 [2833]~P111(x28331)+P111(x28332)+~E(x28331,x28332) % 154.96/154.58 [2834]~P38(x28341)+P38(x28342)+~E(x28341,x28342) % 154.96/154.58 [2835]P28(x28352,x28353)+~E(x28351,x28352)+~P28(x28351,x28353) % 154.96/154.58 [2836]P28(x28363,x28362)+~E(x28361,x28362)+~P28(x28363,x28361) % 154.96/154.58 [2837]~P87(x28371)+P87(x28372)+~E(x28371,x28372) % 154.96/154.58 [2838]~P94(x28381)+P94(x28382)+~E(x28381,x28382) % 154.96/154.58 [2839]~P46(x28391)+P46(x28392)+~E(x28391,x28392) % 154.96/154.58 [2840]~P130(x28401)+P130(x28402)+~E(x28401,x28402) % 154.96/154.58 [2841]P24(x28412,x28413,x28414,x28415,x28416,x28417)+~E(x28411,x28412)+~P24(x28411,x28413,x28414,x28415,x28416,x28417) % 154.96/154.58 [2842]P24(x28423,x28422,x28424,x28425,x28426,x28427)+~E(x28421,x28422)+~P24(x28423,x28421,x28424,x28425,x28426,x28427) % 154.96/154.58 [2843]P24(x28433,x28434,x28432,x28435,x28436,x28437)+~E(x28431,x28432)+~P24(x28433,x28434,x28431,x28435,x28436,x28437) % 154.96/154.58 [2844]P24(x28443,x28444,x28445,x28442,x28446,x28447)+~E(x28441,x28442)+~P24(x28443,x28444,x28445,x28441,x28446,x28447) % 154.96/154.58 [2845]P24(x28453,x28454,x28455,x28456,x28452,x28457)+~E(x28451,x28452)+~P24(x28453,x28454,x28455,x28456,x28451,x28457) % 154.96/154.58 [2846]P24(x28463,x28464,x28465,x28466,x28467,x28462)+~E(x28461,x28462)+~P24(x28463,x28464,x28465,x28466,x28467,x28461) % 154.96/154.58 [2847]~P126(x28471)+P126(x28472)+~E(x28471,x28472) % 154.96/154.58 [2848]~P132(x28481)+P132(x28482)+~E(x28481,x28482) % 154.96/154.58 [2849]~P116(x28491)+P116(x28492)+~E(x28491,x28492) % 154.96/154.58 [2850]~P75(x28501)+P75(x28502)+~E(x28501,x28502) % 154.96/154.58 [2851]~P102(x28511)+P102(x28512)+~E(x28511,x28512) % 154.96/154.58 [2852]P47(x28522,x28523)+~E(x28521,x28522)+~P47(x28521,x28523) % 154.96/154.58 [2853]P47(x28533,x28532)+~E(x28531,x28532)+~P47(x28533,x28531) % 154.96/154.58 [2854]~P131(x28541)+P131(x28542)+~E(x28541,x28542) % 154.96/154.58 [2855]P45(x28552,x28553)+~E(x28551,x28552)+~P45(x28551,x28553) % 154.96/154.58 [2856]P45(x28563,x28562)+~E(x28561,x28562)+~P45(x28563,x28561) % 154.96/154.58 [2857]~P133(x28571)+P133(x28572)+~E(x28571,x28572) % 154.96/154.58 [2858]~P124(x28581)+P124(x28582)+~E(x28581,x28582) % 154.96/154.58 [2859]~P88(x28591)+P88(x28592)+~E(x28591,x28592) % 154.96/154.58 [2860]P42(x28602,x28603,x28604,x28605)+~E(x28601,x28602)+~P42(x28601,x28603,x28604,x28605) % 154.96/154.58 [2861]P42(x28613,x28612,x28614,x28615)+~E(x28611,x28612)+~P42(x28613,x28611,x28614,x28615) % 154.96/154.58 [2862]P42(x28623,x28624,x28622,x28625)+~E(x28621,x28622)+~P42(x28623,x28624,x28621,x28625) % 154.96/154.58 [2863]P42(x28633,x28634,x28635,x28632)+~E(x28631,x28632)+~P42(x28633,x28634,x28635,x28631) % 154.96/154.58 [2864]~P125(x28641)+P125(x28642)+~E(x28641,x28642) % 154.96/154.58 [2865]P15(x28652,x28653,x28654,x28655,x28656,x28657)+~E(x28651,x28652)+~P15(x28651,x28653,x28654,x28655,x28656,x28657) % 154.96/154.58 [2866]P15(x28663,x28662,x28664,x28665,x28666,x28667)+~E(x28661,x28662)+~P15(x28663,x28661,x28664,x28665,x28666,x28667) % 154.96/154.58 [2867]P15(x28673,x28674,x28672,x28675,x28676,x28677)+~E(x28671,x28672)+~P15(x28673,x28674,x28671,x28675,x28676,x28677) % 154.96/154.58 [2868]P15(x28683,x28684,x28685,x28682,x28686,x28687)+~E(x28681,x28682)+~P15(x28683,x28684,x28685,x28681,x28686,x28687) % 154.96/154.58 [2869]P15(x28693,x28694,x28695,x28696,x28692,x28697)+~E(x28691,x28692)+~P15(x28693,x28694,x28695,x28696,x28691,x28697) % 154.96/154.58 [2870]P15(x28703,x28704,x28705,x28706,x28707,x28702)+~E(x28701,x28702)+~P15(x28703,x28704,x28705,x28706,x28707,x28701) % 154.96/154.58 [2871]~P101(x28711)+P101(x28712)+~E(x28711,x28712) % 154.96/154.58 [2872]~P86(x28721)+P86(x28722)+~E(x28721,x28722) % 154.96/154.58 [2873]~P119(x28731)+P119(x28732)+~E(x28731,x28732) % 154.96/154.58 [2874]~P71(x28741)+P71(x28742)+~E(x28741,x28742) % 154.96/154.58 % 154.96/154.58 %------------------------------------------- % 155.00/154.62 cnf(10214,plain, % 155.00/154.62 (~E(f328(a116,x102141),x102141)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(10217,plain, % 155.00/154.62 (E(f328(f259(x102171,x102171),f260(x102171,x102172)),x102172)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(10224,plain, % 155.00/154.62 (~E(f328(a116,x102241),x102241)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(10235,plain, % 155.00/154.62 (~E(f328(a116,x102351),x102351)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(10240,plain, % 155.00/154.62 (~P1(f328(f62(x102401,x102402,f192(f882(x102401,a870))),x102403))), % 155.00/154.62 inference(rename_variables,[],[4550])). % 155.00/154.62 cnf(10243,plain, % 155.00/154.62 (~P1(f328(f62(x102431,x102432,f192(f882(x102431,a870))),x102433))), % 155.00/154.62 inference(rename_variables,[],[4550])). % 155.00/154.62 cnf(10246,plain, % 155.00/154.62 (~E(f328(a116,x102461),x102461)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(10249,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x102491),f2(a875)))), % 155.00/154.62 inference(rename_variables,[],[4530])). % 155.00/154.62 cnf(10252,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x102521),f2(a875)))), % 155.00/154.62 inference(rename_variables,[],[4530])). % 155.00/154.62 cnf(10269,plain, % 155.00/154.62 (~P1(f328(f328(f242(a875),f328(a116,x102691)),x102691))), % 155.00/154.62 inference(rename_variables,[],[4535])). % 155.00/154.62 cnf(10272,plain, % 155.00/154.62 (~E(f328(f328(f148(x102721),x102722),x102723),x102723)), % 155.00/154.62 inference(rename_variables,[],[4490])). % 155.00/154.62 cnf(10278,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x102781),f2(a875)))), % 155.00/154.62 inference(rename_variables,[],[4530])). % 155.00/154.62 cnf(10281,plain, % 155.00/154.62 (E(f328(f259(x102811,x102811),f260(x102811,x102812)),x102812)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(10284,plain, % 155.00/154.62 (E(f328(f259(x102841,x102841),f260(x102841,x102842)),x102842)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(10291,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),f328(f328(f80(a875),x102911),x102912)),x102912))), % 155.00/154.62 inference(rename_variables,[],[4552])). % 155.00/154.62 cnf(10294,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),f328(f328(f80(a875),x102941),x102942)),x102942))), % 155.00/154.62 inference(rename_variables,[],[4552])). % 155.00/154.62 cnf(10315,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x103151),x103151))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(10318,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),f44(a875,x103181,x103182)),x103181))), % 155.00/154.62 inference(rename_variables,[],[3743])). % 155.00/154.62 cnf(10339,plain, % 155.00/154.62 (E(f328(f37(a875),f328(f249(a875),x103391)),x103391)), % 155.00/154.62 inference(rename_variables,[],[3173])). % 155.00/154.62 cnf(10347,plain, % 155.00/154.62 (~E(f328(a116,x103471),x103471)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(10350,plain, % 155.00/154.62 (~E(f328(a116,x103501),x103501)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(10353,plain, % 155.00/154.62 (~E(f328(a116,x103531),x103531)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(10358,plain, % 155.00/154.62 (P1(f328(f328(f243(a875),x103581),f328(a116,x103581)))), % 155.00/154.62 inference(rename_variables,[],[3350])). % 155.00/154.62 cnf(10367,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x103671),x103671))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(10374,plain, % 155.00/154.62 (E(f328(f259(x103741,x103741),f260(x103741,x103742)),x103742)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(10377,plain, % 155.00/154.62 (E(f328(f259(x103771,x103771),f260(x103771,x103772)),x103772)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(10404,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x104041),x104041))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(10409,plain, % 155.00/154.62 (~E(f328(f328(f328(f72(x104091,f879(x104092)),x104093),x104094),f328(f235(x104092),x104095)),f328(f16(f879(x104092),x104091),f205(x104092)))), % 155.00/154.62 inference(rename_variables,[],[4547])). % 155.00/154.62 cnf(10436,plain, % 155.00/154.62 (~E(f328(f328(f148(x104361),x104362),x104363),x104363)), % 155.00/154.62 inference(rename_variables,[],[4490])). % 155.00/154.62 cnf(10439,plain, % 155.00/154.62 (~E(f328(a26,x104391),f33(x104392,x104393))), % 155.00/154.62 inference(rename_variables,[],[4480])). % 155.00/154.62 cnf(10450,plain, % 155.00/154.62 (P1(f328(f328(f242(a1),x104501),x104501))), % 155.00/154.62 inference(rename_variables,[],[3283])). % 155.00/154.62 cnf(10455,plain, % 155.00/154.62 (~E(f328(a116,x104551),x104551)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(10462,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x104621),x104621))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(10475,plain, % 155.00/154.62 (P1(f328(f328(f243(a875),x104751),f328(a116,x104751)))), % 155.00/154.62 inference(rename_variables,[],[3350])). % 155.00/154.62 cnf(10480,plain, % 155.00/154.62 (E(f328(f328(f125(x104801),f117(x104801)),x104802),x104802)), % 155.00/154.62 inference(rename_variables,[],[3235])). % 155.00/154.62 cnf(10498,plain, % 155.00/154.62 (~P1(f328(f62(x104981,x104982,f192(f882(x104981,a870))),x104983))), % 155.00/154.62 inference(rename_variables,[],[4550])). % 155.00/154.62 cnf(10517,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x105171),x105171))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(10532,plain, % 155.00/154.62 (~E(f328(a26,x105321),f33(x105322,x105323))), % 155.00/154.62 inference(rename_variables,[],[4480])). % 155.00/154.62 cnf(10541,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x105411),x105411))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(10546,plain, % 155.00/154.62 (P1(f328(f328(f243(a875),x105461),f328(a116,x105461)))), % 155.00/154.62 inference(rename_variables,[],[3350])). % 155.00/154.62 cnf(10549,plain, % 155.00/154.62 (~P1(f328(f62(x105491,x105492,f192(f882(x105491,a870))),x105493))), % 155.00/154.62 inference(rename_variables,[],[4550])). % 155.00/154.62 cnf(10552,plain, % 155.00/154.62 (~P1(f328(f62(x105521,x105522,f192(f882(x105521,a870))),x105523))), % 155.00/154.62 inference(rename_variables,[],[4550])). % 155.00/154.62 cnf(10557,plain, % 155.00/154.62 (~P1(f328(f62(x105571,x105572,f192(f882(x105571,a870))),x105573))), % 155.00/154.62 inference(rename_variables,[],[4550])). % 155.00/154.62 cnf(10568,plain, % 155.00/154.62 (~E(f328(a116,x105681),x105681)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(10593,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x105931),x105931))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(10596,plain, % 155.00/154.62 (P1(f328(f328(f243(a875),x105961),f328(a116,f328(f328(f80(a875),x105962),x105961))))), % 155.00/154.62 inference(rename_variables,[],[3736])). % 155.00/154.62 cnf(10599,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x105991),f328(f328(f81(a875),x105991),x105991)))), % 155.00/154.62 inference(rename_variables,[],[3554])). % 155.00/154.62 cnf(10602,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x106021),f328(f328(f81(a875),x106021),x106021)))), % 155.00/154.62 inference(rename_variables,[],[3554])). % 155.00/154.62 cnf(10607,plain, % 155.00/154.62 (P1(f328(f328(f243(a875),x106071),f328(a116,x106071)))), % 155.00/154.62 inference(rename_variables,[],[3350])). % 155.00/154.62 cnf(10610,plain, % 155.00/154.62 (P1(f328(f328(f243(a875),x106101),f328(a116,x106101)))), % 155.00/154.62 inference(rename_variables,[],[3350])). % 155.00/154.62 cnf(10613,plain, % 155.00/154.62 (P1(f328(f328(f330(x106131),x106132),f251(f882(x106131,a870))))), % 155.00/154.62 inference(rename_variables,[],[3442])). % 155.00/154.62 cnf(10630,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),f328(f328(f80(a875),x106301),x106302)),x106302))), % 155.00/154.62 inference(rename_variables,[],[4552])). % 155.00/154.62 cnf(10633,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),f328(f328(f80(a875),x106331),x106332)),x106332))), % 155.00/154.62 inference(rename_variables,[],[4552])). % 155.00/154.62 cnf(10636,plain, % 155.00/154.62 (~P1(f328(f328(f242(a875),f328(a116,x106361)),x106361))), % 155.00/154.62 inference(rename_variables,[],[4535])). % 155.00/154.62 cnf(10639,plain, % 155.00/154.62 (~P1(f328(f328(f242(a875),f328(a116,x106391)),x106391))), % 155.00/154.62 inference(rename_variables,[],[4535])). % 155.00/154.62 cnf(10642,plain, % 155.00/154.62 (P1(f328(f251(f882(x106421,a870)),x106422))), % 155.00/154.62 inference(rename_variables,[],[3344])). % 155.00/154.62 cnf(10645,plain, % 155.00/154.62 (E(f328(f37(a875),f328(f249(a875),x106451)),x106451)), % 155.00/154.62 inference(rename_variables,[],[3173])). % 155.00/154.62 cnf(10648,plain, % 155.00/154.62 (P1(f328(f328(f243(a875),x106481),f328(a116,x106481)))), % 155.00/154.62 inference(rename_variables,[],[3350])). % 155.00/154.62 cnf(10655,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x106551),x106551))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(10660,plain, % 155.00/154.62 (P1(f328(f328(f242(a1),x106601),x106601))), % 155.00/154.62 inference(rename_variables,[],[3283])). % 155.00/154.62 cnf(10669,plain, % 155.00/154.62 (E(f328(f259(x106691,x106691),f260(x106691,x106692)),x106692)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(10672,plain, % 155.00/154.62 (P1(f328(f251(f882(x106721,a870)),x106722))), % 155.00/154.62 inference(rename_variables,[],[3344])). % 155.00/154.62 cnf(10675,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),f2(a875)),x106751))), % 155.00/154.62 inference(rename_variables,[],[3304])). % 155.00/154.62 cnf(10678,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x106781,a870)),f192(f882(x106781,a870))),x106782))), % 155.00/154.62 inference(rename_variables,[],[3734])). % 155.00/154.62 cnf(10681,plain, % 155.00/154.62 (P1(f328(f251(f882(x106811,a870)),x106812))), % 155.00/154.62 inference(rename_variables,[],[3344])). % 155.00/154.62 cnf(10684,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x106841),f328(f328(f81(a875),x106841),x106841)))), % 155.00/154.62 inference(rename_variables,[],[3554])). % 155.00/154.62 cnf(10724,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x107241),x107241))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(10735,plain, % 155.00/154.62 (~P1(f328(f328(f192(f882(x107351,f882(x107352,a870))),x107353),x107354))), % 155.00/154.62 inference(rename_variables,[],[4555])). % 155.00/154.62 cnf(10742,plain, % 155.00/154.62 (P1(f328(f328(f243(a875),x107421),f328(a116,x107421)))), % 155.00/154.62 inference(rename_variables,[],[3350])). % 155.00/154.62 cnf(10745,plain, % 155.00/154.62 (P1(f328(f328(f242(a1),x107451),x107451))), % 155.00/154.62 inference(rename_variables,[],[3283])). % 155.00/154.62 cnf(10750,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x107501),f2(a875)))), % 155.00/154.62 inference(rename_variables,[],[4530])). % 155.00/154.62 cnf(10763,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x107631),f2(a875)))), % 155.00/154.62 inference(rename_variables,[],[4530])). % 155.00/154.62 cnf(10766,plain, % 155.00/154.62 (~P1(f328(f328(f243(f882(x107661,a870)),x107662),f192(f882(x107661,a870))))), % 155.00/154.62 inference(rename_variables,[],[4548])). % 155.00/154.62 cnf(10769,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x107691),x107691))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(10772,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x107721),x107721))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(10786,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x107861),f328(f328(f22(a875),x107861),x107862)))), % 155.00/154.62 inference(scs_inference,[],[4465,10214,10224,10235,10246,10347,10350,10353,10455,4480,10439,3072,3240,10217,10281,10284,10374,10377,3218,3115,3178,3143,3122,3211,3235,10480,4547,4490,10272,3173,10339,4071,3926,4559,3194,3649,3588,3350,10358,10475,10546,10607,10610,10648,3738,3266,4530,10249,10252,10278,10750,4542,3725,3496,3874,3310,3312,3285,4527,4485,4035,4024,4548,3282,10367,10462,10593,10655,10724,10769,10772,3283,10450,10660,3284,4526,10315,10404,10517,10541,3442,4538,3344,10642,10672,3378,3805,3743,10318,4535,10269,10636,10639,3304,4115,4533,4516,4518,3257,3258,4517,4520,4521,4550,10240,10243,10498,10549,10552,4557,3734,3554,10599,10602,4554,4555,3765,4552,10291,10294,10630,3736,4574,4600,4649,4651,4681,4698,4705,4706,4745,4775,4781,4866,4891,4892,4927,4952,4953,4975,4976,4989,4993,5016,5023,5041,5044,5045,5046,5051,5052,5074,5099,5100,5110,5115,5121,5165,5166,5174,5183,5188,5190,5200,5202,5208,5212,5227,5234,5237,5238,5239,5243,5279,5292,5299,5301,5302,5306,5307,5308,5316,5319,5323,5324,5325,5332,5336,5337,5338,5346,5350,5351,5352,5357,5370,5379,5391,5393,5401,5402,5406,5410,5435,5441,5451,5452,5467,5479,5501,5507,5523,5524,5527,5546,5554,5555,5560,5561,5571,5572,5585,5589,5598,5599,5601,5616,5621,5631,5632,5644,5651,5665,5669,5672,5678,5679,5680,5683,5688,5726,5727,5730,5732,5735,5736,5737,5739,5741,5743,5748,5755,5770,5784,5789,5790,5803,5804,5809,5813,5815,5820,5861,5873,5882,5886,5897,5901,5902,5910,5923,5929,5947,5950,5960,5985,5999,6024,6044,6045,6048,6063,6065,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6168,6175,6179,6215,6217,6219,6221,6230,6232,6234,6240,6242,6248,6251,6259,6266,6267,6268,6273,6295,6296,6297,6299,6305,6310,6344,6345,6348,6349,6350,6351,6352,6353,6354,6361,6394,6395,6404,6425,6426,6446,6449,6460,6461,6467,6497,6499,6513,6550,6552,6553,6606,6631,6674,6694,6703,6704,6705,6706,6725,6726,6732,6745,6748,6750,6752,6753,6754,6756,6770])). % 155.00/154.62 cnf(10787,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x107871),x107871))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(10796,plain, % 155.00/154.62 (~P1(f328(f328(f330(x107961),x107962),f192(f882(x107961,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(10805,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x108051),x108051))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(10808,plain, % 155.00/154.62 (~P1(f328(f328(f330(x108081),x108082),f192(f882(x108081,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(10811,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x108111,a870)),f328(f307(x108112,x108111,x108113),f328(f308(x108112,x108111,x108113),x108114))),x108114))), % 155.00/154.62 inference(rename_variables,[],[4175])). % 155.00/154.62 cnf(10818,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x108181,a870)),f328(f170(x108181),f328(f133(x108181,x108182),x108183))),f328(f170(x108181),x108183)))), % 155.00/154.62 inference(rename_variables,[],[3936])). % 155.00/154.62 cnf(10821,plain, % 155.00/154.62 (E(f328(f307(x108211,x108211,f5(x108211)),x108212),x108212)), % 155.00/154.62 inference(rename_variables,[],[3340])). % 155.00/154.62 cnf(10826,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),f2(a875)),x108261))), % 155.00/154.62 inference(rename_variables,[],[3304])). % 155.00/154.62 cnf(10829,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x108291),x108291))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(10832,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x108321),x108321))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(10835,plain, % 155.00/154.62 (~P1(f328(f328(f192(f882(x108351,f882(x108352,a870))),x108353),x108354))), % 155.00/154.62 inference(rename_variables,[],[4555])). % 155.00/154.62 cnf(10842,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x108421),x108421))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(10856,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x108561),f328(f328(f81(a875),x108561),x108561)))), % 155.00/154.62 inference(rename_variables,[],[3554])). % 155.00/154.62 cnf(10866,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x108661),x108661))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(10869,plain, % 155.00/154.62 (P1(f328(f328(f242(a1),x108691),x108691))), % 155.00/154.62 inference(rename_variables,[],[3283])). % 155.00/154.62 cnf(10872,plain, % 155.00/154.62 (~E(f328(a116,x108721),x108721)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(10877,plain, % 155.00/154.62 (P1(f328(f328(f330(x108771),x108772),f251(f882(x108771,a870))))), % 155.00/154.62 inference(rename_variables,[],[3442])). % 155.00/154.62 cnf(10882,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x108821),f2(a875)))), % 155.00/154.62 inference(rename_variables,[],[4530])). % 155.00/154.62 cnf(10897,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),f2(a875)),x108971))), % 155.00/154.62 inference(rename_variables,[],[3304])). % 155.00/154.62 cnf(10904,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x109041),x109041))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(10913,plain, % 155.00/154.62 (~P1(f328(f328(f330(x109131),x109132),f192(f882(x109131,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(10921,plain, % 155.00/154.62 (P1(f328(f328(f330(x109211),x109212),f251(f882(x109211,a870))))), % 155.00/154.62 inference(rename_variables,[],[3442])). % 155.00/154.62 cnf(10924,plain, % 155.00/154.62 (~P1(f328(f328(f330(f881(f876(x109241),f876(x109241))),f328(f328(f263(f876(x109241),f876(x109241)),x109242),f117(x109241))),f142(x109241,x109243)))), % 155.00/154.62 inference(rename_variables,[],[4559])). % 155.00/154.62 cnf(10931,plain, % 155.00/154.62 (~P1(f328(f328(f330(x109311),x109312),f192(f882(x109311,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(10934,plain, % 155.00/154.62 (~P1(f328(f328(f330(x109341),x109342),f192(f882(x109341,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(10937,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x109371,a870)),x109372),f328(f328(f306(x109371),x109373),x109372)))), % 155.00/154.62 inference(rename_variables,[],[3732])). % 155.00/154.62 cnf(10940,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x109401),x109401))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(10943,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x109431,a870)),x109432),f328(f328(f306(x109431),x109433),x109432)))), % 155.00/154.62 inference(rename_variables,[],[3732])). % 155.00/154.62 cnf(10958,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x109581,a870)),x109582),f328(f328(f306(x109581),x109583),x109582)))), % 155.00/154.62 inference(rename_variables,[],[3732])). % 155.00/154.62 cnf(10965,plain, % 155.00/154.62 (~P1(f328(f62(x109651,x109652,f192(f882(x109651,a870))),x109653))), % 155.00/154.62 inference(rename_variables,[],[4550])). % 155.00/154.62 cnf(10978,plain, % 155.00/154.62 (P1(f328(f328(f243(a875),x109781),f328(a116,x109781)))), % 155.00/154.62 inference(rename_variables,[],[3350])). % 155.00/154.62 cnf(10988,plain, % 155.00/154.62 (~E(f328(f307(x109881,f882(x109881,a870),x109882),x109883),f328(f305(x109881),x109883))), % 155.00/154.62 inference(rename_variables,[],[4536])). % 155.00/154.62 cnf(10991,plain, % 155.00/154.62 (~P1(f328(f328(f330(x109911),x109912),f192(f882(x109911,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(10994,plain, % 155.00/154.62 (P1(f328(f328(f330(f881(x109941,x109941)),f328(f328(f263(x109941,x109941),x109942),x109942)),f304(x109941,x109943)))), % 155.00/154.62 inference(rename_variables,[],[3926])). % 155.00/154.62 cnf(10997,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x109971,a870)),x109972),f251(f882(x109971,a870))))), % 155.00/154.62 inference(rename_variables,[],[3668])). % 155.00/154.62 cnf(11000,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x110001,a870)),f328(f170(x110001),f174(x110001,x110002,x110003))),f328(f170(x110001),x110002)))), % 155.00/154.62 inference(rename_variables,[],[3987])). % 155.00/154.62 cnf(11016,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x110161,a870)),f192(f882(x110161,a870))),x110162))), % 155.00/154.62 inference(rename_variables,[],[3734])). % 155.00/154.62 cnf(11027,plain, % 155.00/154.62 (~P1(f328(f328(f330(f881(f876(x110271),f876(x110271))),f328(f328(f263(f876(x110271),f876(x110271)),x110272),f117(x110271))),f144(x110271,x110273)))), % 155.00/154.62 inference(rename_variables,[],[4560])). % 155.00/154.62 cnf(11038,plain, % 155.00/154.62 (~E(f328(a116,x110381),x110381)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(11041,plain, % 155.00/154.62 (~E(f328(a116,x110411),x110411)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(11053,plain, % 155.00/154.62 (P27(x110531,x110531,f5(x110531),x110532)), % 155.00/154.62 inference(rename_variables,[],[3526])). % 155.00/154.62 cnf(11058,plain, % 155.00/154.62 (~E(f328(f307(x110581,f882(x110581,a870),x110582),x110583),f328(f305(x110581),x110583))), % 155.00/154.62 inference(rename_variables,[],[4536])). % 155.00/154.62 cnf(11063,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x110631,a870)),x110632),f251(f882(x110631,a870))))), % 155.00/154.62 inference(rename_variables,[],[3668])). % 155.00/154.62 cnf(11077,plain, % 155.00/154.62 (~P1(f328(f328(f330(x110771),x110772),f192(f882(x110771,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(11080,plain, % 155.00/154.62 (~P1(f328(f328(f242(a875),f328(a116,x110801)),x110801))), % 155.00/154.62 inference(rename_variables,[],[4535])). % 155.00/154.62 cnf(11085,plain, % 155.00/154.62 (~P1(f328(f328(f330(x110851),x110852),f192(f882(x110851,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(11098,plain, % 155.00/154.62 (~P1(f328(f328(f242(a875),f328(a116,x110981)),x110981))), % 155.00/154.62 inference(rename_variables,[],[4535])). % 155.00/154.62 cnf(11101,plain, % 155.00/154.62 (~P1(f328(f328(f330(x111011),x111012),f192(f882(x111011,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(11111,plain, % 155.00/154.62 (E(f328(x111111,f712(f328(x111111,x111112),f328(f235(x111113),x111112),x111111,x111114,x111113)),f328(x111111,x111112))), % 155.00/154.62 inference(scs_inference,[],[3526,4465,10214,10224,10235,10246,10347,10350,10353,10455,10568,10872,11038,4480,10439,10532,3072,3125,3240,10217,10281,10284,10374,10377,3218,3745,3115,3178,3143,3122,3340,3211,3235,10480,3388,4547,3924,4490,10272,4536,10988,3389,3173,10339,4071,3926,10994,4559,10924,4560,3194,3487,3649,3588,3801,3350,10358,10475,10546,10607,10610,10648,10742,10978,3738,3266,4530,10249,10252,10278,10750,10763,10882,4542,3725,3496,3874,3310,3312,3285,4527,4485,4035,3936,10818,3987,3650,4024,3668,10997,4548,3282,10367,10462,10593,10655,10724,10769,10772,10805,10829,10866,10904,3283,10450,10660,10745,3284,4526,10315,10404,10517,10541,10787,10832,3442,10613,10877,10921,4538,10796,10808,10913,10931,10934,10991,11077,11085,3344,10642,10672,3378,3805,3743,10318,4535,10269,10636,10639,11080,3304,10675,10826,4115,4533,3813,4516,4518,3257,3258,4517,4520,4521,4550,10240,10243,10498,10549,10552,10557,4557,3891,3732,10937,10943,3734,10678,3554,10599,10602,10684,10856,4554,4555,10735,4175,3765,4552,10291,10294,10630,3736,10596,4008,4574,4600,4649,4651,4681,4698,4705,4706,4745,4775,4781,4866,4891,4892,4927,4952,4953,4975,4976,4989,4993,5016,5023,5041,5044,5045,5046,5051,5052,5074,5099,5100,5110,5115,5121,5165,5166,5174,5183,5188,5190,5200,5202,5208,5212,5227,5234,5237,5238,5239,5243,5279,5292,5299,5301,5302,5306,5307,5308,5316,5319,5323,5324,5325,5332,5336,5337,5338,5346,5350,5351,5352,5357,5370,5379,5391,5393,5401,5402,5406,5410,5435,5441,5451,5452,5467,5479,5501,5507,5523,5524,5527,5546,5554,5555,5560,5561,5571,5572,5585,5589,5598,5599,5601,5616,5621,5631,5632,5644,5651,5665,5669,5672,5678,5679,5680,5683,5688,5726,5727,5730,5732,5735,5736,5737,5739,5741,5743,5748,5755,5770,5784,5789,5790,5803,5804,5809,5813,5815,5820,5861,5873,5882,5886,5897,5901,5902,5910,5923,5929,5947,5950,5960,5985,5999,6024,6044,6045,6048,6063,6065,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6168,6175,6179,6215,6217,6219,6221,6230,6232,6234,6240,6242,6248,6251,6259,6266,6267,6268,6273,6295,6296,6297,6299,6305,6310,6344,6345,6348,6349,6350,6351,6352,6353,6354,6361,6394,6395,6404,6425,6426,6446,6449,6460,6461,6467,6497,6499,6513,6550,6552,6553,6606,6631,6674,6694,6703,6704,6705,6706,6725,6726,6732,6745,6748,6750,6752,6753,6754,6756,6770,6781,6783,6784,6797,6801,6852,6864,6866,6870,6887,6888,6922,6934,6965,6997,7051,7079,7134,7155,7164,7167,7224,7232,7290,7292,7307,7315,7318,7319,7338,7344,7346,7395,7405,7408,7424,7475,7476,7480,7523,7524,7542,7611,7630,7653,7676,7691,7706,7716,7725,7726,7753,7756,7758,7769,7807,7819,7844,7902,7936,7968,8007,8023,8039,8040,8116,8173,8192,8221,8242,8266,8267,8364,8366,8372,8386,8390,8408,8430,8438,8440,8452,8458,8462,8483,8497,8498,8517,8518,8523,8524,8525,8526,8527,8549,8550,8551,8562,8576,8578,8590,8594,8596,8597,8598,8606,8611,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8814,8815,8826,8870,8876,8882,8893,8898,8900])). % 155.00/154.62 cnf(11120,plain, % 155.00/154.62 (P1(f328(f328(f330(f881(x111201,x111201)),f328(f328(f263(x111201,x111201),x111202),x111202)),f304(x111201,x111203)))), % 155.00/154.62 inference(rename_variables,[],[3926])). % 155.00/154.62 cnf(11125,plain, % 155.00/154.62 (~P1(f328(f328(f330(f881(f876(x111251),f876(x111251))),f328(f328(f263(f876(x111251),f876(x111251)),x111252),f117(x111251))),f142(x111251,x111253)))), % 155.00/154.62 inference(rename_variables,[],[4559])). % 155.00/154.62 cnf(11128,plain, % 155.00/154.62 (~P1(f328(f328(f330(f881(f876(x111281),f876(x111281))),f328(f328(f263(f876(x111281),f876(x111281)),x111282),f117(x111281))),f144(x111281,x111283)))), % 155.00/154.62 inference(rename_variables,[],[4560])). % 155.00/154.62 cnf(11131,plain, % 155.00/154.62 (~P1(f328(f328(f330(f881(f876(x111311),f876(x111311))),f328(f328(f263(f876(x111311),f876(x111311)),x111312),f117(x111311))),f154(x111311,x111313)))), % 155.00/154.62 inference(rename_variables,[],[4561])). % 155.00/154.62 cnf(11136,plain, % 155.00/154.62 (~P1(f328(f328(f243(f882(x111361,a870)),x111362),f192(f882(x111361,a870))))), % 155.00/154.62 inference(rename_variables,[],[4548])). % 155.00/154.62 cnf(11139,plain, % 155.00/154.62 (~P1(f328(f328(f330(x111391),x111392),f192(f882(x111391,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(11146,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x111461,a870)),x111462),f251(f882(x111461,a870))))), % 155.00/154.62 inference(rename_variables,[],[3668])). % 155.00/154.62 cnf(11149,plain, % 155.00/154.62 (~P1(f328(f328(f192(f882(x111491,f882(x111492,a870))),x111493),x111494))), % 155.00/154.62 inference(rename_variables,[],[4555])). % 155.00/154.62 cnf(11158,plain, % 155.00/154.62 (~P1(f328(f328(f330(x111581),x111582),f192(f882(x111581,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(11161,plain, % 155.00/154.62 (~P1(f328(f328(f330(f881(x111611,x111611)),f328(f328(f263(x111611,x111611),x111612),x111613)),f150(x111611,f117(f882(x111611,a875)))))), % 155.00/154.62 inference(rename_variables,[],[4557])). % 155.00/154.62 cnf(11164,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x111641,a870)),x111642),x111642))), % 155.00/154.62 inference(rename_variables,[],[3584])). % 155.00/154.62 cnf(11167,plain, % 155.00/154.62 (~P1(f328(f328(f330(x111671),x111672),f192(f882(x111671,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(11170,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x111701,a870)),f192(f882(x111701,a870))),x111702))), % 155.00/154.62 inference(rename_variables,[],[3734])). % 155.00/154.62 cnf(11173,plain, % 155.00/154.62 (P1(f328(f328(f330(f881(x111731,x111731)),f328(f328(f263(x111731,x111731),x111732),x111732)),f304(x111731,x111733)))), % 155.00/154.62 inference(rename_variables,[],[3926])). % 155.00/154.62 cnf(11187,plain, % 155.00/154.62 (~P1(f328(f328(f330(f881(f876(x111871),f876(x111871))),f328(f328(f263(f876(x111871),f876(x111871)),f117(x111871)),x111872)),f142(x111871,x111873)))), % 155.00/154.62 inference(rename_variables,[],[4562])). % 155.00/154.62 cnf(11195,plain, % 155.00/154.62 (P1(f328(f328(f330(x111951),x111952),f251(f882(x111951,a870))))), % 155.00/154.62 inference(rename_variables,[],[3442])). % 155.00/154.62 cnf(11200,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x112001,a870)),f192(f882(x112001,a870))),x112002))), % 155.00/154.62 inference(rename_variables,[],[3734])). % 155.00/154.62 cnf(11203,plain, % 155.00/154.62 (~P1(f328(f328(f330(x112031),x112032),f192(f882(x112031,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(11206,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x112061,a870)),x112062),f251(f882(x112061,a870))))), % 155.00/154.62 inference(rename_variables,[],[3668])). % 155.00/154.62 cnf(11211,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x112111,a870)),f192(f882(x112111,a870))),x112112))), % 155.00/154.62 inference(rename_variables,[],[3734])). % 155.00/154.62 cnf(11224,plain, % 155.00/154.62 (P1(f328(f251(f882(x112241,a870)),x112242))), % 155.00/154.62 inference(rename_variables,[],[3344])). % 155.00/154.62 cnf(11232,plain, % 155.00/154.62 (~P1(f328(f328(f330(f881(f876(x112321),f876(x112321))),f328(f328(f263(f876(x112321),f876(x112321)),x112322),f117(x112321))),f142(x112321,x112323)))), % 155.00/154.62 inference(rename_variables,[],[4559])). % 155.00/154.62 cnf(11235,plain, % 155.00/154.62 (~P1(f328(f328(f330(f881(f876(x112351),f876(x112351))),f328(f328(f263(f876(x112351),f876(x112351)),x112352),f117(x112351))),f144(x112351,x112353)))), % 155.00/154.62 inference(rename_variables,[],[4560])). % 155.00/154.62 cnf(11238,plain, % 155.00/154.62 (~E(f328(f328(f148(x112381),x112382),x112383),x112383)), % 155.00/154.62 inference(rename_variables,[],[4490])). % 155.00/154.62 cnf(11241,plain, % 155.00/154.62 (~E(f328(a116,x112411),x112411)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(11244,plain, % 155.00/154.62 (~P1(f328(f328(f330(x112441),x112442),f192(f882(x112441,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(11249,plain, % 155.00/154.62 (P1(f328(f328(f330(f881(f876(x112491),f876(x112491))),f328(f328(f263(f876(x112491),f876(x112491)),x112492),x112492)),f155(x112491,f304(x112491,x112493))))), % 155.00/154.62 inference(rename_variables,[],[4065])). % 155.00/154.62 cnf(11254,plain, % 155.00/154.62 (~P1(f328(f328(f330(f881(f876(x112541),f876(x112541))),f328(f328(f263(f876(x112541),f876(x112541)),x112542),f117(x112541))),f142(x112541,x112543)))), % 155.00/154.62 inference(rename_variables,[],[4559])). % 155.00/154.62 cnf(11264,plain, % 155.00/154.62 (~P1(f328(f328(f330(x112641),x112642),f192(f882(x112641,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(11267,plain, % 155.00/154.62 (~P1(f328(f328(f330(x112671),x112672),f192(f882(x112671,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(11270,plain, % 155.00/154.62 (~P1(f328(f328(f330(x112701),x112702),f192(f882(x112701,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(11273,plain, % 155.00/154.62 (P1(f328(f328(f330(x112731),x112732),f251(f882(x112731,a870))))), % 155.00/154.62 inference(rename_variables,[],[3442])). % 155.00/154.62 cnf(11276,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x112761),f2(a875)))), % 155.00/154.62 inference(rename_variables,[],[4530])). % 155.00/154.62 cnf(11281,plain, % 155.00/154.62 (~P1(f328(f328(f330(f881(x112811,x112811)),f328(f328(f263(x112811,x112811),x112812),x112813)),f150(x112811,f117(f882(x112811,a875)))))), % 155.00/154.62 inference(rename_variables,[],[4557])). % 155.00/154.62 cnf(11284,plain, % 155.00/154.62 (~E(f328(f307(x112841,f882(x112841,a870),x112842),x112843),f328(f305(x112841),x112843))), % 155.00/154.62 inference(rename_variables,[],[4536])). % 155.00/154.62 cnf(11287,plain, % 155.00/154.62 (~E(f328(f307(x112871,f882(x112871,a870),x112872),x112873),f328(f305(x112871),x112873))), % 155.00/154.62 inference(rename_variables,[],[4536])). % 155.00/154.62 cnf(11292,plain, % 155.00/154.62 (~P1(f328(f328(f330(f881(f876(x112921),f876(x112921))),f328(f328(f263(f876(x112921),f876(x112921)),x112922),f117(x112921))),f142(x112921,x112923)))), % 155.00/154.62 inference(rename_variables,[],[4559])). % 155.00/154.62 cnf(11298,plain, % 155.00/154.62 (~P1(f328(f328(f330(f881(f876(x112981),f876(x112981))),f328(f328(f263(f876(x112981),f876(x112981)),x112982),f117(x112981))),f142(x112981,x112983)))), % 155.00/154.62 inference(rename_variables,[],[4559])). % 155.00/154.62 cnf(11301,plain, % 155.00/154.62 (~P1(f328(f328(f330(x113011),x113012),f192(f882(x113011,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(11308,plain, % 155.00/154.62 (~P1(f328(f328(f330(x113081),x113082),f192(f882(x113081,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(11311,plain, % 155.00/154.62 (~P1(f328(f328(f330(x113111),x113112),f192(f882(x113111,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(11314,plain, % 155.00/154.62 (P1(f328(f328(f330(x113141),f328(x113142,x113143)),f328(f307(x113144,x113141,x113142),f251(f882(x113144,a870)))))), % 155.00/154.62 inference(rename_variables,[],[3891])). % 155.00/154.62 cnf(11317,plain, % 155.00/154.62 (~P1(f328(f328(f330(f881(x113171,x113171)),f328(f328(f263(x113171,x113171),x113172),x113173)),f150(x113171,f117(f882(x113171,a875)))))), % 155.00/154.62 inference(rename_variables,[],[4557])). % 155.00/154.62 cnf(11325,plain, % 155.00/154.62 (E(f118(x113251,f117(x113251)),f117(x113251))), % 155.00/154.62 inference(rename_variables,[],[3125])). % 155.00/154.62 cnf(11328,plain, % 155.00/154.62 (~E(f328(a116,x113281),x113281)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(11335,plain, % 155.00/154.62 (~E(f328(a116,x113351),x113351)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(11340,plain, % 155.00/154.62 (E(f328(f259(x113401,x113401),f260(x113401,x113402)),x113402)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(11343,plain, % 155.00/154.62 (E(f328(f259(x113431,x113431),f260(x113431,x113432)),x113432)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(11349,plain, % 155.00/154.62 (~E(f328(a116,x113491),x113491)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(11356,plain, % 155.00/154.62 (~E(f328(f328(f80(a1),x113561),x113561),a101)), % 155.00/154.62 inference(rename_variables,[],[4488])). % 155.00/154.62 cnf(11365,plain, % 155.00/154.62 (E(f328(f328(f22(a875),f2(a875)),x113651),f2(a875))), % 155.00/154.62 inference(rename_variables,[],[3195])). % 155.00/154.62 cnf(11368,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x113681),f2(a875)))), % 155.00/154.62 inference(rename_variables,[],[4530])). % 155.00/154.62 cnf(11375,plain, % 155.00/154.62 (E(f328(f328(f80(a1),f328(f328(f81(a1),x113751),f328(f328(f38(a1),x113752),x113751))),f44(a1,x113752,x113751)),x113752)), % 155.00/154.62 inference(rename_variables,[],[3837])). % 155.00/154.62 cnf(11401,plain, % 155.00/154.62 (~E(f328(a116,x114011),x114011)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(11404,plain, % 155.00/154.62 (~E(f328(a116,x114041),x114041)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(11430,plain, % 155.00/154.62 (~P1(f328(f62(x114301,x114302,f192(f882(x114301,a870))),x114303))), % 155.00/154.62 inference(rename_variables,[],[4550])). % 155.00/154.62 cnf(11433,plain, % 155.00/154.62 (~P1(f328(f328(f192(f882(x114331,f882(x114332,a870))),x114333),x114334))), % 155.00/154.62 inference(rename_variables,[],[4555])). % 155.00/154.62 cnf(11436,plain, % 155.00/154.62 (P1(f328(f328(f330(x114361),x114362),f251(f882(x114361,a870))))), % 155.00/154.62 inference(rename_variables,[],[3442])). % 155.00/154.62 cnf(11448,plain, % 155.00/154.62 (~E(f328(a116,x114481),x114481)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(11451,plain, % 155.00/154.62 (P1(f328(f328(f242(a1),x114511),x114511))), % 155.00/154.62 inference(rename_variables,[],[3283])). % 155.00/154.62 cnf(11458,plain, % 155.00/154.62 (P1(f328(f66(x114581,x114582,x114583,x114584,f192(f882(x114581,a870))),x114584))), % 155.00/154.62 inference(rename_variables,[],[4214])). % 155.00/154.62 cnf(11459,plain, % 155.00/154.62 (E(f328(f259(x114591,x114591),f260(x114591,x114592)),x114592)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(11464,plain, % 155.00/154.62 (~P1(f328(f328(f192(f882(x114641,f882(x114642,a870))),x114643),x114644))), % 155.00/154.62 inference(rename_variables,[],[4555])). % 155.00/154.62 cnf(11475,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),f328(f328(f80(a875),x114751),x114752)),x114752))), % 155.00/154.62 inference(rename_variables,[],[4552])). % 155.00/154.62 cnf(11478,plain, % 155.00/154.62 (~P1(f328(f328(f243(a1),f328(f104(a1),x114781)),f2(a1)))), % 155.00/154.62 inference(rename_variables,[],[4542])). % 155.00/154.62 cnf(11494,plain, % 155.00/154.62 (~E(f328(f328(f105(a875),f328(a116,x114941)),x114941),f328(a116,x114941))), % 155.00/154.62 inference(scs_inference,[],[3526,4465,10214,10224,10235,10246,10347,10350,10353,10455,10568,10872,11038,11041,11241,11328,11335,11349,11401,11404,4480,10439,10532,3199,2880,2885,2895,2897,2899,2905,2910,2923,2934,2935,2936,2951,2952,2953,2958,2961,2962,3021,3022,3035,3054,3061,3072,4461,3125,11325,3240,10217,10281,10284,10374,10377,10669,11340,11343,3218,3745,3115,3837,11375,3178,3143,3122,3340,3211,3235,10480,3388,4547,3924,4490,10272,10436,4536,10988,11058,11284,11287,3389,3173,10339,10645,3174,3094,3195,11365,4071,3926,10994,11120,11173,4559,10924,11125,11232,11254,11292,11298,4560,11027,11128,11235,4561,11131,4562,11187,4563,3194,3487,3649,4488,3588,3801,3350,10358,10475,10546,10607,10610,10648,10742,10978,3738,3266,4530,10249,10252,10278,10750,10763,10882,11276,11368,4542,3725,3496,3874,3310,3312,3285,4527,4485,3479,4543,4065,11249,3609,4035,3936,10818,3987,3650,4024,3668,10997,11063,11146,4548,10766,11136,3282,10367,10462,10593,10655,10724,10769,10772,10805,10829,10866,10904,3283,10450,10660,10745,10869,3284,4526,10315,10404,10517,10541,10787,10832,3442,10613,10877,10921,11195,11273,4538,10796,10808,10913,10931,10934,10991,11077,11085,11101,11139,11158,11167,11203,11244,11264,11267,11270,11301,11308,3344,10642,10672,10681,3378,3805,3743,10318,4535,10269,10636,10639,11080,11098,3304,10675,10826,4115,4533,3813,4516,4518,3257,3258,4517,4520,4521,4214,4550,10240,10243,10498,10549,10552,10557,10965,4557,11161,11281,3891,3732,10937,10943,3584,3734,10678,11016,11170,11200,3554,10599,10602,10684,10856,4554,4544,4555,10735,10835,11149,11433,4175,4076,3765,4552,10291,10294,10630,10633,3736,10596,4008,4574,4600,4649,4651,4681,4698,4705,4706,4745,4775,4781,4866,4891,4892,4927,4952,4953,4975,4976,4989,4993,5016,5023,5041,5044,5045,5046,5051,5052,5074,5099,5100,5110,5115,5121,5165,5166,5174,5183,5188,5190,5200,5202,5208,5212,5227,5234,5237,5238,5239,5243,5279,5292,5299,5301,5302,5306,5307,5308,5316,5319,5323,5324,5325,5332,5336,5337,5338,5346,5350,5351,5352,5357,5370,5379,5391,5393,5401,5402,5406,5410,5435,5441,5451,5452,5467,5479,5501,5507,5523,5524,5527,5546,5554,5555,5560,5561,5571,5572,5585,5589,5598,5599,5601,5616,5621,5631,5632,5644,5651,5665,5669,5672,5678,5679,5680,5683,5688,5726,5727,5730,5732,5735,5736,5737,5739,5741,5743,5748,5755,5770,5784,5789,5790,5803,5804,5809,5813,5815,5820,5861,5873,5882,5886,5897,5901,5902,5910,5923,5929,5947,5950,5960,5985,5999,6024,6044,6045,6048,6063,6065,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6168,6175,6179,6215,6217,6219,6221,6230,6232,6234,6240,6242,6248,6251,6259,6266,6267,6268,6273,6295,6296,6297,6299,6305,6310,6344,6345,6348,6349,6350,6351,6352,6353,6354,6361,6394,6395,6404,6425,6426,6446,6449,6460,6461,6467,6497,6499,6513,6550,6552,6553,6606,6631,6674,6694,6703,6704,6705,6706,6725,6726,6732,6745,6748,6750,6752,6753,6754,6756,6770,6781,6783,6784,6797,6801,6852,6864,6866,6870,6887,6888,6922,6934,6965,6997,7051,7079,7134,7155,7164,7167,7224,7232,7290,7292,7307,7315,7318,7319,7338,7344,7346,7395,7405,7408,7424,7475,7476,7480,7523,7524,7542,7611,7630,7653,7676,7691,7706,7716,7725,7726,7753,7756,7758,7769,7807,7819,7844,7902,7936,7968,8007,8023,8039,8040,8116,8173,8192,8221,8242,8266,8267,8364,8366,8372,8386,8390,8408,8430,8438,8440,8452,8458,8462,8483,8497,8498,8517,8518,8523,8524,8525,8526,8527,8549,8550,8551,8562,8576,8578,8590,8594,8596,8597,8598,8606,8611,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8814,8815,8826,8870,8876,8882,8893,8898,8900,8903,8904,8908,8918,9000,9031,9032,9033,9048,9065,9072,9073,9102,9103,9144,9147,9173,9218,9219,9220,9235,9260,9274,9280,9283,9305,9306,9334,9395,9431,9432,9433,9458,9459,9477,9495,9501,9515,9539,9561,9569,9570,9571,9572,9587,9589,9594,9625,9626,9632,9633,9677,9678,9710,9719,9729,9731,9732,9741,9755,9758,9786,9819,9821,9825,9882,9923,9924,9926,9936,9937,9957,9962,10003,10054,10127,10128,10182,10198,2,8,9,4587,4588,4606,4637,4639,4640,4667,4673,4674,4685,4734,4736,4766,4780,4810,4906,4907,4920,4940,4996,4997,5000,5001,5003,5005,5006,5015,5019,5020,5030,5042,5043,5049,5069,5070,5087,5092,5093,5094,5095,5098,5106,5109,5116,5180,5186,5187,5194,5224,5235,5241,5257,5277,5278,5285,5286,5287,5296,5305,5312,5314,5315,5321,5328,5329,5342,5343,5344,5345,5347,5348,5353,5354])). % 155.00/154.62 cnf(11501,plain, % 155.00/154.62 (E(f328(f259(x115011,x115011),f260(x115011,x115012)),x115012)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(11506,plain, % 155.00/154.62 (E(f328(f259(x115061,x115061),f260(x115061,x115062)),x115062)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(11509,plain, % 155.00/154.62 (~P1(f328(f328(f243(a1),f328(f104(a1),x115091)),f2(a1)))), % 155.00/154.62 inference(rename_variables,[],[4542])). % 155.00/154.62 cnf(11514,plain, % 155.00/154.62 (~E(f328(a116,x115141),x115141)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(11523,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x115231),x115231))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(11544,plain, % 155.00/154.62 (~P1(f328(f328(f243(a1),f328(f104(a1),x115441)),f2(a1)))), % 155.00/154.62 inference(rename_variables,[],[4542])). % 155.00/154.62 cnf(11557,plain, % 155.00/154.62 (P1(f328(f328(f242(a1),x115571),x115571))), % 155.00/154.62 inference(rename_variables,[],[3283])). % 155.00/154.62 cnf(11560,plain, % 155.00/154.62 (~P1(f328(f328(f242(a875),f328(a116,x115601)),x115601))), % 155.00/154.62 inference(rename_variables,[],[4535])). % 155.00/154.62 cnf(11561,plain, % 155.00/154.62 (~E(f328(a116,x115611),x115611)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(11571,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),f328(f328(f80(a875),x115711),x115712)),x115711))), % 155.00/154.62 inference(rename_variables,[],[4553])). % 155.00/154.62 cnf(11574,plain, % 155.00/154.62 (~P1(f328(f328(f243(a1),f328(f104(a1),x115741)),f2(a1)))), % 155.00/154.62 inference(rename_variables,[],[4542])). % 155.00/154.62 cnf(11577,plain, % 155.00/154.62 (~E(f328(a116,x115771),x115771)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(11591,plain, % 155.00/154.62 (~P1(f328(f328(f242(a1),f2(a1)),f328(f79(a1),f328(f104(a1),f328(a116,x115911)))))), % 155.00/154.62 inference(rename_variables,[],[4554])). % 155.00/154.62 cnf(11594,plain, % 155.00/154.62 (P1(f328(f328(f243(a875),f328(f328(f22(a875),x115941),x115942)),f328(a116,x115941)))), % 155.00/154.62 inference(rename_variables,[],[3738])). % 155.00/154.62 cnf(11597,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),f44(a875,x115971,x115972)),x115971))), % 155.00/154.62 inference(rename_variables,[],[3743])). % 155.00/154.62 cnf(11603,plain, % 155.00/154.62 (E(f328(f259(x116031,x116031),f260(x116031,x116032)),x116032)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(11608,plain, % 155.00/154.62 (E(f328(f328(f125(x116081),f168(x116081,x116082,x116083)),f168(x116081,x116084,x116083)),f328(f328(f125(x116081),f168(x116081,x116084,x116083)),f168(x116081,x116082,x116083)))), % 155.00/154.62 inference(rename_variables,[],[3852])). % 155.00/154.62 cnf(11613,plain, % 155.00/154.62 (~P1(f328(f328(f242(a875),f328(a116,x116131)),x116131))), % 155.00/154.62 inference(rename_variables,[],[4535])). % 155.00/154.62 cnf(11622,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x116221),x116221))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(11625,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),f44(a875,x116251,x116252)),x116251))), % 155.00/154.62 inference(rename_variables,[],[3743])). % 155.00/154.62 cnf(11626,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),f2(a875)),x116261))), % 155.00/154.62 inference(rename_variables,[],[3304])). % 155.00/154.62 cnf(11643,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x116431),x116431))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(11646,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x116461),x116461))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(11649,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x116491),x116491))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(11652,plain, % 155.00/154.62 (P1(f328(f328(f330(x116521),f328(x116522,x116523)),f328(f307(x116524,x116521,x116522),f251(f882(x116524,a870)))))), % 155.00/154.62 inference(rename_variables,[],[3891])). % 155.00/154.62 cnf(11653,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),f328(f328(f80(a875),x116531),x116532)),x116532))), % 155.00/154.62 inference(rename_variables,[],[4552])). % 155.00/154.62 cnf(11656,plain, % 155.00/154.62 (P1(f328(f328(f330(x116561),f328(x116562,x116563)),f328(f307(x116564,x116561,x116562),f251(f882(x116564,a870)))))), % 155.00/154.62 inference(rename_variables,[],[3891])). % 155.00/154.62 cnf(11657,plain, % 155.00/154.62 (~P1(f328(f328(f242(a875),f328(a116,x116571)),x116571))), % 155.00/154.62 inference(rename_variables,[],[4535])). % 155.00/154.62 cnf(11662,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),f328(f328(f80(a875),x116621),x116622)),x116621))), % 155.00/154.62 inference(rename_variables,[],[4553])). % 155.00/154.62 cnf(11665,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x116651),x116651))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(11668,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x116681),x116681))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(11674,plain, % 155.00/154.62 (~P37(x116741,x116742,f117(x116741))), % 155.00/154.62 inference(rename_variables,[],[4499])). % 155.00/154.62 cnf(11677,plain, % 155.00/154.62 (P1(f328(f328(f330(x116771),x116772),f251(f882(x116771,a870))))), % 155.00/154.62 inference(rename_variables,[],[3442])). % 155.00/154.62 cnf(11678,plain, % 155.00/154.62 (~P1(f328(f328(f242(a875),f328(a116,x116781)),x116781))), % 155.00/154.62 inference(rename_variables,[],[4535])). % 155.00/154.62 cnf(11681,plain, % 155.00/154.62 (~P1(f328(f62(x116811,x116812,f192(f882(x116811,a870))),x116813))), % 155.00/154.62 inference(rename_variables,[],[4550])). % 155.00/154.62 cnf(11694,plain, % 155.00/154.62 (~P1(f328(f328(f330(x116941),x116942),f192(f882(x116941,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(11697,plain, % 155.00/154.62 (E(f328(f328(f16(x116971,x116972),x116973),x116974),x116973)), % 155.00/154.62 inference(rename_variables,[],[3273])). % 155.00/154.62 cnf(11700,plain, % 155.00/154.62 (E(f328(f328(f16(x117001,x117002),x117003),x117004),x117003)), % 155.00/154.62 inference(rename_variables,[],[3273])). % 155.00/154.62 cnf(11712,plain, % 155.00/154.62 (P1(f328(f328(f243(a875),f2(a875)),f328(a116,x117121)))), % 155.00/154.62 inference(rename_variables,[],[3362])). % 155.00/154.62 cnf(11715,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x117151),x117151))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(11718,plain, % 155.00/154.62 (P1(f328(f328(f330(x117181),f328(x117182,x117183)),f328(f307(x117184,x117181,x117182),f251(f882(x117184,a870)))))), % 155.00/154.62 inference(rename_variables,[],[3891])). % 155.00/154.62 cnf(11721,plain, % 155.00/154.62 (P1(f328(f61(x117211),f328(f170(x117211),x117212)))), % 155.00/154.62 inference(rename_variables,[],[3323])). % 155.00/154.62 cnf(11724,plain, % 155.00/154.62 (P1(f328(f61(x117241),f328(f170(x117241),x117242)))), % 155.00/154.62 inference(rename_variables,[],[3323])). % 155.00/154.62 cnf(11727,plain, % 155.00/154.62 (P1(f328(f328(f242(a1),f328(f79(a1),f328(f104(a1),x117271))),f328(f104(a1),x117272)))), % 155.00/154.62 inference(rename_variables,[],[3766])). % 155.00/154.62 cnf(11730,plain, % 155.00/154.62 (~P1(f328(f328(f330(x117301),x117302),f192(f882(x117301,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(11742,plain, % 155.00/154.62 (~P1(f328(f328(f330(a875),x117421),f328(f249(a875),f2(a875))))), % 155.00/154.62 inference(scs_inference,[],[3526,4498,4499,4465,10214,10224,10235,10246,10347,10350,10353,10455,10568,10872,11038,11041,11241,11328,11335,11349,11401,11404,11448,11514,11561,4480,10439,10532,3199,2880,2885,2886,2895,2897,2898,2899,2905,2906,2910,2923,2934,2935,2936,2951,2952,2953,2954,2957,2958,2961,2962,2965,3021,3022,3024,3035,3054,3061,3072,4461,3852,11608,3125,11325,3240,10217,10281,10284,10374,10377,10669,11340,11343,11459,11501,11506,3218,3745,3115,3489,3837,11375,3178,3143,3138,3122,3340,3211,3235,10480,3388,4547,3924,4490,10272,10436,3273,11697,4536,10988,11058,11284,11287,3389,3173,10339,10645,3174,3447,3094,3195,11365,4071,3926,10994,11120,11173,4559,10924,11125,11232,11254,11292,11298,4560,11027,11128,11235,4561,11131,4562,11187,4563,3194,3487,3649,4354,4355,4488,3588,3801,3350,10358,10475,10546,10607,10610,10648,10742,10978,3738,11594,3266,3362,4530,10249,10252,10278,10750,10763,10882,11276,11368,4542,11478,11509,11544,3725,3496,3874,3310,3312,3285,4527,4485,3479,4543,4065,11249,3609,3323,11721,4035,3936,10818,3987,3650,4024,3668,10997,11063,11146,4548,10766,11136,3282,10367,10462,10593,10655,10724,10769,10772,10805,10829,10866,10904,10940,11668,3283,10450,10660,10745,10869,11451,3284,3358,4526,10315,10404,10517,10541,10787,10832,10842,11523,11622,11643,11646,11649,3442,10613,10877,10921,11195,11273,11436,4538,10796,10808,10913,10931,10934,10991,11077,11085,11101,11139,11158,11167,11203,11244,11264,11267,11270,11301,11308,11311,11694,3344,10642,10672,10681,3384,3378,3805,3743,10318,11597,4535,10269,10636,10639,11080,11098,11560,11613,11657,3304,10675,10826,10897,3766,4115,4533,3813,4516,4518,3257,3258,4517,4520,4521,3599,4214,4550,10240,10243,10498,10549,10552,10557,10965,11430,4557,11161,11281,4001,3891,11314,11652,11656,3732,10937,10943,3584,3734,10678,11016,11170,11200,3554,10599,10602,10684,10856,4554,11591,4544,4555,10735,10835,11149,11433,4175,4076,3765,3712,4552,10291,10294,10630,10633,11475,4553,11571,3736,10596,4008,4574,4600,4649,4651,4681,4698,4705,4706,4745,4775,4781,4866,4891,4892,4927,4952,4953,4975,4976,4989,4993,5016,5023,5041,5044,5045,5046,5051,5052,5074,5099,5100,5110,5115,5121,5165,5166,5174,5183,5188,5190,5200,5202,5208,5212,5227,5234,5237,5238,5239,5243,5279,5292,5299,5301,5302,5306,5307,5308,5316,5319,5323,5324,5325,5332,5336,5337,5338,5346,5350,5351,5352,5357,5370,5379,5391,5393,5401,5402,5406,5410,5435,5441,5451,5452,5467,5479,5501,5507,5523,5524,5527,5546,5554,5555,5560,5561,5571,5572,5585,5589,5598,5599,5601,5616,5621,5631,5632,5644,5651,5665,5669,5672,5678,5679,5680,5683,5688,5726,5727,5730,5732,5735,5736,5737,5739,5741,5743,5748,5755,5770,5784,5789,5790,5803,5804,5809,5813,5815,5820,5861,5873,5882,5886,5897,5901,5902,5910,5923,5929,5947,5950,5960,5985,5999,6024,6044,6045,6048,6063,6065,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6168,6175,6179,6215,6217,6219,6221,6230,6232,6234,6240,6242,6248,6251,6259,6266,6267,6268,6273,6295,6296,6297,6299,6305,6310,6344,6345,6348,6349,6350,6351,6352,6353,6354,6361,6394,6395,6404,6425,6426,6446,6449,6460,6461,6467,6497,6499,6513,6550,6552,6553,6606,6631,6674,6694,6703,6704,6705,6706,6725,6726,6732,6745,6748,6750,6752,6753,6754,6756,6770,6781,6783,6784,6797,6801,6852,6864,6866,6870,6887,6888,6922,6934,6965,6997,7051,7079,7134,7155,7164,7167,7224,7232,7290,7292,7307,7315,7318,7319,7338,7344,7346,7395,7405,7408,7424,7475,7476,7480,7523,7524,7542,7611,7630,7653,7676,7691,7706,7716,7725,7726,7753,7756,7758,7769,7807,7819,7844,7902,7936,7968,8007,8023,8039,8040,8116,8173,8192,8221,8242,8266,8267,8364,8366,8372,8386,8390,8408,8430,8438,8440,8452,8458,8462,8483,8497,8498,8517,8518,8523,8524,8525,8526,8527,8549,8550,8551,8562,8576,8578,8590,8594,8596,8597,8598,8606,8611,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8814,8815,8826,8870,8876,8882,8893,8898,8900,8903,8904,8908,8918,9000,9031,9032,9033,9048,9065,9072,9073,9102,9103,9144,9147,9173,9218,9219,9220,9235,9260,9274,9280,9283,9305,9306,9334,9395,9431,9432,9433,9458,9459,9477,9495,9501,9515,9539,9561,9569,9570,9571,9572,9587,9589,9594,9625,9626,9632,9633,9677,9678,9710,9719,9729,9731,9732,9741,9755,9758,9786,9819,9821,9825,9882,9923,9924,9926,9936,9937,9957,9962,10003,10054,10127,10128,10182,10198,2,8,9,4587,4588,4606,4637,4639,4640,4667,4673,4674,4685,4734,4736,4766,4780,4810,4906,4907,4920,4940,4996,4997,5000,5001,5003,5005,5006,5015,5019,5020,5030,5042,5043,5049,5069,5070,5087,5092,5093,5094,5095,5098,5106,5109,5116,5180,5186,5187,5194,5224,5235,5241,5257,5277,5278,5285,5286,5287,5296,5305,5312,5314,5315,5321,5328,5329,5342,5343,5344,5345,5347,5348,5353,5354,5355,5356,5387,5388,5389,5397,5398,5399,5400,5446,5448,5450,5486,5488,5489,5491,5492,5494,5495,5497,5506,5511,5513,5514,5515,5516,5517,5518,5525,5535,5538,5549,5565,5566,5569,5578,5581,5582,5583,5608,5618,5634,5635,5645,5646,5648,5650,5655,5690,5695,5697,5757,5791,5792,5796,5802,5805,5806,5807,5808,5814,5825,5826,5828,5829,5837,5858,5889,5905,5908,5909,5911,5920,5937,5940,5944,5945,5946,5962,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120])). % 155.00/154.62 cnf(11749,plain, % 155.00/154.62 (P1(f328(f328(f242(a1),x117491),x117491))), % 155.00/154.62 inference(rename_variables,[],[3283])). % 155.00/154.62 cnf(11752,plain, % 155.00/154.62 (P1(f328(f328(f242(a1),x117521),x117521))), % 155.00/154.62 inference(rename_variables,[],[3283])). % 155.00/154.62 cnf(11761,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x117611),f2(a875)))), % 155.00/154.62 inference(rename_variables,[],[4530])). % 155.00/154.62 cnf(11764,plain, % 155.00/154.62 (P1(f328(f328(f242(a1),x117641),x117641))), % 155.00/154.62 inference(rename_variables,[],[3283])). % 155.00/154.62 cnf(11769,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x117691),f2(a875)))), % 155.00/154.62 inference(rename_variables,[],[4530])). % 155.00/154.62 cnf(11776,plain, % 155.00/154.62 (P1(f328(f251(f882(x117761,a870)),x117762))), % 155.00/154.62 inference(rename_variables,[],[3344])). % 155.00/154.62 cnf(11781,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),f2(a875)),x117811))), % 155.00/154.62 inference(rename_variables,[],[3304])). % 155.00/154.62 cnf(11782,plain, % 155.00/154.62 (~P1(f328(f328(f242(a875),f328(a116,x117821)),x117821))), % 155.00/154.62 inference(rename_variables,[],[4535])). % 155.00/154.62 cnf(11785,plain, % 155.00/154.62 (~P1(f328(f62(x117851,x117852,f192(f882(x117851,a870))),x117853))), % 155.00/154.62 inference(rename_variables,[],[4550])). % 155.00/154.62 cnf(11807,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x118071),x118071))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(11810,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x118101),x118101))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(11813,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x118131),x118131))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(11816,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x118161),x118161))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(11819,plain, % 155.00/154.62 (~P1(f328(f328(f242(a875),f328(a116,x118191)),x118191))), % 155.00/154.62 inference(rename_variables,[],[4535])). % 155.00/154.62 cnf(11822,plain, % 155.00/154.62 (~P1(f328(f328(f242(a875),f328(a116,x118221)),x118221))), % 155.00/154.62 inference(rename_variables,[],[4535])). % 155.00/154.62 cnf(11825,plain, % 155.00/154.62 (~P1(f328(f328(f242(a875),f328(a116,x118251)),x118251))), % 155.00/154.62 inference(rename_variables,[],[4535])). % 155.00/154.62 cnf(11828,plain, % 155.00/154.62 (~P1(f328(f328(f242(a875),f328(a116,x118281)),x118281))), % 155.00/154.62 inference(rename_variables,[],[4535])). % 155.00/154.62 cnf(11845,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x118451),x118451))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(11851,plain, % 155.00/154.62 (P1(f328(f328(f242(a1),x118511),x118511))), % 155.00/154.62 inference(rename_variables,[],[3283])). % 155.00/154.62 cnf(11862,plain, % 155.00/154.62 (P1(f328(f328(f242(a1),x118621),x118621))), % 155.00/154.62 inference(rename_variables,[],[3283])). % 155.00/154.62 cnf(11865,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(f881(f876(x118651),f876(x118651)),a870)),f155(x118651,x118652)),f304(f876(x118651),f154(x118651,x118652))))), % 155.00/154.62 inference(rename_variables,[],[3992])). % 155.00/154.62 cnf(11872,plain, % 155.00/154.62 (P1(f328(f328(f243(a875),x118721),f328(a116,x118721)))), % 155.00/154.62 inference(rename_variables,[],[3350])). % 155.00/154.62 cnf(11875,plain, % 155.00/154.62 (P1(f328(f328(f330(f882(x118751,a870)),x118752),f328(f305(x118751),x118752)))), % 155.00/154.62 inference(rename_variables,[],[3650])). % 155.00/154.62 cnf(11876,plain, % 155.00/154.62 (~E(f328(a116,x118761),x118761)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(11883,plain, % 155.00/154.62 (P1(f328(f328(f242(a1),x118831),x118831))), % 155.00/154.62 inference(rename_variables,[],[3283])). % 155.00/154.62 cnf(11888,plain, % 155.00/154.62 (P1(f328(f328(f242(a1),x118881),x118881))), % 155.00/154.62 inference(rename_variables,[],[3283])). % 155.00/154.62 cnf(11897,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x118971,a870)),x118972),f328(f328(f306(x118971),x118973),x118972)))), % 155.00/154.62 inference(rename_variables,[],[3732])). % 155.00/154.62 cnf(11900,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x119001),x119001))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(11901,plain, % 155.00/154.62 (~E(f328(a116,x119011),x119011)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(11912,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x119121),x119121))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(11913,plain, % 155.00/154.62 (~E(f328(a116,x119131),x119131)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(11916,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x119161),x119161))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(11919,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x119191),x119191))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(11922,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x119221),x119221))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(11925,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x119251),x119251))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(11928,plain, % 155.00/154.62 (P1(f328(f328(f242(a1),x119281),x119281))), % 155.00/154.62 inference(rename_variables,[],[3283])). % 155.00/154.62 cnf(11931,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x119311),x119311))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(11934,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x119341),x119341))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(11935,plain, % 155.00/154.62 (P1(f328(f328(f243(a875),x119351),f328(a116,x119351)))), % 155.00/154.62 inference(rename_variables,[],[3350])). % 155.00/154.62 cnf(11942,plain, % 155.00/154.62 (~E(f328(a116,x119421),x119421)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(11947,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x119471),x119471))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(11948,plain, % 155.00/154.62 (~E(f328(a116,x119481),x119481)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(11953,plain, % 155.00/154.62 (P1(f328(f328(f242(a1),x119531),x119531))), % 155.00/154.62 inference(rename_variables,[],[3283])). % 155.00/154.62 cnf(11968,plain, % 155.00/154.62 (P1(f328(f328(f242(a1),x119681),x119681))), % 155.00/154.62 inference(rename_variables,[],[3283])). % 155.00/154.62 cnf(11973,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),f2(a875)),x119731))), % 155.00/154.62 inference(rename_variables,[],[3304])). % 155.00/154.62 cnf(11990,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x119901),f2(a875)))), % 155.00/154.62 inference(rename_variables,[],[4530])). % 155.00/154.62 cnf(11993,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x119931),f2(a875)))), % 155.00/154.62 inference(rename_variables,[],[4530])). % 155.00/154.62 cnf(11996,plain, % 155.00/154.62 (~P1(f328(f328(f330(x119961),x119962),f192(f882(x119961,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(11999,plain, % 155.00/154.62 (~P1(f328(f328(f330(x119991),x119992),f192(f882(x119991,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(12002,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x120021),x120021))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(12005,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x120051),x120051))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(12008,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x120081),x120081))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(12011,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x120111),x120111))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(12014,plain, % 155.00/154.62 (P1(f328(f328(f243(a875),x120141),f328(a116,x120141)))), % 155.00/154.62 inference(rename_variables,[],[3350])). % 155.00/154.62 cnf(12021,plain, % 155.00/154.62 (P1(f328(f328(f330(f882(x120211,a870)),x120212),f328(f305(x120211),x120212)))), % 155.00/154.62 inference(rename_variables,[],[3650])). % 155.00/154.62 cnf(12026,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x120261,a870)),x120262),f328(f328(f306(x120261),x120263),x120262)))), % 155.00/154.62 inference(rename_variables,[],[3732])). % 155.00/154.62 cnf(12033,plain, % 155.00/154.62 (~P1(f328(f328(f330(x120331),x120332),f192(f882(x120331,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(12042,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x120421,a870)),x120422),f251(f882(x120421,a870))))), % 155.00/154.62 inference(rename_variables,[],[3668])). % 155.00/154.62 cnf(12043,plain, % 155.00/154.62 (~E(f328(a116,x120431),x120431)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(12046,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x120461,a870)),f192(f882(x120461,a870))),x120462))), % 155.00/154.62 inference(rename_variables,[],[3734])). % 155.00/154.62 cnf(12049,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x120491,a870)),f328(f170(x120491),f328(f133(x120491,x120492),x120493))),f328(f170(x120491),x120493)))), % 155.00/154.62 inference(rename_variables,[],[3936])). % 155.00/154.62 cnf(12055,plain, % 155.00/154.62 (P1(f328(f328(f243(a875),x120551),f328(a116,x120551)))), % 155.00/154.62 inference(rename_variables,[],[3350])). % 155.00/154.62 cnf(12064,plain, % 155.00/154.62 (E(f328(f259(x120641,x120641),f260(x120641,x120642)),x120642)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(12075,plain, % 155.00/154.62 (P1(f328(f61(x120751),f192(f882(x120751,a870))))), % 155.00/154.62 inference(rename_variables,[],[3358])). % 155.00/154.62 cnf(12076,plain, % 155.00/154.62 (~P1(f328(f328(f330(x120761),x120762),f192(f882(x120761,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(12081,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x120811),f2(a875)))), % 155.00/154.62 inference(rename_variables,[],[4530])). % 155.00/154.62 cnf(12082,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x120821),x120821))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(12087,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x120871,a870)),f328(f170(x120871),f174(x120871,x120872,x120873))),f328(f170(x120871),x120872)))), % 155.00/154.62 inference(rename_variables,[],[3987])). % 155.00/154.62 cnf(12090,plain, % 155.00/154.62 (P27(x120901,x120901,f5(x120901),x120902)), % 155.00/154.62 inference(rename_variables,[],[3526])). % 155.00/154.62 cnf(12095,plain, % 155.00/154.62 (P1(f328(f328(f330(f882(x120951,a870)),x120952),f328(f305(x120951),x120952)))), % 155.00/154.62 inference(rename_variables,[],[3650])). % 155.00/154.62 cnf(12102,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x121021),x121021))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(12105,plain, % 155.00/154.62 (~P1(f328(f328(f330(x121051),x121052),f192(f882(x121051,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(12108,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x121081,a870)),x121082),f328(f328(f306(x121081),x121083),x121082)))), % 155.00/154.62 inference(rename_variables,[],[3732])). % 155.00/154.62 cnf(12109,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x121091,a870)),x121092),f251(f882(x121091,a870))))), % 155.00/154.62 inference(rename_variables,[],[3668])). % 155.00/154.62 cnf(12116,plain, % 155.00/154.62 (P1(f328(f328(f243(a875),x121161),f328(a116,x121161)))), % 155.00/154.62 inference(rename_variables,[],[3350])). % 155.00/154.62 cnf(12119,plain, % 155.00/154.62 (P1(f328(f328(f243(a875),x121191),f328(a116,x121191)))), % 155.00/154.62 inference(rename_variables,[],[3350])). % 155.00/154.62 cnf(12122,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x121221),x121221))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(12125,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x121251),x121251))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(12128,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x121281),x121281))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(12131,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x121311),x121311))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(12134,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x121341,a870)),x121342),x121342))), % 155.00/154.62 inference(rename_variables,[],[3584])). % 155.00/154.62 cnf(12141,plain, % 155.00/154.62 (P1(f328(f328(f330(f882(x121411,a870)),x121412),f328(f305(x121411),x121412)))), % 155.00/154.62 inference(rename_variables,[],[3650])). % 155.00/154.62 cnf(12150,plain, % 155.00/154.62 (~E(f328(a116,x121501),x121501)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(12151,plain, % 155.00/154.62 (E(f328(f307(x121511,x121511,f5(x121511)),x121512),x121512)), % 155.00/154.62 inference(rename_variables,[],[3340])). % 155.00/154.62 cnf(12154,plain, % 155.00/154.62 (P34(x121541,x121542,f117(x121541),f117(x121541))), % 155.00/154.62 inference(rename_variables,[],[3535])). % 155.00/154.62 cnf(12157,plain, % 155.00/154.62 (~E(f328(a116,x121571),x121571)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(12160,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x121601,a870)),f328(f170(x121601),f174(x121601,x121602,x121603))),f328(f170(x121601),x121602)))), % 155.00/154.62 inference(rename_variables,[],[3987])). % 155.00/154.62 cnf(12161,plain, % 155.00/154.62 (P1(f328(f61(x121611),f328(f170(x121611),x121612)))), % 155.00/154.62 inference(rename_variables,[],[3323])). % 155.00/154.62 cnf(12172,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x121721),x121721))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(12175,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x121751),x121751))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(12184,plain, % 155.00/154.62 (P16(a875,f328(f166(a875),f328(f328(f151(f876(x121841),a875),f193(f876(x121841))),f178(x121841,x121842))))), % 155.00/154.62 inference(rename_variables,[],[3847])). % 155.00/154.62 cnf(12187,plain, % 155.00/154.62 (P27(x121871,x121871,f5(x121871),x121872)), % 155.00/154.62 inference(rename_variables,[],[3526])). % 155.00/154.62 cnf(12190,plain, % 155.00/154.62 (P1(f328(f328(f330(f876(x121901)),f117(x121901)),f158(x121901,x121902)))), % 155.00/154.62 inference(rename_variables,[],[3487])). % 155.00/154.62 cnf(12193,plain, % 155.00/154.62 (~P1(f328(f328(f192(f882(x121931,f882(x121932,a870))),x121933),x121934))), % 155.00/154.62 inference(rename_variables,[],[4555])). % 155.00/154.62 cnf(12198,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x121981),x121981))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(12199,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),f2(a875)),x121991))), % 155.00/154.62 inference(rename_variables,[],[3304])). % 155.00/154.62 cnf(12201,plain, % 155.00/154.62 (P1(f328(f328(f242(a1),f2(a1)),f504(x122011,f192(f882(x122012,f882(x122013,a870))),f78(a1))))), % 155.00/154.62 inference(scs_inference,[],[4566,3526,11053,12090,3535,4498,4499,4483,4465,10214,10224,10235,10246,10347,10350,10353,10455,10568,10872,11038,11041,11241,11328,11335,11349,11401,11404,11448,11514,11561,11577,11876,11901,11913,11942,11948,12043,12150,4480,10439,10532,3495,3199,2880,2885,2886,2895,2897,2898,2899,2905,2906,2910,2923,2934,2935,2936,2948,2951,2952,2953,2954,2957,2958,2960,2961,2962,2964,2965,2991,3021,3022,3024,3035,3044,3054,3061,3072,4461,3852,11608,3125,11325,3240,10217,10281,10284,10374,10377,10669,11340,11343,11459,11501,11506,11603,3218,3225,3745,3984,3115,3489,3837,11375,3178,3143,3138,3122,3129,3158,3340,10821,3211,3235,10480,3388,4547,3924,4490,10272,10436,3273,11697,4536,10988,11058,11284,11287,3389,3173,10339,10645,3174,3447,3094,3195,11365,4071,3926,10994,11120,11173,4559,10924,11125,11232,11254,11292,11298,4560,11027,11128,11235,4561,11131,4562,11187,4563,3194,3487,3649,4354,4355,4488,3588,3801,3847,3473,3727,3350,10358,10475,10546,10607,10610,10648,10742,10978,11872,11935,12014,12055,12116,3738,11594,3266,3362,3551,4530,10249,10252,10278,10750,10763,10882,11276,11368,11761,11769,11990,11993,12081,4542,11478,11509,11544,11574,3725,3496,3874,3310,3312,3285,4527,4485,3479,4543,4065,11249,3609,3323,11721,11724,4035,3992,3936,10818,3987,11000,12087,3650,11875,12021,12095,12141,4024,3668,10997,11063,11146,11206,12042,4548,10766,11136,3282,10367,10462,10593,10655,10724,10769,10772,10805,10829,10866,10904,10940,11668,11715,11845,11900,11916,11919,11922,11925,12102,12122,12125,12128,12131,3283,10450,10660,10745,10869,11451,11557,11749,11752,11764,11851,11862,11883,11888,11928,11953,3284,3358,12075,4526,10315,10404,10517,10541,10787,10832,10842,11523,11622,11643,11646,11649,11665,11807,11810,11813,11816,11912,11931,11934,11947,12002,12005,12008,12011,12082,12172,3442,10613,10877,10921,11195,11273,11436,11677,4538,10796,10808,10913,10931,10934,10991,11077,11085,11101,11139,11158,11167,11203,11244,11264,11267,11270,11301,11308,11311,11694,11730,11996,11999,12033,12076,3344,10642,10672,10681,11224,3384,3378,3805,3743,10318,11597,11625,4535,10269,10636,10639,11080,11098,11560,11613,11657,11678,11782,11819,11822,11825,11828,3304,10675,10826,10897,11626,11781,11973,3766,4115,4533,3777,3813,4516,4518,3257,3258,4517,4520,4521,3784,3599,4214,4550,10240,10243,10498,10549,10552,10557,10965,11430,11681,11785,4557,11161,11281,4001,3891,11314,11652,11656,3732,10937,10943,10958,11897,12026,3584,11164,3734,10678,11016,11170,11200,11211,3554,10599,10602,10684,10856,4554,11591,4544,4555,10735,10835,11149,11433,11464,12193,4175,4076,3765,3712,4552,10291,10294,10630,10633,11475,4553,11571,3736,10596,4008,4574,4600,4649,4651,4681,4698,4705,4706,4745,4775,4781,4866,4891,4892,4927,4952,4953,4975,4976,4989,4993,5016,5023,5041,5044,5045,5046,5051,5052,5074,5099,5100,5110,5115,5121,5165,5166,5174,5183,5188,5190,5200,5202,5208,5212,5227,5234,5237,5238,5239,5243,5279,5292,5299,5301,5302,5306,5307,5308,5316,5319,5323,5324,5325,5332,5336,5337,5338,5346,5350,5351,5352,5357,5370,5379,5391,5393,5401,5402,5406,5410,5435,5441,5451,5452,5467,5479,5501,5507,5523,5524,5527,5546,5554,5555,5560,5561,5571,5572,5585,5589,5598,5599,5601,5616,5621,5631,5632,5644,5651,5665,5669,5672,5678,5679,5680,5683,5688,5726,5727,5730,5732,5735,5736,5737,5739,5741,5743,5748,5755,5770,5784,5789,5790,5803,5804,5809,5813,5815,5820,5861,5873,5882,5886,5897,5901,5902,5910,5923,5929,5947,5950,5960,5985,5999,6024,6044,6045,6048,6063,6065,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6168,6175,6179,6215,6217,6219,6221,6230,6232,6234,6240,6242,6248,6251,6259,6266,6267,6268,6273,6295,6296,6297,6299,6305,6310,6344,6345,6348,6349,6350,6351,6352,6353,6354,6361,6394,6395,6404,6425,6426,6446,6449,6460,6461,6467,6497,6499,6513,6550,6552,6553,6606,6631,6674,6694,6703,6704,6705,6706,6725,6726,6732,6745,6748,6750,6752,6753,6754,6756,6770,6781,6783,6784,6797,6801,6852,6864,6866,6870,6887,6888,6922,6934,6965,6997,7051,7079,7134,7155,7164,7167,7224,7232,7290,7292,7307,7315,7318,7319,7338,7344,7346,7395,7405,7408,7424,7475,7476,7480,7523,7524,7542,7611,7630,7653,7676,7691,7706,7716,7725,7726,7753,7756,7758,7769,7807,7819,7844,7902,7936,7968,8007,8023,8039,8040,8116,8173,8192,8221,8242,8266,8267,8364,8366,8372,8386,8390,8408,8430,8438,8440,8452,8458,8462,8483,8497,8498,8517,8518,8523,8524,8525,8526,8527,8549,8550,8551,8562,8576,8578,8590,8594,8596,8597,8598,8606,8611,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8814,8815,8826,8870,8876,8882,8893,8898,8900,8903,8904,8908,8918,9000,9031,9032,9033,9048,9065,9072,9073,9102,9103,9144,9147,9173,9218,9219,9220,9235,9260,9274,9280,9283,9305,9306,9334,9395,9431,9432,9433,9458,9459,9477,9495,9501,9515,9539,9561,9569,9570,9571,9572,9587,9589,9594,9625,9626,9632,9633,9677,9678,9710,9719,9729,9731,9732,9741,9755,9758,9786,9819,9821,9825,9882,9923,9924,9926,9936,9937,9957,9962,10003,10054,10127,10128,10182,10198,2,8,9,4587,4588,4606,4637,4639,4640,4667,4673,4674,4685,4734,4736,4766,4780,4810,4906,4907,4920,4940,4996,4997,5000,5001,5003,5005,5006,5015,5019,5020,5030,5042,5043,5049,5069,5070,5087,5092,5093,5094,5095,5098,5106,5109,5116,5180,5186,5187,5194,5224,5235,5241,5257,5277,5278,5285,5286,5287,5296,5305,5312,5314,5315,5321,5328,5329,5342,5343,5344,5345,5347,5348,5353,5354,5355,5356,5387,5388,5389,5397,5398,5399,5400,5446,5448,5450,5486,5488,5489,5491,5492,5494,5495,5497,5506,5511,5513,5514,5515,5516,5517,5518,5525,5535,5538,5549,5565,5566,5569,5578,5581,5582,5583,5608,5618,5634,5635,5645,5646,5648,5650,5655,5690,5695,5697,5757,5791,5792,5796,5802,5805,5806,5807,5808,5814,5825,5826,5828,5829,5837,5858,5889,5905,5908,5909,5911,5920,5937,5940,5944,5945,5946,5962,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6180,6233,6269,6271,6292,6293,6298,6301,6302,6306,6312,6321,6337,6356,6357,6362,6372,6387,6407,6413,6415,6430,6431,6434,6435,6437,6439,6440,6441,6443,6445,6448,6454,6455,6456,6457,6463,6465,6507,6512,6527,6528,6529,6530,6564,6569,6571,6576,6577,6585,6589,6602,6627,6628,6629,6630,6642,6647,6664,6668,6687,6720,6721,6722,6727,6741,6762,6764,6766,6768,6771,6777,6779,6794,6799,6802,6838,6841,6842,6855,6856,6857,6858,6878,6879,6894,6920,6942,6953,6955,6956,6958,6960,6961,6994,6995,7000,7001,7002,7003,7005,7007,7032,7041,7042,7054,7064,7103,7113,7117,7124,7135,7141,7143,7149,7157,7158,7173,7190,7208,7210,7227,7276,7278,7279,7280,7286,7291,7314,7359,7392,7406,7423,7455,7458,7484,7508,7525,7528,7529,7539,7557,7558,7560,7562,7564,7566,7594,7619,7620,7652,7654,7655,7656,7661,7683,7692,7702,7707,7713,7715,7721,7733,7734,7736,7767,7790,7857,7858,7905,7913,7914,7938,7939])). % 155.00/154.62 cnf(12202,plain, % 155.00/154.62 (~P1(f328(f328(f192(f882(x122021,f882(x122022,a870))),x122023),x122024))), % 155.00/154.62 inference(rename_variables,[],[4555])). % 155.00/154.62 cnf(12205,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(f881(f876(x122051),f876(x122051)),a870)),f155(x122051,x122052)),f304(f876(x122051),f154(x122051,x122052))))), % 155.00/154.62 inference(rename_variables,[],[3992])). % 155.00/154.62 cnf(12211,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x122111,a870)),f192(f882(x122111,a870))),x122112))), % 155.00/154.62 inference(rename_variables,[],[3734])). % 155.00/154.62 cnf(12214,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x122141,a870)),f328(f307(x122142,x122141,x122143),f328(f308(x122142,x122141,x122143),x122144))),x122144))), % 155.00/154.62 inference(rename_variables,[],[4175])). % 155.00/154.62 cnf(12217,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x122171,a870)),f328(f170(x122171),f174(x122171,x122172,x122173))),f328(f170(x122171),x122172)))), % 155.00/154.62 inference(rename_variables,[],[3987])). % 155.00/154.62 cnf(12218,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x122181,a870)),f328(f170(x122181),f328(f133(x122181,x122182),x122183))),f328(f170(x122181),x122183)))), % 155.00/154.62 inference(rename_variables,[],[3936])). % 155.00/154.62 cnf(12221,plain, % 155.00/154.62 (P27(x122211,f879(x122211),f235(x122211),x122212)), % 155.00/154.62 inference(rename_variables,[],[3536])). % 155.00/154.62 cnf(12226,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x122261,a870)),f328(f307(x122262,x122261,x122263),f328(f308(x122262,x122261,x122263),x122264))),x122264))), % 155.00/154.62 inference(rename_variables,[],[4175])). % 155.00/154.62 cnf(12229,plain, % 155.00/154.62 (P1(f328(f61(f879(x122291)),f328(f307(x122292,f879(x122291),f328(f176(x122292,x122291),x122293)),f251(f882(x122292,a870)))))), % 155.00/154.62 inference(rename_variables,[],[4001])). % 155.00/154.62 cnf(12234,plain, % 155.00/154.62 (P1(f328(f328(f330(f876(x122341)),f117(x122341)),f158(x122341,x122342)))), % 155.00/154.62 inference(rename_variables,[],[3487])). % 155.00/154.62 cnf(12237,plain, % 155.00/154.62 (~P1(f328(f328(f330(f881(f876(x122371),f876(x122371))),f328(f328(f263(f876(x122371),f876(x122371)),x122372),f117(x122371))),f142(x122371,x122373)))), % 155.00/154.62 inference(rename_variables,[],[4559])). % 155.00/154.62 cnf(12240,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x122401),f2(a875)))), % 155.00/154.62 inference(rename_variables,[],[4530])). % 155.00/154.62 cnf(12242,plain, % 155.00/154.62 (~P1(f328(f61(x122421),f251(f882(x122421,a870))))), % 155.00/154.62 inference(scs_inference,[],[4566,3526,11053,12090,3535,3536,3251,4498,4499,3152,4483,4465,10214,10224,10235,10246,10347,10350,10353,10455,10568,10872,11038,11041,11241,11328,11335,11349,11401,11404,11448,11514,11561,11577,11876,11901,11913,11942,11948,12043,12150,4480,10439,10532,3495,3199,2880,2885,2886,2895,2897,2898,2899,2905,2906,2910,2923,2934,2935,2936,2948,2951,2952,2953,2954,2957,2958,2960,2961,2962,2964,2965,2985,2991,3021,3022,3024,3035,3044,3054,3061,3072,4461,3852,11608,3125,11325,3240,10217,10281,10284,10374,10377,10669,11340,11343,11459,11501,11506,11603,3218,3225,3745,3984,3115,3489,3837,11375,3178,3143,3138,3122,3129,3158,3340,10821,3211,3235,10480,3388,4547,3924,4490,10272,10436,3273,11697,4536,10988,11058,11284,11287,3389,3173,10339,10645,3174,3447,3094,3195,11365,4071,3926,10994,11120,11173,4559,10924,11125,11232,11254,11292,11298,4560,11027,11128,11235,4561,11131,4562,11187,4563,3194,3487,12190,12234,3649,4354,4355,4488,3588,3801,3847,3473,3727,3350,10358,10475,10546,10607,10610,10648,10742,10978,11872,11935,12014,12055,12116,3738,11594,3266,3362,3551,4530,10249,10252,10278,10750,10763,10882,11276,11368,11761,11769,11990,11993,12081,4542,11478,11509,11544,11574,3725,3496,3874,3310,3312,3285,4527,4485,3479,4543,4065,11249,3609,3323,11721,11724,4035,3992,11865,12205,3936,10818,12049,3987,11000,12087,12160,3650,11875,12021,12095,12141,4024,3668,10997,11063,11146,11206,12042,4548,10766,11136,3282,10367,10462,10593,10655,10724,10769,10772,10805,10829,10866,10904,10940,11668,11715,11845,11900,11916,11919,11922,11925,12102,12122,12125,12128,12131,3283,10450,10660,10745,10869,11451,11557,11749,11752,11764,11851,11862,11883,11888,11928,11953,3284,3358,12075,4526,10315,10404,10517,10541,10787,10832,10842,11523,11622,11643,11646,11649,11665,11807,11810,11813,11816,11912,11931,11934,11947,12002,12005,12008,12011,12082,12172,3442,10613,10877,10921,11195,11273,11436,11677,4538,10796,10808,10913,10931,10934,10991,11077,11085,11101,11139,11158,11167,11203,11244,11264,11267,11270,11301,11308,11311,11694,11730,11996,11999,12033,12076,3344,10642,10672,10681,11224,3384,3378,3805,3743,10318,11597,11625,4535,10269,10636,10639,11080,11098,11560,11613,11657,11678,11782,11819,11822,11825,11828,3304,10675,10826,10897,11626,11781,11973,3766,4115,4533,3777,3813,4516,4518,3257,3258,4517,4520,4521,3784,3599,4214,4550,10240,10243,10498,10549,10552,10557,10965,11430,11681,11785,4557,11161,11281,4001,3891,11314,11652,11656,3732,10937,10943,10958,11897,12026,3584,11164,12134,3734,10678,11016,11170,11200,11211,12046,3554,10599,10602,10684,10856,4554,11591,4544,4555,10735,10835,11149,11433,11464,12193,4175,10811,12214,4076,3765,3712,4552,10291,10294,10630,10633,11475,4553,11571,3736,10596,4008,4574,4600,4649,4651,4681,4698,4705,4706,4745,4775,4781,4866,4891,4892,4927,4952,4953,4975,4976,4989,4993,5016,5023,5041,5044,5045,5046,5051,5052,5074,5099,5100,5110,5115,5121,5165,5166,5174,5183,5188,5190,5200,5202,5208,5212,5227,5234,5237,5238,5239,5243,5279,5292,5299,5301,5302,5306,5307,5308,5316,5319,5323,5324,5325,5332,5336,5337,5338,5346,5350,5351,5352,5357,5370,5379,5391,5393,5401,5402,5406,5410,5435,5441,5451,5452,5467,5479,5501,5507,5523,5524,5527,5546,5554,5555,5560,5561,5571,5572,5585,5589,5598,5599,5601,5616,5621,5631,5632,5644,5651,5665,5669,5672,5678,5679,5680,5683,5688,5726,5727,5730,5732,5735,5736,5737,5739,5741,5743,5748,5755,5770,5784,5789,5790,5803,5804,5809,5813,5815,5820,5861,5873,5882,5886,5897,5901,5902,5910,5923,5929,5947,5950,5960,5985,5999,6024,6044,6045,6048,6063,6065,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6168,6175,6179,6215,6217,6219,6221,6230,6232,6234,6240,6242,6248,6251,6259,6266,6267,6268,6273,6295,6296,6297,6299,6305,6310,6344,6345,6348,6349,6350,6351,6352,6353,6354,6361,6394,6395,6404,6425,6426,6446,6449,6460,6461,6467,6497,6499,6513,6550,6552,6553,6606,6631,6674,6694,6703,6704,6705,6706,6725,6726,6732,6745,6748,6750,6752,6753,6754,6756,6770,6781,6783,6784,6797,6801,6852,6864,6866,6870,6887,6888,6922,6934,6965,6997,7051,7079,7134,7155,7164,7167,7224,7232,7290,7292,7307,7315,7318,7319,7338,7344,7346,7395,7405,7408,7424,7475,7476,7480,7523,7524,7542,7611,7630,7653,7676,7691,7706,7716,7725,7726,7753,7756,7758,7769,7807,7819,7844,7902,7936,7968,8007,8023,8039,8040,8116,8173,8192,8221,8242,8266,8267,8364,8366,8372,8386,8390,8408,8430,8438,8440,8452,8458,8462,8483,8497,8498,8517,8518,8523,8524,8525,8526,8527,8549,8550,8551,8562,8576,8578,8590,8594,8596,8597,8598,8606,8611,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8814,8815,8826,8870,8876,8882,8893,8898,8900,8903,8904,8908,8918,9000,9031,9032,9033,9048,9065,9072,9073,9102,9103,9144,9147,9173,9218,9219,9220,9235,9260,9274,9280,9283,9305,9306,9334,9395,9431,9432,9433,9458,9459,9477,9495,9501,9515,9539,9561,9569,9570,9571,9572,9587,9589,9594,9625,9626,9632,9633,9677,9678,9710,9719,9729,9731,9732,9741,9755,9758,9786,9819,9821,9825,9882,9923,9924,9926,9936,9937,9957,996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% 155.00/154.62 cnf(12243,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x122431,a870)),x122432),x122432))), % 155.00/154.62 inference(rename_variables,[],[3584])). % 155.00/154.62 cnf(12246,plain, % 155.00/154.62 (~P1(f328(f328(f330(x122461),x122462),f192(f882(x122461,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(12249,plain, % 155.00/154.62 (~P1(f328(f328(f192(f882(x122491,f882(x122492,a870))),x122493),x122494))), % 155.00/154.62 inference(rename_variables,[],[4555])). % 155.00/154.62 cnf(12253,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x122531,a870)),x122532),x122532))), % 155.00/154.62 inference(rename_variables,[],[3584])). % 155.00/154.62 cnf(12258,plain, % 155.00/154.62 (E(f328(f259(x122581,x122581),f260(x122581,x122582)),x122582)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(12261,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x122611,a870)),f328(f170(x122611),f174(x122611,x122612,x122613))),f328(f170(x122611),x122612)))), % 155.00/154.62 inference(rename_variables,[],[3987])). % 155.00/154.62 cnf(12262,plain, % 155.00/154.62 (P1(f328(f61(x122621),f328(f170(x122621),x122622)))), % 155.00/154.62 inference(rename_variables,[],[3323])). % 155.00/154.62 cnf(12265,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x122651),x122651))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(12268,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x122681),x122681))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(12271,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x122711),x122711))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(12282,plain, % 155.00/154.62 (P27(x122821,x122821,f5(x122821),x122822)), % 155.00/154.62 inference(rename_variables,[],[3526])). % 155.00/154.62 cnf(12287,plain, % 155.00/154.62 (~P1(f328(f328(f330(x122871),x122872),f192(f882(x122871,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(12290,plain, % 155.00/154.62 (P1(f328(f328(f330(f881(x122901,x122901)),f328(f328(f263(x122901,x122901),x122902),x122902)),f304(x122901,x122903)))), % 155.00/154.62 inference(rename_variables,[],[3926])). % 155.00/154.62 cnf(12293,plain, % 155.00/154.62 (~P1(f328(f328(f330(x122931),x122932),f192(f882(x122931,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(12296,plain, % 155.00/154.62 (P1(f328(f328(f330(f881(x122961,x122961)),f328(f328(f263(x122961,x122961),x122962),x122962)),f304(x122961,x122963)))), % 155.00/154.62 inference(rename_variables,[],[3926])). % 155.00/154.62 cnf(12306,plain, % 155.00/154.62 (~E(f328(f328(f148(x123061),x123062),x123063),x123063)), % 155.00/154.62 inference(rename_variables,[],[4490])). % 155.00/154.62 cnf(12309,plain, % 155.00/154.62 (P1(f328(f328(f330(x123091),x123092),f251(f882(x123091,a870))))), % 155.00/154.62 inference(rename_variables,[],[3442])). % 155.00/154.62 cnf(12310,plain, % 155.00/154.62 (~E(f328(a116,x123101),x123101)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(12313,plain, % 155.00/154.62 (P1(f328(f328(f330(f876(x123131)),f117(x123131)),f158(x123131,x123132)))), % 155.00/154.62 inference(rename_variables,[],[3487])). % 155.00/154.62 cnf(12314,plain, % 155.00/154.62 (~E(f328(f328(f148(x123141),x123142),x123143),f117(x123141))), % 155.00/154.62 inference(rename_variables,[],[4497])). % 155.00/154.62 cnf(12317,plain, % 155.00/154.62 (P1(f328(f328(f330(x123171),f328(x123172,x123173)),f328(f307(x123174,x123171,x123172),f251(f882(x123174,a870)))))), % 155.00/154.62 inference(rename_variables,[],[3891])). % 155.00/154.62 cnf(12318,plain, % 155.00/154.62 (P27(x123181,x123181,f5(x123181),x123182)), % 155.00/154.62 inference(rename_variables,[],[3526])). % 155.00/154.62 cnf(12321,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x123211,a870)),f192(f882(x123211,a870))),x123212))), % 155.00/154.62 inference(rename_variables,[],[3734])). % 155.00/154.62 cnf(12322,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x123221,a870)),x123222),x123222))), % 155.00/154.62 inference(rename_variables,[],[3584])). % 155.00/154.62 cnf(12325,plain, % 155.00/154.62 (P1(f328(f328(f330(x123251),f328(x123252,x123253)),f328(f307(x123254,x123251,x123252),f251(f882(x123254,a870)))))), % 155.00/154.62 inference(rename_variables,[],[3891])). % 155.00/154.62 cnf(12326,plain, % 155.00/154.62 (P27(x123261,x123261,f5(x123261),x123262)), % 155.00/154.62 inference(rename_variables,[],[3526])). % 155.00/154.62 cnf(12329,plain, % 155.00/154.62 (P1(f328(f328(f330(f881(f876(x123291),f876(x123291))),f328(f328(f263(f876(x123291),f876(x123291)),f117(x123291)),f117(x123291))),f155(x123291,x123292)))), % 155.00/154.62 inference(rename_variables,[],[4071])). % 155.00/154.62 cnf(12332,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x123321),x123321))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(12333,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x123331),f2(a875)))), % 155.00/154.62 inference(rename_variables,[],[4530])). % 155.00/154.62 cnf(12339,plain, % 155.00/154.62 (P27(x123391,x123391,f5(x123391),x123392)), % 155.00/154.62 inference(rename_variables,[],[3526])). % 155.00/154.62 cnf(12342,plain, % 155.00/154.62 (E(f328(f328(f125(x123421),x123422),f117(x123421)),x123422)), % 155.00/154.62 inference(rename_variables,[],[3212])). % 155.00/154.62 cnf(12343,plain, % 155.00/154.62 (~E(f328(f328(f148(x123431),x123432),x123433),x123433)), % 155.00/154.62 inference(rename_variables,[],[4490])). % 155.00/154.62 cnf(12346,plain, % 155.00/154.62 (E(f328(f328(f125(x123461),x123462),f117(x123461)),x123462)), % 155.00/154.62 inference(rename_variables,[],[3212])). % 155.00/154.62 cnf(12350,plain, % 155.00/154.62 (E(f328(f328(f125(x123501),x123502),f117(x123501)),x123502)), % 155.00/154.62 inference(rename_variables,[],[3212])). % 155.00/154.62 cnf(12359,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x123591,a870)),x123592),f251(f882(x123591,a870))))), % 155.00/154.62 inference(rename_variables,[],[3668])). % 155.00/154.62 cnf(12363,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x123631),x123631))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(12364,plain, % 155.00/154.62 (~E(f328(a116,x123641),x123641)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(12370,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x123701),x123701))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(12373,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x123731,a870)),x123732),x123732))), % 155.00/154.62 inference(rename_variables,[],[3584])). % 155.00/154.62 cnf(12381,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x123811,a870)),x123812),x123812))), % 155.00/154.62 inference(rename_variables,[],[3584])). % 155.00/154.62 cnf(12382,plain, % 155.00/154.62 (~P1(f328(f328(f330(x123821),x123822),f192(f882(x123821,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(12385,plain, % 155.00/154.62 (~P1(f328(f328(f330(x123851),x123852),f192(f882(x123851,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(12394,plain, % 155.00/154.62 (P27(x123941,x123941,f5(x123941),x123942)), % 155.00/154.62 inference(rename_variables,[],[3526])). % 155.00/154.62 cnf(12397,plain, % 155.00/154.62 (E(f328(f193(f876(x123971)),f328(f165(x123971),x123972)),f328(f193(f876(x123971)),x123972))), % 155.00/154.62 inference(rename_variables,[],[3295])). % 155.00/154.62 cnf(12400,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x124001),x124001))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(12401,plain, % 155.00/154.62 (P1(f328(f251(f882(x124011,a870)),x124012))), % 155.00/154.62 inference(rename_variables,[],[3344])). % 155.00/154.62 cnf(12404,plain, % 155.00/154.62 (~P1(f328(f328(f330(x124041),x124042),f192(f882(x124041,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(12407,plain, % 155.00/154.62 (P1(f328(f328(f330(x124071),f328(x124072,x124073)),f328(f307(x124074,x124071,x124072),f251(f882(x124074,a870)))))), % 155.00/154.62 inference(rename_variables,[],[3891])). % 155.00/154.62 cnf(12408,plain, % 155.00/154.62 (P1(f328(f328(f330(f881(x124081,x124081)),f328(f328(f263(x124081,x124081),x124082),x124082)),f304(x124081,x124083)))), % 155.00/154.62 inference(rename_variables,[],[3926])). % 155.00/154.62 cnf(12411,plain, % 155.00/154.62 (P1(f328(f328(f330(f881(x124111,x124111)),f328(f328(f263(x124111,x124111),x124112),x124112)),f304(x124111,x124113)))), % 155.00/154.62 inference(rename_variables,[],[3926])). % 155.00/154.62 cnf(12414,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x124141),x124141))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(12415,plain, % 155.00/154.62 (P1(f328(f251(f882(x124151,a870)),x124152))), % 155.00/154.62 inference(rename_variables,[],[3344])). % 155.00/154.62 cnf(12418,plain, % 155.00/154.62 (P1(f328(f61(x124181),f328(f170(x124181),x124182)))), % 155.00/154.62 inference(rename_variables,[],[3323])). % 155.00/154.62 cnf(12431,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x124311,a870)),x124312),f251(f882(x124311,a870))))), % 155.00/154.62 inference(rename_variables,[],[3668])). % 155.00/154.62 cnf(12434,plain, % 155.00/154.62 (P1(f328(f328(f330(f881(x124341,x124341)),f328(f328(f263(x124341,x124341),x124342),x124342)),f304(x124341,x124343)))), % 155.00/154.62 inference(rename_variables,[],[3926])). % 155.00/154.62 cnf(12437,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),f328(f328(f80(a875),x124371),x124372)),x124372))), % 155.00/154.62 inference(rename_variables,[],[4552])). % 155.00/154.62 cnf(12438,plain, % 155.00/154.62 (P1(f328(f328(f243(a875),x124381),f328(a116,x124381)))), % 155.00/154.62 inference(rename_variables,[],[3350])). % 155.00/154.62 cnf(12444,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x124441,a870)),x124442),f251(f882(x124441,a870))))), % 155.00/154.62 inference(rename_variables,[],[3668])). % 155.00/154.62 cnf(12447,plain, % 155.00/154.62 (E(f328(f259(x124471,x124471),f260(x124471,x124472)),x124472)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(12458,plain, % 155.00/154.62 (~P1(f328(f328(f330(x124581),x124582),f192(f882(x124581,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(12459,plain, % 155.00/154.62 (P1(f328(f328(f330(f881(f876(x124591),f876(x124591))),f328(f328(f263(f876(x124591),f876(x124591)),f117(x124591)),f117(x124591))),f155(x124591,x124592)))), % 155.00/154.62 inference(rename_variables,[],[4071])). % 155.00/154.62 cnf(12464,plain, % 155.00/154.62 (~P1(f328(f328(f330(x124641),x124642),f192(f882(x124641,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(12467,plain, % 155.00/154.62 (P33(x124671,x124672,f117(x124671))), % 155.00/154.62 inference(rename_variables,[],[3217])). % 155.00/154.62 cnf(12470,plain, % 155.00/154.62 (E(f328(f193(f876(x124701)),f328(f165(x124701),x124702)),f328(f193(f876(x124701)),x124702))), % 155.00/154.62 inference(rename_variables,[],[3295])). % 155.00/154.62 cnf(12473,plain, % 155.00/154.62 (~P1(f328(f328(f330(x124731),x124732),f192(f882(x124731,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(12479,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x124791),x124791))), % 155.00/154.62 inference(rename_variables,[],[4526])). % 155.00/154.62 cnf(12482,plain, % 155.00/154.62 (P1(f328(f328(f330(x124821),x124822),f251(f882(x124821,a870))))), % 155.00/154.62 inference(rename_variables,[],[3442])). % 155.00/154.62 cnf(12485,plain, % 155.00/154.62 (P1(f328(f328(f242(f882(x124851,a870)),x124852),x124852))), % 155.00/154.62 inference(rename_variables,[],[3584])). % 155.00/154.62 cnf(12488,plain, % 155.00/154.62 (~P1(f328(f328(f330(x124881),x124882),f192(f882(x124881,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(12491,plain, % 155.00/154.62 (P1(f328(f328(f242(a1),f2(a1)),f328(f328(f253(a1),f328(f75(a1),x124911)),x124912)))), % 155.00/154.62 inference(rename_variables,[],[3765])). % 155.00/154.62 cnf(12494,plain, % 155.00/154.62 (~E(f328(a116,x124941),x124941)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(12496,plain, % 155.00/154.62 (E(f328(f259(x124961,x124961),f260(x124961,x124962)),x124962)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(12503,plain, % 155.00/154.62 (E(f328(f259(x125031,x125031),f260(x125031,x125032)),x125032)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(12505,plain, % 155.00/154.62 (E(f328(f259(x125051,x125051),f260(x125051,x125052)),x125052)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(12507,plain, % 155.00/154.62 (E(f328(f259(x125071,x125071),f260(x125071,x125072)),x125072)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(12509,plain, % 155.00/154.62 (E(f328(f259(x125091,x125091),f260(x125091,x125092)),x125092)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(12511,plain, % 155.00/154.62 (P41(x125111,x125112,f260(x125111,x125112))), % 155.00/154.62 inference(rename_variables,[],[3250])). % 155.00/154.62 cnf(12513,plain, % 155.00/154.62 (P41(x125131,x125132,f260(x125131,x125132))), % 155.00/154.62 inference(rename_variables,[],[3250])). % 155.00/154.62 cnf(12517,plain, % 155.00/154.62 (E(f328(f259(x125171,x125171),f260(x125171,x125172)),x125172)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(12519,plain, % 155.00/154.62 (P27(x125191,x125191,f5(x125191),x125192)), % 155.00/154.62 inference(rename_variables,[],[3526])). % 155.00/154.62 cnf(12534,plain, % 155.00/154.62 (E(f328(f259(x125341,x125341),f260(x125341,x125342)),x125342)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(12540,plain, % 155.00/154.62 (P52(x125401,f192(f882(x125401,a870)),x125402)), % 155.00/154.62 inference(rename_variables,[],[3302])). % 155.00/154.62 cnf(12545,plain, % 155.00/154.62 (P39(x125451,f150(x125451,x125452))), % 155.00/154.62 inference(rename_variables,[],[3152])). % 155.00/154.62 cnf(12549,plain, % 155.00/154.62 (E(f328(f259(x125491,x125491),f260(x125491,x125492)),x125492)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(12553,plain, % 155.00/154.62 (E(f328(f259(x125531,x125531),f260(x125531,x125532)),x125532)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(12555,plain, % 155.00/154.62 (P44(x125551,x125552,x125553,x125554,f192(f882(x125551,a870)),x125554)), % 155.00/154.62 inference(rename_variables,[],[4238])). % 155.00/154.62 cnf(12558,plain, % 155.00/154.62 (P44(x125581,x125582,x125583,x125584,f192(f882(x125581,a870)),x125584)), % 155.00/154.62 inference(rename_variables,[],[4238])). % 155.00/154.62 cnf(12566,plain, % 155.00/154.62 (P26(x125661,x125662,f192(f882(f874(x125661),a870)))), % 155.00/154.62 inference(rename_variables,[],[3338])). % 155.00/154.62 cnf(12572,plain, % 155.00/154.62 (P34(x125721,x125722,f117(x125721),f117(x125721))), % 155.00/154.62 inference(rename_variables,[],[3535])). % 155.00/154.62 cnf(12574,plain, % 155.00/154.62 (P34(x125741,x125742,f117(x125741),f117(x125741))), % 155.00/154.62 inference(rename_variables,[],[3535])). % 155.00/154.62 cnf(12580,plain, % 155.00/154.62 (P29(x125801,f2(a875),f328(f328(f328(f92(x125801),x125802),f328(a26,x125803)),x125804))), % 155.00/154.62 inference(rename_variables,[],[3661])). % 155.00/154.62 cnf(12597,plain, % 155.00/154.62 (E(f328(f259(x125971,x125971),f260(x125971,x125972)),x125972)), % 155.00/154.62 inference(rename_variables,[],[3240])). % 155.00/154.62 cnf(12600,plain, % 155.00/154.62 (P17(x126001,f882(x126001,a870),f306(x126001))), % 155.00/154.62 inference(rename_variables,[],[3254])). % 155.00/154.62 cnf(12604,plain, % 155.00/154.62 (P51(x126041,x126041,f260(x126041,x126042))), % 155.00/154.62 inference(rename_variables,[],[3251])). % 155.00/154.62 cnf(12612,plain, % 155.00/154.62 (~E(f328(a116,x126121),x126121)), % 155.00/154.62 inference(rename_variables,[],[4465])). % 155.00/154.62 cnf(12618,plain, % 155.00/154.62 (P1(f328(f328(f243(a875),x126181),f328(a116,x126181)))), % 155.00/154.62 inference(rename_variables,[],[3350])). % 155.00/154.62 cnf(12623,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x126231),f2(a875)))), % 155.00/154.62 inference(rename_variables,[],[4530])). % 155.00/154.62 cnf(12626,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x126261),f2(a875)))), % 155.00/154.62 inference(rename_variables,[],[4530])). % 155.00/154.62 cnf(12633,plain, % 155.00/154.62 (~P1(f328(f328(f243(a1),f328(f104(a1),x126331)),f328(f79(a1),f328(f104(a1),x126332))))), % 155.00/154.62 inference(rename_variables,[],[4549])). % 155.00/154.62 cnf(12643,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x126431),f2(a875)))), % 155.00/154.62 inference(rename_variables,[],[4530])). % 155.00/154.62 cnf(12646,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x126461),f2(a875)))), % 155.00/154.62 inference(rename_variables,[],[4530])). % 155.00/154.62 cnf(12649,plain, % 155.00/154.62 (P1(f328(f61(a875),f301(a875,x126491,x126492)))), % 155.00/154.62 inference(rename_variables,[],[3497])). % 155.00/154.62 cnf(12652,plain, % 155.00/154.62 (P1(f328(f61(a875),f301(a875,x126521,x126522)))), % 155.00/154.62 inference(rename_variables,[],[3497])). % 155.00/154.62 cnf(12655,plain, % 155.00/154.62 (P1(f328(f61(a875),f301(a875,x126551,x126552)))), % 155.00/154.62 inference(rename_variables,[],[3497])). % 155.00/154.62 cnf(12658,plain, % 155.00/154.62 (P1(f328(f61(a875),f301(a875,x126581,x126582)))), % 155.00/154.62 inference(rename_variables,[],[3497])). % 155.00/154.62 cnf(12665,plain, % 155.00/154.62 (P1(f328(f328(f242(a1),f328(f79(a1),f328(f104(a1),x126651))),f328(f104(a1),x126652)))), % 155.00/154.62 inference(rename_variables,[],[3766])). % 155.00/154.62 cnf(12668,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x126681),f2(a875)))), % 155.00/154.62 inference(rename_variables,[],[4530])). % 155.00/154.62 cnf(12669,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x126691),x126691))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(12676,plain, % 155.00/154.62 (P1(f328(f328(f243(a875),x126761),f328(a116,x126761)))), % 155.00/154.62 inference(rename_variables,[],[3350])). % 155.00/154.62 cnf(12685,plain, % 155.00/154.62 (P1(f328(f328(f242(a1),x126851),x126851))), % 155.00/154.62 inference(rename_variables,[],[3283])). % 155.00/154.62 cnf(12688,plain, % 155.00/154.62 (P1(f328(f61(a875),f301(a875,x126881,x126882)))), % 155.00/154.62 inference(rename_variables,[],[3497])). % 155.00/154.62 cnf(12694,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x126941),x126941))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(12707,plain, % 155.00/154.62 (P1(f328(f328(f243(a875),x127071),f328(a116,x127071)))), % 155.00/154.62 inference(rename_variables,[],[3350])). % 155.00/154.62 cnf(12712,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),f44(a875,x127121,x127122)),x127121))), % 155.00/154.62 inference(rename_variables,[],[3743])). % 155.00/154.62 cnf(12719,plain, % 155.00/154.62 (P1(f328(f328(f243(a875),x127191),f328(a116,x127191)))), % 155.00/154.62 inference(rename_variables,[],[3350])). % 155.00/154.62 cnf(12720,plain, % 155.00/154.62 (~P1(f328(f328(f243(a875),x127201),f2(a875)))), % 155.00/154.62 inference(rename_variables,[],[4530])). % 155.00/154.62 cnf(12729,plain, % 155.00/154.62 (~P1(f328(f328(f243(a1),f328(f104(a1),x127291)),f2(a1)))), % 155.00/154.62 inference(rename_variables,[],[4542])). % 155.00/154.62 cnf(12730,plain, % 155.00/154.62 (P1(f328(f251(f882(x127301,a870)),x127302))), % 155.00/154.62 inference(rename_variables,[],[3344])). % 155.00/154.62 cnf(12733,plain, % 155.00/154.62 (~P1(f328(f328(f243(a1),f328(f104(a1),x127331)),f2(a1)))), % 155.00/154.62 inference(rename_variables,[],[4542])). % 155.00/154.62 cnf(12734,plain, % 155.00/154.62 (P1(f328(f251(f882(x127341,a870)),x127342))), % 155.00/154.62 inference(rename_variables,[],[3344])). % 155.00/154.62 cnf(12737,plain, % 155.00/154.62 (P1(f328(f251(f882(x127371,a870)),x127372))), % 155.00/154.62 inference(rename_variables,[],[3344])). % 155.00/154.62 cnf(12748,plain, % 155.00/154.62 (~P1(f328(f328(f330(x127481),x127482),f192(f882(x127481,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(12749,plain, % 155.00/154.62 (P1(f328(f61(x127491),f192(f882(x127491,a870))))), % 155.00/154.62 inference(rename_variables,[],[3358])). % 155.00/154.62 cnf(12761,plain, % 155.00/154.62 (P1(f328(f328(f243(a875),x127611),f328(a116,x127611)))), % 155.00/154.62 inference(rename_variables,[],[3350])). % 155.00/154.62 cnf(12765,plain, % 155.00/154.62 (~P1(f328(f328(f330(x127651),x127652),f192(f882(x127651,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(12768,plain, % 155.00/154.62 (~P1(f328(f328(f330(x127681),x127682),f192(f882(x127681,a870))))), % 155.00/154.62 inference(rename_variables,[],[4538])). % 155.00/154.62 cnf(12771,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x127711),x127711))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(12778,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x127781),x127781))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(12782,plain, % 155.00/154.62 (P1(f328(f328(f243(a875),x127821),f328(a116,x127821)))), % 155.00/154.62 inference(rename_variables,[],[3350])). % 155.00/154.62 cnf(12785,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x127851),x127851))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(12790,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x127901),x127901))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(12793,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x127931),x127931))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(12796,plain, % 155.00/154.62 (P1(f328(f328(f242(a875),x127961),x127961))), % 155.00/154.62 inference(rename_variables,[],[3282])). % 155.00/154.62 cnf(12799,plain, % 155.00/154.62 (E(f328(f328(f22(f882(x127991,a870)),f192(f882(x127991,a870))),x127992),f192(f882(x127991,a870)))), % 155.00/154.62 inference(rename_variables,[],[3557])). % 155.00/154.62 cnf(12800,plain, % 155.00/154.62 (P1(f328(f61(x128001),f192(f882(x128001,a870))))), % 155.00/154.62 inference(rename_variables,[],[3358])). % 155.00/154.62 cnf(12803,plain, % 155.00/154.62 (E(f328(f328(f22(f882(x128031,a870)),f192(f882(x128031,a870))),x128032),f192(f882(x128031,a870)))), % 155.00/154.62 inference(rename_variables,[],[3557])). % 155.00/154.62 cnf(12804,plain, % 155.00/154.62 (P1(f328(f61(x128041),f192(f882(x128041,a870))))), % 155.00/154.62 inference(rename_variables,[],[3358])). % 155.00/154.62 cnf(12807,plain, % 155.00/154.62 (E(f328(f328(f22(f882(x128071,a870)),f192(f882(x128071,a870))),x128072),f192(f882(x128071,a870)))), % 155.00/154.62 inference(rename_variables,[],[3557])). % 155.00/154.62 cnf(12808,plain, % 155.00/154.62 (P1(f328(f61(x128081),f192(f882(x128081,a870))))), % 155.00/154.62 inference(rename_variables,[],[3358])). % 155.00/154.62 cnf(12811,plain, % 155.00/154.62 (E(f328(f328(f22(f882(x128111,a870)),f192(f882(x128111,a870))),x128112),f192(f882(x128111,a870)))), % 155.00/154.62 inference(rename_variables,[],[3557])). % 155.00/154.62 cnf(12812,plain, % 155.00/154.62 (P1(f328(f61(x128121),f192(f882(x128121,a870))))), % 155.00/154.63 inference(rename_variables,[],[3358])). % 155.00/154.63 cnf(12821,plain, % 155.00/154.63 (E(f328(f328(f22(f882(x128211,a870)),f192(f882(x128211,a870))),x128212),f192(f882(x128211,a870)))), % 155.00/154.63 inference(rename_variables,[],[3557])). % 155.00/154.63 cnf(12822,plain, % 155.00/154.63 (P1(f328(f61(x128221),f192(f882(x128221,a870))))), % 155.00/154.63 inference(rename_variables,[],[3358])). % 155.00/154.63 cnf(12826,plain, % 155.00/154.63 (P1(f328(f61(x128261),f192(f882(x128261,a870))))), % 155.00/154.63 inference(rename_variables,[],[3358])). % 155.00/154.63 cnf(12829,plain, % 155.00/154.63 (P1(f328(f328(f242(a875),x128291),x128291))), % 155.00/154.63 inference(rename_variables,[],[3282])). % 155.00/154.63 cnf(12835,plain, % 155.00/154.63 (P1(f328(f328(f242(a1),x128351),x128351))), % 155.00/154.63 inference(rename_variables,[],[3283])). % 155.00/154.63 cnf(12838,plain, % 155.00/154.63 (P1(f328(f328(f243(a875),x128381),f328(a116,x128381)))), % 155.00/154.63 inference(rename_variables,[],[3350])). % 155.00/154.63 cnf(12841,plain, % 155.00/154.63 (P1(f328(f328(f242(a875),x128411),x128411))), % 155.00/154.63 inference(rename_variables,[],[3282])). % 155.00/154.63 cnf(12844,plain, % 155.00/154.63 (P1(f328(f328(f243(a875),x128441),f328(a116,x128441)))), % 155.00/154.63 inference(rename_variables,[],[3350])). % 155.00/154.63 cnf(12859,plain, % 155.00/154.63 (P1(f328(f328(f242(a875),x128591),x128591))), % 155.00/154.63 inference(rename_variables,[],[3282])). % 155.00/154.63 cnf(12862,plain, % 155.00/154.63 (P1(f328(f328(f242(a1),x128621),x128621))), % 155.00/154.63 inference(rename_variables,[],[3283])). % 155.00/154.63 cnf(12888,plain, % 155.00/154.63 (~P1(f328(f328(f243(a875),x128881),f2(a875)))), % 155.00/154.63 inference(rename_variables,[],[4530])). % 155.00/154.63 cnf(12889,plain, % 155.00/154.63 (P1(f328(f328(f242(a1),x128891),x128891))), % 155.00/154.63 inference(rename_variables,[],[3283])). % 155.00/154.63 cnf(12893,plain, % 155.00/154.63 (~P1(f328(f328(f243(a875),x128931),f2(a875)))), % 155.00/154.63 inference(rename_variables,[],[4530])). % 155.00/154.63 cnf(12894,plain, % 155.00/154.63 (P1(f328(f328(f242(a1),x128941),x128941))), % 155.00/154.63 inference(rename_variables,[],[3283])). % 155.00/154.63 cnf(12903,plain, % 155.00/154.63 (P1(f328(f328(f242(a875),x129031),x129031))), % 155.00/154.63 inference(rename_variables,[],[3282])). % 155.00/154.63 cnf(12917,plain, % 155.00/154.63 (~P1(f328(f328(f243(a875),x129171),f2(a875)))), % 155.00/154.63 inference(rename_variables,[],[4530])). % 155.00/154.63 cnf(12918,plain, % 155.00/154.63 (P1(f328(f328(f242(a1),x129181),x129181))), % 155.00/154.63 inference(rename_variables,[],[3283])). % 155.00/154.63 cnf(12928,plain, % 155.00/154.63 (P1(f328(f328(f242(a875),x129281),x129281))), % 155.00/154.63 inference(rename_variables,[],[3282])). % 155.00/154.63 cnf(12930,plain, % 155.00/154.63 (~P1(f328(f328(f242(f882(a875,a870)),f299(a875,f328(a116,x129301),f328(a116,x129301))),f299(a875,x129302,x129301)))), % 155.00/154.63 inference(scs_inference,[],[4566,3526,11053,12090,12187,12282,12318,12326,12339,12394,12519,3535,12154,12572,12574,3536,12221,3250,12511,12513,3251,12604,3217,12467,4498,4499,11674,4238,12555,12558,3254,12600,3093,3152,12545,4483,3586,4465,10214,10224,10235,10246,10347,10350,10353,10455,10568,10872,11038,11041,11241,11328,11335,11349,11401,11404,11448,11514,11561,11577,11876,11901,11913,11942,11948,12043,12150,12157,12310,12364,12494,12612,4480,10439,10532,3339,3302,12540,3495,3199,4475,2879,2880,2885,2886,2894,2895,2897,2898,2899,2905,2906,2910,2923,2934,2935,2936,2940,2945,2948,2951,2952,2953,2954,2957,2958,2960,2961,2962,2964,2965,2968,2985,2988,2991,2998,3004,3005,3021,3022,3024,3025,3035,3043,3044,3045,3054,3061,4460,3072,3151,4461,3624,3852,11608,3125,11325,3264,3240,10217,10281,10284,10374,10377,10669,11340,11343,11459,11501,11506,11603,12064,12258,12447,12496,12503,12505,12507,12509,12517,12534,12549,12553,12597,3865,3212,12342,12346,12350,3218,3225,3745,3984,3115,4477,3489,3837,11375,3338,12566,3178,3143,3661,12580,3138,3958,3666,3122,3103,3129,3158,3295,12397,12470,3340,10821,12151,3210,3211,3235,10480,3388,4547,10409,3924,4490,10272,10436,11238,12306,12343,4497,12314,3273,11697,11700,4536,10988,11058,11284,11287,3686,3389,3610,3353,3173,10339,10645,3174,3447,3166,3094,3195,11365,4071,12329,12459,3926,10994,11120,11173,12290,12296,12408,12411,12434,4559,10924,11125,11232,11254,11292,11298,12237,4560,11027,11128,11235,4561,11131,4562,11187,4563,3194,3487,12190,12234,12313,3649,4354,4355,3578,4488,11356,3588,3627,3801,3557,12799,12803,12807,12811,12821,3847,12184,3473,3727,3350,10358,10475,10546,10607,10610,10648,10742,10978,11872,11935,12014,12055,12116,12119,12438,12618,12676,12707,12719,12761,12782,12838,12844,3738,11594,3266,3362,11712,3551,4530,10249,10252,10278,10750,10763,10882,11276,11368,11761,11769,11990,11993,12081,12240,12333,12623,12626,12643,12646,12668,12720,12888,12893,12917,4542,11478,11509,11544,11574,12729,12733,3725,3496,3497,12649,12652,12655,12658,12688,3874,3310,3312,3285,4527,3172,4485,3677,4208,3993,3479,4543,4065,11249,3609,3323,11721,11724,12161,12262,12418,4035,3992,11865,12205,3936,10818,12049,12218,3987,11000,12087,12160,12217,12261,3650,11875,12021,12095,12141,4024,3668,10997,11063,11146,11206,12042,12109,12359,12431,12444,4548,10766,11136,3282,10367,10462,10593,10655,10724,10769,10772,10805,10829,10866,10904,10940,11668,11715,11845,11900,11916,11919,11922,11925,12102,12122,12125,12128,12131,12198,12265,12370,12414,12669,12694,12771,12778,12785,12790,12793,12796,12829,12841,12859,12903,12928,3283,10450,10660,10745,10869,11451,11557,11749,11752,11764,11851,11862,11883,11888,11928,11953,11968,12685,12835,12862,12889,12894,12918,3284,3358,12075,12749,12800,12804,12808,12812,12822,12826,4526,10315,10404,10517,10541,10787,10832,10842,11523,11622,11643,11646,11649,11665,11807,11810,11813,11816,11912,11931,11934,11947,12002,12005,12008,12011,12082,12172,12175,12268,12271,12332,12363,12400,12479,3442,10613,10877,10921,11195,11273,11436,11677,12309,12482,4538,10796,10808,10913,10931,10934,10991,11077,11085,11101,11139,11158,11167,11203,11244,11264,11267,11270,11301,11308,11311,11694,11730,11996,11999,12033,12076,12105,12246,12287,12293,12382,12385,12404,12458,12464,12473,12488,12748,12765,12768,3344,10642,10672,10681,11224,11776,12401,12415,12730,12734,12737,3384,3378,3805,3743,10318,11597,11625,12712,4535,10269,10636,10639,11080,11098,11560,11613,11657,11678,11782,11819,11822,11825,11828,3304,10675,10826,10897,11626,11781,11973,12199,3766,11727,12665,4115,3502,4533,3777,3813,4516,4518,4519,3257,3258,4517,4520,4521,4416,3784,3599,4214,11458,4550,10240,10243,10498,10549,10552,10557,10965,11430,11681,11785,4557,11161,11281,11317,4001,12229,3891,11314,11652,11656,11718,12317,12325,12407,3732,10937,10943,10958,11897,12026,12108,3584,11164,12134,12243,12253,12322,12373,12381,12485,3622,4069,3734,10678,11016,11170,11200,11211,12046,12211,12321,3554,10599,10602,10684,10856,3553,4554,11591,4544,4549,12633,4555,10735,10835,11149,11433,11464,12193,12202,12249,4175,10811,12214,12226,4076,3765,12491,3712,3713,4552,10291,10294,10630,10633,11475,11653,12437,4553,11571,11662,3736,10596,4008,4574,4600,4649,4651,4681,4698,4705,4706,4745,4775,4781,4866,4891,4892,4927,4952,4953,4975,4976,4989,4993,5016,5023,5041,5044,5045,5046,5051,5052,5074,5099,5100,5110,5115,5121,5165,5166,5174,5183,5188,5190,5200,5202,5208,5212,5227,5234,5237,5238,5239,5243,5279,5292,5299,5301,5302,5306,5307,5308,5316,5319,5323,5324,5325,5332,5336,5337,5338,5346,5350,5351,5352,5357,5370,5379,5391,5393,5401,5402,5406,5410,5435,5441,5451,5452,5467,5479,5501,5507,5523,5524,5527,5546,5554,5555,5560,5561,5571,5572,5585,5589,5598,5599,5601,5616,5621,5631,5632,5644,5651,5665,5669,5672,5678,5679,5680,5683,5688,5726,5727,5730,5732,5735,5736,5737,5739,5741,5743,5748,5755,5770,5784,5789,5790,5803,5804,5809,5813,5815,5820,5861,5873,5882,5886,5897,5901,5902,5910,5923,5929,5947,5950,5960,5985,5999,6024,6044,6045,6048,6063,6065,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6168,6175,6179,6215,6217,6219,6221,6230,6232,6234,6240,6242,6248,6251,6259,6266,6267,6268,6273,6295,6296,6297,6299,6305,6310,6344,6345,6348,6349,6350,6351,6352,6353,6354,6361,6394,6395,6404,6425,6426,6446,6449,6460,6461,6467,6497,6499,6513,6550,6552,6553,6606,6631,6674,6694,6703,6704,6705,6706,6725,6726,6732,6745,6748,6750,6752,6753,6754,6756,6770,6781,6783,6784,6797,6801,6852,6864,6866,6870,6887,6888,6922,6934,6965,6997,7051,7079,7134,7155,7164,7167,7224,7232,7290,7292,7307,7315,7318,7319,7338,7344,7346,7395,7405,7408,7424,7475,7476,7480,7523,7524,7542,7611,7630,7653,7676,7691,7706,7716,7725,7726,7753,7756,7758,7769,7807,7819,7844,7902,7936,7968,8007,8023,8039,8040,8116,8173,8192,8221,8242,8266,8267,8364,8366,8372,8386,8390,8408,8430,8438,8440,8452,8458,8462,8483,8497,8498,8517,8518,8523,8524,8525,8526,8527,8549,8550,8551,8562,8576,8578,8590,8594,8596,8597,8598,8606,8611,8641,8642,8673,8686,8690,8708,8730,8731,8732,8733,8745,8746,8768,8778,8788,8789,8790,8791,8793,8814,8815,8826,8870,8876,8882,8893,8898,8900,8903,8904,8908,8918,9000,9031,9032,9033,9048,9065,9072,9073,9102,9103,9144,9147,9173,9218,9219,9220,9235,9260,9274,9280,9283,9305,9306,9334,9395,9431,9432,9433,9458,9459,9477,9495,9501,9515,9539,9561,9569,9570,9571,9572,9587,9589,9594,9625,9626,9632,9633,9677,9678,9710,9719,9729,9731,9732,9741,9755,9758,9786,9819,9821,9825,9882,9923,9924,9926,9936,9937,9957,9962,10003,10054,10127,10128,10182,10198,2,8,9,4587,4588,4606,4637,4639,4640,4667,4673,4674,4685,4734,4736,4766,4780,4810,4906,4907,4920,4940,4996,4997,5000,5001,5003,5005,5006,5015,5019,5020,5030,5042,5043,5049,5069,5070,5087,5092,5093,5094,5095,5098,5106,5109,5116,5180,5186,5187,5194,5224,5235,5241,5257,5277,5278,5285,5286,5287,5296,5305,5312,5314,5315,5321,5328,5329,5342,5343,5344,5345,5347,5348,5353,5354,5355,5356,5387,5388,5389,5397,5398,5399,5400,5446,5448,5450,5486,5488,5489,5491,5492,5494,5495,5497,5506,5511,5513,5514,5515,5516,5517,5518,5525,5535,5538,5549,5565,5566,5569,5578,5581,5582,5583,5608,5618,5634,5635,5645,5646,5648,5650,5655,5690,5695,5697,5757,5791,5792,5796,5802,5805,5806,5807,5808,5814,5825,5826,5828,5829,5837,5858,5889,5905,5908,5909,5911,5920,5937,5940,5944,5945,5946,5962,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6180,6233,6269,6271,6292,6293,6298,6301,6302,6306,6312,6321,6337,6356,6357,6362,6372,6387,6407,6413,6415,6430,6431,6434,6435,6437,6439,6440,6441,6443,6445,6448,6454,6455,6456,6457,6463,6465,6507,6512,6527,6528,6529,6530,6564,6569,6571,6576,6577,6585,6589,6602,6627,6628,6629,6630,6642,6647,6664,6668,6687,6720,6721,6722,6727,6741,6762,6764,6766,6768,6771,6777,6779,6794,6799,6802,6838,6841,6842,6855,6856,6857,6858,6878,6879,6894,6920,6942,6953,6955,6956,6958,6960,6961,6994,6995,7000,7001,7002,7003,7005,7007,7032,7041,7042,7054,7064,7103,7113,7117,7124,7135,7141,7143,7149,7157,7158,7173,7190,7208,7210,7227,7276,7278,7279,7280,7286,7291,7314,7359,7392,7406,7423,7455,7458,7484,7508,7525,7528,7529,7539,7557,7558,7560,7562,7564,7566,7594,7619,7620,7652,7654,7655,7656,7661,7683,7692,7702,7707,7713,7715,7721,7733,7734,7736,7767,7790,7857,7858,7905,7913,7914,7938,7939,7956,7957,8015,8016,8017,8042,8075,8082,8084,8094,8106,8137,8145,8152,8165,8187,8193,8220,8264,8293,8306,8324,8327,8357,8380,8441,8442,8445,8447,8553,8554,8555,8556,8585,8614,8645,8689,8707,8762,8807,8810,8823,8830,8867,8886,8914,8915,8933,8934,9076,9080,9100,9110,9133,9135,9138,9142,9145,9146,9159,9160,9180,9186,9198,9246,9264,9318,9319,9326,9387,9392,9428,9435,9438,9441,9442,9457,9473,9482,9494,9504,9505,9508,9510,9537,9660,9705,9706,9748,9793,9909,9966,10105,10119,10124,3,2621,2624,2625,2626,2627,2631,2632,2634,2635,2639,2640,2641,2643,2646,2647,2648,2649,2651,2652,2653,2660,2661,2662,2663,2668,2669,2671,2672,2675,2676,2682,2685,2686,2687,2705,2707,2711,2713,2716,2717,2718,2726,2727,2728,2730,2731,2732,2746,2748,2749,2760,2765,2766,2767,2769,2770,2771,2772,2773,2774,2794,2795,2807,2810,2821,2823,2825,2826,2827,2852,5216,5276,5373,5454,5460,5461,5536,5633,5664,5698,5714,5716,5722,5785,5786,5787,5788,5794,5827,5957,6000,6023,6060,6099,6249,6256,6290,6291,6311,6314,6316,6323,6324,6325,6326,6327,6328,6329,6330,6409,6477,6478,6562,6596,6597,6639,6640,6778,6793,6867,6868,6875,6895,6918,6926,6928,6975,6998,6999,7015,7016,7017,7053,7097,7098,7197,7258,7259,7260,7261,7275,7308,7364,7365,7374,7380,7382,7394,7426,7427,7428,7429,7574,7575,7581,7582,7584,7586,7798,7800,7801,7817,7855,7934,7973,8026,8047,8048,8063,8123,8235,8303,8304,8307,8342,8404,8405,8471,8490,8491])). % 155.00/154.63 cnf(13366,plain, % 155.00/154.63 (~P1(f328(f328(f330(a875),x133661),f328(f249(a875),f2(a875))))), % 155.00/154.63 inference(rename_variables,[],[11742])). % 155.00/154.63 cnf(13386,plain, % 155.00/154.63 ($false), % 155.00/154.63 inference(scs_inference,[],[4554,4517,3738,3936,3584,4560,4553,11494,12201,11111,12930,12242,11742,13366,10786,2888,8,8550,5370,7338,8498,8526,6770,5402,6712,5219,9477,9073,5174,7434,5110,6783,4681]), % 155.00/154.63 ['proof']). % 155.00/154.63 % SZS output end Proof % 155.00/154.63 % Total time :132.430000s %------------------------------------------------------------------------------